tmdpresentation- tatical ballistic missile
TRANSCRIPT
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2/24/2008 ELF 1
Professional DevelopmentShort Course on
Tactical Missile Design
Professional DevelopmentShort Course on
Tactical Missile Design
Eugene L. FleemanTactical Missi le DesignE-mail: [email protected]
Web Site: http://genefleeman.home.mindspring.com
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Outline Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration Sizing Examples
Development Process
Summary and Lessons Learned References and Communication
Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,Conversion Factors, Syllabus )
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Emphasis Is on Physics-Based, Analytical Sizing
of Aerodynamic Configuration
Emphasis Is on Physics-Based, Analytical Sizing
of Aerodynamic Configuration
Safe, Arm, and Fuzing
Power Supply
Seeker, Sensors, and Electronics
Launch Platform Integration
Additional Measures of Merit
Cost
Miss Distance
WarheadWeight
Structure
Propulsion
Aero Flight Performance
Aero Stability & Control
Aero Configuration Sizing
Emphasis Area
Primary Emphasis
Secondary Emphasis
Tertiary EmphasisNot Addressed- -
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Superior Better Comparable Inferior
Axial Acceleration AGM-88
Maneuverability AA-11Speed / altitude SM-3
Dynamic pressure PAC-3
Size Javelin
Weight FIM-92
Production cost GBU-31
Observables AGM-129
Range AGM-86Kills per use Storm Shadow
Target acquisition LOCAAS
Tactical MissileCharacteristics
Comparison WithFighter Aircraft
– –
–
–
Tactical Missiles Are Different from Fighter Aircraft Tactical Missiles Are Different from Fighter Aircraft
Example of State-of-the-Art
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Aero Configuration Sizing Parameters Emphasized in This Course
Aero Configuration Sizing Parameters Emphasized in This Course
Nose FinenessDiameter
Propulsion Sizing /Propellant or Fuel
Wing Geometry / Size
Stabilizer
Geometry / Size
Flight Control
Geometry / Size
Length
ThrustProfile
Flight Conditions ( α, M, h )
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Conceptual Design Process Requires Evaluation
of Alternatives and Iteration
Conceptual Design Process Requires Evaluation
of Alternatives and Iteration
• Mission / ScenarioDefinition
• WeaponRequirements,Trade Studiesand Sensitivity
Analysis
• Launch PlatformIntegration
• Weapon ConceptDesign Synthesis
• Technology Assessment andDev Roadmap
InitialTech
InitialReqs
BaselineSelected
Al tConcepts
Initial Carriage /Launch
Iteration
RefineWeapons
Req
Initial Revised
Trades / Eval Effectiveness / Eval
TechTrades
InitialRoadmap
RevisedRoadmap
Al ternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine
Update
Note: Typical conceptual design cycle is 3 to 9 months. House of Quality may be used to translate customer requirementsto engineering characteris tics . DOE may be used to efficiently evaluate the broad range of design solut ions.
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Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Yes
Define Mission Requirements
Establish Baseline
Aerodynamics
Propulsion
Weight
Trajectory
Meet
Performance?
Measures of Merit and ConstraintsNo
No
Yes
Resize / Alt Conf ig / Subsystems / Tech
Al t Mission
Al t Baseline
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Examples of Air-Launched Missile Missions /
Types
Examples of Air-Launched Missile Missions /
Types
Air-to-air Example SOTA
• Short range ATA. AA-11. Maneuverability
• Medium range ATA. AIM-120. Performance / weight
• Long range ATA. Meteor. Range
Air-to-surface
• Short range ATS. AGM-114. Versatility
• Medium range ATS. AGM-88. Speed
• Long range ATS. Storm Shadow. Modularity
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
10 feet
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Surface-to-surface Example SOTA
• Short range STS. Javelin. Size
• Medium range STS. MGM-140. Modularity
• Long range STS. BGM-109. Range
Surface-to-air
• Short range STA. FIM-92. Weight
• Medium range STA. PAC-3. Accuracy
• Long range STA. SM-3. High altitude
Examples of Surface-Launched Missile Missions /
Types
Examples of Surface-Launched Missile Missions /
Types
Permission of Missile.Index. Copyright 1997©Missile.Index All Rights Reserved
10 feet
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Aero Conf iguration Range / Time to Robust- Miss Observ- LaunchSizing Parameter Weight Maneuver Target ness Lethality Distance ables Survivability Cost Platform
Nose Fineness
Diameter
Length
Wing Geometry / Size
Stabilizer Geometry / Size
Flight ControlGeometry / Size
Propellant / Fuel
Thrust Profile
Flight Conditions( α, M, h )
Aero Configuration Sizing Has High Impact on Mission Requirements
Aero Configuration Sizing Has High Impact on Mission Requirements
Impact on Weapon Requirement
Aero Measures of Meri t Other Measures of Meri t Const raint
–Very Strong Strong Moderate Relatively Low
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–
Alternatives for Precision Str ikeCost per
ShotFuture Systems
Standoff platforms / hypersonic missiles
Overhead loitering UCAVs / hypersonic missiles
Overhead lo itering UCAVs / light weight PGMs
Current Systems
Penetrating aircraft / subsonic PGMs
Standoff platforms / subsonic missiles
Note: Superior Good Average Poor
Number of Launch Platforms
Required
TCT
Effectiveness
– –
–
Example of Assessment of Alternatives to Establish Future Mission Requirements
Example of Assessment of Alternatives to Establish Future Mission Requirements
Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivity
time of less than 2 m and target location error ( TLE ) of less than 1 m for mot ion suspended target.
Measures of Merit
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C4ISR Tactical Satellites and UAVs Have High
Impact on Mission Capability
C4ISR Tactical Satellites and UAVs Have High
Impact on Mission Capability Launch Platforms
•Fighter Aircraft
•Bomber
•Ship / Submarine
•UCAV
Precision Strike Weapons•Hypersonic SOW
•Subsonic PGM
•Subsonic CM
Launch Platforms
•Fighter Aircraft
•Bomber
•Ship / Submarine
•UCAV
Precision Strike Weapons
•Hypersonic SOW
•Subsonic PGM
•Subsonic CM
Off-board Sensors•Tactical Satellite
•UAV
Off-board Sensors
•Tactical Satellite
•UAV
Note: C4ISR targeting state-of-the-art for year 2010 projected to provide sensor-to-shooter / weapon connectivitytime of less than 2 m and target location error ( TLE ) of less than 1 m for mot ion suspended target.
Time Critical Targets
•TBM / TEL
•SAM
•C3
•Other Strategic
Time Critical Targets•TBM / TEL
•SAM
•C3
•Other Strategic
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Example of System-o -Systems Analysis to
Develop Future Mission Requirements
Example of System-o -Systems Analysis to
Develop Future Mission Requirements 1. Compare Targeting of Subsonic Cruise Missile
Versus Hypersonic Missile
t0 t1
TBM
Launch
Launch
Pt Rcvd
t2 t3
Cruise Missile Launch
HM Intercept
at XXX nm
Range 3 > R2
Range 2 > R1
Range 1
1000 2000 3000 4000 5000
Average Speed, fps
T i m e
, M i n
120
0
20
4060
80
100
20
4060
80
100
020000 4000 6000
Average Speed to Survive, fps
A l t i t u d e –
1 0 0 0 f t
L e t h a l i t y / C o n c r e t e
P e n e t r a t i o n ( f t )50
40
30
20
10
01000 2000 3000 40000Impact Velocity, fps
W/H W3 > W2
W/H W2 > W1
Warhead W1
0
2. Time To Target
3. Alt / Speed / RCS RequiredFor Survivability
4. Lethality
Selected For All :• Value of Speed /
Range• Time Urgent Targets• High Threat
Environments
• Buried Targets• Launch Platform Al ternat ives
• Operating and At tri ti on Cost inCampaign
• Weapon Cost inCampaign• Mix of Weapons in
Campaign• Cost Per Target Ki ll• C4ISR Interface
5. Campaign Model WeaponsMix ( CM, Hypersonic
Missi le ) Resul ts( eg., Korean Scenario )
Hypersonic
Missile Launch
RCS1 RCS2 > RCS1
1 - 2
3 - 4 2
- 3
4 - 5
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Example of Technological Surprise Driving
Immediate Mission Requirements
Example of Technological Surprise Driving
Immediate Mission Requirements
Archer AA-11 / R-73 ( IOC 1987 )
Performance
•> +/- 60 deg off boresight
•20 nm range
New Technologies
•TVC
•Split canard
•Near-neutral static margin
•+/- 90 deg gimbal seeker
•Helmet mounted sight
Sidewinder AIM-9L ( IOC 1977 )Performance
•+/- 25 deg off boresight
•6.5 nm range
Note: AIM-9L maneuverability shortfall compared to Archer drove sudden development of AIM-9X.
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Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Yes
Establish Baseline
Aerodynamics
Propulsion
Weight
Trajectory
Meet
Performance?
Measures of Merit and ConstraintsNo
No
Yes
Resize / Alt Conf ig / Subsystems / Tech
Al t Mission
Al t Baseline
Define Mission Requirements
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Baseline Design Benefits and Guidelines Baseline Design Benefits and Guidelines
Benefits of Baseline Design Allows simple, conceptual design methods to be used with good
accuracy
Well documented benchmark / configuration control / traceabili tybetween cause and effect
Balanced subsystems
Gives fast startup / default values for design effort
Provides sensitivity trends for changing design Baselines can cover reasonable range of starting points
Baselines can normally be extrapolated to ±50% with good accuracy
Guidelines
Don’t get locked-in by baseline Be creative
Project state-of-the-art ( SOTA ) if baseline has obsolete subsystems Sensors and electronics almost always need to be updated
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Baseline Design Data Allows Correction of Computed Parameters in Conceptual Design Baseline Design Data Allows Correction of Computed Parameters in Conceptual Design
PCD, C Parameter of conceptual design, corrected
PB, C Parameter of baseline, corrected ( actual data )
PB, U Parameter of baseline, uncorrected ( computed ) PCD, U Parameter of conceptual design, uncorrected (computed )
Example• Ramjet Baseline with RJ-5 fuel ( heating value = 11,300,000 ft-lbf / lbm )
• Advanced Concept with slurry fuel ( 40% JP-10 / 60% boron carbide =18,500,000 ft-lbf / lbm )
• Flight condi tions: Mach 3.5 cruise, 60k ft altitude, combustion temperature4,000 R
• Calculate specific impulse ( ISP )CD,C for conceptual design, based on correctedbaseline data – ( ISP )B, C = 1,120 s
– ( ISP )B, U = 1387 s
– ( ISP )CD, U = 2,271 s
– ( ISP )CD, C = [( ISP )B, C / ( ISP )B, U ] ( ISP )CD, U = [( 1120 ) / ( 1387 )] ( 2271 ) = 0.807 ( 2271 )
= 1,834 s
PCD, C = ( PB, C / PB, U ) PCD, U
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Summary of This Chapter Summary of This Chapter
Overview of Missile Design Process
Examples Tactical missile characteristics
Conceptual design process
SOTA of tactical missiles
Aerodynamic configuration sizing parameters Processes that establish mission requirements
Process for correcting design predictions
Discussion / Questions?
Classroom Exercise
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Introduction Problems Introduction Problems
1. The missile design team should address the areas of mission / scenariodefinition, weapon requirements, launch platform integration, design, andt_______ a_________.
2. The steps to evaluate missile flight performance require computingaerodynamics, propulsion, weight, and flight t_________.
3. Air-to-air missile characteristics include light weight, high speed, and highm______________.
4. Air-to-surface missiles are often versatile and m______.5. Four aeromechanics measures of merit are weight, range, maneuverability,
and t___ to target.
6. The launch platform often constrains the missile span, length, and w_____.
7. An enabling capability for hypersonic strike missiles is fast and accurateC____.
8. An enabling capability for large off boresight air-to-air missiles is a h_____m______ sight.
9. A baseline design improves the accuracy and s____ of the design process.
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Outline Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
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Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Yes
Establish Baseline
Propulsion
Weight
Trajectory
Meet
Performance?
Measures of Merit and ConstraintsNo
No
Yes
Resize / Alt Conf ig / Subsystems / Tech
Al t Mission
Al t Baseline
Define Mission Requirements
Aerodynamics
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Missile Diameter Tradeoff Missile Diameter Tradeoff
Drivers toward Small Diameter • Decrease drag
• Launch platform diameter constraint Drivers toward Large Diameter
• Increase seeker range and signal-to-noise, better resolut ion and tracking
• Increase blast frag and shaped charge warhead effectiveness ( larger diameter
⇒ higher velocity fragments or higher velocity jet )• Increase body bending frequency
• Subsystem diameter packaging
• Launch platform length constraint
Typical Range in Body Fineness Ratio 5 < l / d < 25• Man-portable anti-armor missiles are low l / d ( Javelin l / d = 8.5 )
• Surface-to-air and air-to-air missiles are high l / d ( AIM-120 l / d = 20.5 )
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Small Diameter Missiles Have Low Drag Small Diameter Missiles Have Low Drag
10
100
1000
10000
100000
4 8 12 16 20
d, Diameter, in
D / C D ,
D r a g
/ D r a g C o e f f i c
i e n t , l b
Dynamic Pressure =1,000 psf
Dynamic Pressure =5,000 psf
Dynamic Pressure =10,000 psf
Example for Rocket Baseline:
d = 8 in = 0.667 ft
Mach 2, h = 20k ft, ( CD0 )Powered = 0.95q = 1/2 ρ V2 = 1/2 ρ ( M a )2
= 1/2 ( 0.001267 ) [( 2 ) ( 1037 )] 2 = 2,725 psf
D0 / CD0= 0.785 ( 2725 ) ( 0.667 )2 = 952
D0 = 0.95 ( 952 ) = 900 lb
D = CD q SRef = 0.785 CD q d2
Note: D = drag in lb, CD = drag coefficient, q = dynamic pressure in psf,d = diameter ( reference length ) in ft
L Di R d S k P id LL Di t R d S k P id L
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Large Diameter Radar Seeker Provides Longer
Detection Range and Better Resolution
Large Diameter Radar Seeker Provides Longer
Detection Range and Better Resolution
1
10
100
0 5 10 15 20
d, Diameter, Inches
Example Seeker Range for Transmitted Power Pt = 100 W, nm
Example Seeker Range for Transmitted Power Pt = 1,000 W, nm
Example Seeker Range for Transmitted Power Pt = 10,000 W, nm
Example Seeker Beam Width, deg
RD = { π σ n3/4 / [ 64 λ2 K T B F L ( S / N ) ]}1/4 Pt1/4 d
θ3dB = 1.02 λ / d, θ3dB in rad
Assumptions: Negl ig ib le clut ter , interference, andatmospheric attenuation; non-coherent radar ( onlysignal amplitude integrated ); uniformly ill uminatedcircular aperture; receiver sensitivi ty limited bythermal noise
Symbols:
σ = Target radar cross section, m2
n = Number of pu lses integratedλ = Wavelength, mK = Boltzman’s constant = 1.38 x 10-23 J / KT = Receiver temperature, KB = Receiver bandwidth, HzF = Receiver noise factor L = Transmitter loss factor S / N = Signal-to-noise ratio for target detectionPt = Transmitted power, Wd = Antenna diameter
Example: Rocket Baselined = 8 in = 0.20 m, Pt = 1000 W, λ = 0.03 m ( f = 10 GHz )RD = Target detection range = { π ( 10 ) ( 100 )3/4 / [ 64 (
0.03 )2 ( 1.38 x 10-23 ) ( 290 ) ( 106 ) ( 5 ) ( 5 )( 10 )]}1/4 (1000 )1/4 ( 0.203 ) = 13,073 m or 7.1 nm
θ3dB = 3-dB beam width = 1.02 ( 0.03 ) / 0.203 = 0.1507
rad or 8.6 deg
Note for figure: σ = 10 m2, n = 100, λ = 0.03 m ( f = Transmi tter frequency = 10 x 109 Hz ), T = 290 K, B = 106 Hz ( 10-6 s pulse ), F
= 5, L = 5, S / N = 10
L Di t IR S k P id LL Di t IR S k P id L
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Large Diameter IR Seeker Provides Longer
Detection Range and Better Resolution
Large Diameter IR Seeker Provides Longer
Detection Range and Better Resolution
1
10
100
0 2 4 6 8 10
do, Optics Diameter, Inches
Example Seeker Range for Exo-atmospheric, km
Example Seeker Range for Humidity at 7.5 g / m3, km
Example Seeker Range for Rain at 4 mm / hr, km
Example Seeker IFOV, 10-5 rad
RD = { ( IT )Δλ ηa Ao { D* / [( Δf p )1/2 ( Ad )1/2 ]} ( S / N )D-1 }1/2
IFOV= dp / [ ( f-number ) do ]
Example: do = 5 in = 0.127 m, exo-atmosphericLλ = 3.74 x 104 / { 45 { e{ 1.44 x 104 / [ 4 ( 300 ) ]} – 1 }} = 0.000224 W cm -2 sr -2
μm-1, ( IT )Δλ = 0.5 ( 0.000224 ) ( 4.2 – 3.8 ) 2896 = 0.1297 W / sr, Ad =256 x 256 x ( 20 μm )2 = 0.262 cm2, f-number = 20 / [ 2.44 ( 4 ) ] = 2.05
RD = { 0.1297 ( 1 ) ( 0.01267 ) { 8 x 1011 / [( 250 )1/2 ( 0.262 )1/2 ]} ( 1 )-1
}1/2 = 12, 740 m
IFOV = 0.000020 / [ 2.05 ( 0.127 )] = 0.0000769 rad
Figure: dT = 2 ft ( 60.96 cm ), TT = 300 K, λ1 = 3.8 μm,λ
2= 4.2 μm, ε = 0.5, λ = 4 μm, FPA ( 256 x 256, 20 μm
), D* = 8 x 1011 cm Hz1/2 / W, ( S / N )D = 1, Δf p = 250 Hz.
RD = Target detection range, m
( IT )Δλ = Target radiant intensity between λ1 and λ2= εLλ ( λ2 - λ1 ) AT, W / sr
ηa = Atmospheric transmission Ao = Optics aperture area, m2
D* = Specif ic detectivity, cm Hz1/2 / WΔf p = Pixel bandwidth, Hz Ad = Detectors total area, cm2
( S / N )D = Signal-to-noise ratio required for detection
ε = Emissivity coefficient
Lλ = Spectral radiance ( Planck’s Law ) = 3.74 x 104 / {
λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }} , W cm-2 sr -2 μm-1
λ2 = Upper cutoff wavelength for detection, μm
λ1 = Lower cutoff wavelength for detection, μm AT = Target planform area, cm2
λ = Average wavelength, μm
TT = Target temperature, K
IFOV = Instantaneous f ield-of-view of pixel, radf-number = dspot / ( 2.44 λ )
dp = Pixel diameter, either μm
dspot = Spot resolution i f diff raction limi ted = dp, μm
Mi il Fi R ti M B Li it d bMissile Fineness Ratio Ma Be Limited b
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Missile Fineness Ratio May Be Limited by
Impact of Body Bending on Flight Control
Missile Fineness Ratio May Be Limited by
Impact of Body Bending on Flight Control
100
1000
10000
0 10 20 30
l / d, length / diameter
F i r s t M o d e B o d y B e
n d i n g F r e q u e n c
y , r a d / s
E t / W = 1,000 per in
E t / W = 10,0000 per in
E t / W = 100,000 per in
Derived from: AIAA Aerospace Design Engineers Guide, American Institute of Aeronautics and Astronautics, 1993.
ωBB = 18.75 { E t / [ W ( l / d ) ]}1/2
Example for Rocket Baseline:
l / d = 18E AVG = 19.5 x 106 psit AVG = 0.12 in
W = 500 lbE t / W = 19.5 x 106 ( 0.12 ) / 500 = 4680 per inωBB = 18.75 ( 4680 / 18 )1/2 = 302 rad / sec = 48 Hzω Ac tuator = 100 rad / sec = 16 HzωBB / ω Ac tuator = 302 / 100 = 3.02 > 2
Assumes body cylinder st ructure, th in skin, h ighfineness ratio, uniform weight dist ribution, free-freemotion. Neglects bulkhead, wing / tail s tiffness.
ωBB = First mode body bending frequency, rad / s
E = Modulus of elasticity in ps i
t = Thickness in inchesW = Weight in lb
l / d = Fineness ratio
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Nose Fineness Tradeoff Nose Fineness Tradeoff
d
Example: lN / d = 5 tangent ogive
Example: lN / d = 0.5 ( hemisphere )
High Nose Fineness Superior Aerodynamically, Low Observables
Low Nose Fineness Ideal Electromagnetically, High Propellant Length / Volume
Moderate Nose Fineness Compromise Dome
d
Examples: lN / d = 2 tangent ogive lN / d = 2 faceted lN / d = 2 window lN / d = 2 mult i-lens
d
W i n d o w
Faceted and Flat Window Domes Can Have LowFaceted and Flat Window Domes Can Have Low
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Firestreak
Mistral
SLAM-ER
JASSM
THAAD
Faceted and Flat Window Domes Can Have Low
Dome Error Slope, Low Drag, and Low RCS
Faceted and Flat Window Domes Can Have Low
Dome Error Slope, Low Drag, and Low RCS
Faceted Dome ( Mistral ) Video
Supersonic Body Drag Driven by Nose FinenessSupersonic Body Drag Driven by Nose Fineness
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Supersonic Body Drag Driven by Nose Fineness
while Subsonic Drag Driven by Wetted Area
Supersonic Body Drag Driven by Nose Fineness
while Subsonic Drag Driven by Wetted Area
0.01
0.1
1
10
0 1 2 3 4 5
M, Mach Number
(CD0)Body,Wave;lN / d = 0.5
(CD0)Body,Wave;lN / d = 1
(CD0)Body,Wave;lN / d = 2
(CD0)Body,Wave;lN / d = 5
(CD)Base,Coast
Example for Rocket Baseline:
( CD0 )Body, Wave ( CD0 )Body, Friction ( CD )Base
lN / d = 2.4, Ae = 11.22 in2, SRef = 50.26 in2, M =2, h = 20k ft , q = 2725 psf, l / d = 18, l = 12 ft
( CD0)Body, Friction = 0.053 ( 18 ) { ( 2 ) / [( 2725 )
( 12 ) ]}0.2
= 0.14( CD )Base Coast = 0.25 / 2 = 0.13
( CD )Base Powered = ( 1 - 0.223 ) ( 0.25 / 2 ) = 0.10
( CD0)Body, Wave = 0.14
( CD0)Body, Coast = 0.14 + 0.13 + 0.14 = 0.41
( CD0 )Body, Powered = 0.14 + 0.10 + 0.14 = 0.38
( CD0)Body = (CD0
)Body,Friction + ( CD0)Base + ( CD0
)Body, Wave
(CD0)Body,Friction = 0.053 ( l / d ) [ M / ( q l )]0.2. Based on Jerger reference, turbulent boundary layer, q in psf, l in ft.
( CD0)Base,Coast = 0.25 / M, if M > 1 and (CD0
)Base,Coast = ( 0.12 + 0.13 M2 ), if M < 1
( CD0)Base,Powered = ( 1 – Ae / SRef ) ( 0.25 / M ), if M > 1 and ( CD0
)Base,Powered = ( 1 – Ae / SRef ) ( 0.12 + 0.13 M2 ), if M < 1
( CD0)Body, Wave = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69, for M > 1. Based on Bonney reference, tan-1 in rad.
Note: ( CD0)Body,Wave = body zero-lif t wave drag coefficient, ( CD0
)Base = body base drag coefficient, ( CD0)Body, Friction = body skin
friction drag coefficient, ( CD0)Body = body zero-lift drag coefficient, lN = nose length, d = missi le diameter, l = missile body
length, Ae = nozzle exit area, SRef = reference area, q = dynamic pressure, tan-1 [ 0.5 / ( lN / d )] in rad.
Moderate Nose Tip Bluntness Causes aModerate Nose Tip Bluntness Causes a
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Moderate Nose Tip Bluntness Causes a
Negligible Change in Supersonic Drag
Moderate Nose Tip Bluntness Causes a
Negligible Change in Supersonic Drag
Steps to Calculate Wave Drag of a Blunted Nose1. Relate blunted nose tip geometry to pointed nose tip geometry
2. Compute (CD0)Wave,SharpNose for sharp nose, based on the body reference area
( CD0)Wave,SharpNose = ( 1.59 + 1.83 / M2 ) { tan-1 [ 0.5 / ( lN / d )]}1.69
3. Compute ( CD0)Wave,Hemi of the hemispherical nose tip ( lNoseTip / dNoseTip = 0.5 ), based on the
nose tip area
( CD0)Wave,Hemi = ( 1.59 + 1.83 / M2 ) {[ tan-1 ( 0.5 / ( 0.5 )]}1.69 = 0.665 ( 1.59 + 1.83 / M2 )
4. Final ly, compute ( CD0)Wave,BluntNose of the blunt nose, based on the body reference area
( CD0)Wave,BluntNose = ( CD0
)Wave,SharpNose ( SRef - SNoseTip ) / SRef + ( CD0)Wave,Hemi SNoseTipi / SRef
Example Rocket Baseline ( dRef = 8 in ) with 10% Nose Tip Bluntness at Mach 2
• ( CD0)Wave,SharpNose = [ 1.59 + 1.83 / ( 2 )2 ] [ tan-1 ( 0.5 / 2.4)]1.69 = 0.14
• dNoseTip = 0.10 ( 8 ) = 0.8 in
• SNoseTip = π dNoseTip2 / 4 = 3.1416 ( 0.8 )2 / 4 = 0.503 in2 = 0.00349 ft2
• ( CD0)Wave,Hemi = 0.665 [ 1.59 + 1.83 / ( 2 )2 ] = 1.36
• ( CD0 )Wave,BluntNose = 0.14 ( 0.349 - 0.003 ) / 0.349 + ( 1.36 ) ( 0.003 ) / ( 0.349 ) = 0.14 + 0.01 = 0.15
dRef dNoseTip
lN
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Boattail Decreases Base Pressure Drag Area Boattail Decreases Base Pressure Drag Area
Without Boattail
With Boattail
During Motor Burn After Motor Burnout
Base Pressure Drag Area
θBT
Note: Boattail angle θBT and boattail diameter dBT limi ted by propuls ion nozzle packaging, tail flightcontrol packaging, and flow separation
dRef
dBT
Reference: Chin, S. S., Missile Configuration Design , McGraw-Hill Book Company, New York, 1961
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Boattailing Reduces Drag for Subsonic Missiles Boattailing Reduces Drag for Subsonic Missiles
0.45
0.40
0.05
0.10
0.15
0.20
0.25
0.30
0.35
C
D O ,
E x a m p l e Z e r o - L i f t D r a g C o e f f i c i e n t
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5M∞
Note: Boatail half angle should be less than 10 deg, to avoid flow separattion.Source: Mason, L.A., Devan, L. and Moore, F.G., “ Aerodynamic Design Manual for Tactical Weapons,” NSWC TR 81-156, July1981
3.00 6.00 1.50
Center bodyNose
10.50
dBT / dRef = 1.0dBT / dRef = 0.9dBT / dRef = 0.8dBT / dRef = 0.6
dBT / dRef = 0.4
Boattail
Note:d
BT
= Boattail Diameter dRef = Body Reference Diameter
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Note:If α negative, CN negativeBased on slender body theory ( Pitts, et al ) and cross f low theory ( Jorgensen ) references
Valid for l / d > 5Example l / d = length / diameter = 20d = 2 ( a b )1/2
φ = 0°
Lifting Body Has Higher Normal Force Lifting Body Has Higher Normal Force
CN,ExampleNormalForce
Coefficientfor l / d = 20
150
100
50
00 20 40 60 80 100
α, Angle of Attack, Deg
φ2a
2b
a / b = 3
a / b = 2
a / b = 1
⏐ CN ⏐ = [⏐( a / b ) cos2 φ + ( b / a ) sin2 φ ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]
CN
L / D Is Impacted by C Body Fineness andL / D Is Impacted by CD Body Fineness and
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L / D Is Impacted by C D 0 , Body Fineness, and Lifting Body Cross Section Geometry
L / D Is Impacted by C D 0 , Body Fineness, and Lifting Body Cross Section Geometry
L / D,Lift / Drag
4
3
2
1
0 0 20 40 60 80 100
α, Angle of Attack, DegNote:• If α negative, L / D negative•d = 2 ( a b )1/2
•Launch platform span constraints ( e.g., VLS launcher ) and length constraints ( e.g., aircraft compatibil ity )
may limit missile aero configuration enhancements
L / D = CL / CD = ( CN cos α – CD0 sin α ) / ( CN sin α + CD0 cos α )For a lifting body, ⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]
High drag, low fineness body ( a / b = 1, l / d = 10, CDO = 0.5 )Low drag nose ( a / b = 1, l / d = 10, CDO = 0.2 )High fineness, low drag ( a / b = 1, l / d = 20, CDO = 0.2 )
Lif ting body, high fineness, low drag ( a / b = 2 @ φ = 0°, l / d =20, CDO = 0.2 )
φ2a
2bCN
Lifting Body Requires Flight at Low DynamicLifting Body Requires Flight at Low Dynamic
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Lifting Body Requires Flight at Low Dynamic
Pressure to Achieve High Aero Efficiency
Lifting Body Requires Flight at Low Dynamic
Pressure to Achieve High Aero Efficiency
0
1
2
3
4
100 1000 10000 100000
q, Dynamic Pressure, lb / ft2
E x a m
p l e L / D ,
L i f t / D r
a g
Circular Cross Section ( a / b = 1 ) Lif t ing Body ( a / b = 2 )
L / D = CL / CD = ( CN cos α – CDOsin α ) / ( CN sin α + CDO
cos α )⏐ CN ⏐ = [⏐( a / b ) cos2 ( φ ) + ( b / a ) sin2 ( φ ) ⏐] [⏐ sin ( 2α ) cos ( α / 2 ) ⏐ + 2 ( l / d ) sin2 α ]
Note. Example figure based on following assumptions:Body l ift only ( no surfaces ), cruise flight ( lift = weight ), W = L = 2,000 lb, d = 2 ( a b )1/2, S = 2 ft2,l / d = 10, CD0
= 0.2
Example:
q = 500 psf •a / b = 1 ⇒ L / D = 2.40
•a / b = 2 ⇒ L / D = 3.37
q = 5,000 psf
•a / b = 1 ⇒ L / D = 0.91•a / b = 2 ⇒ L / D = 0.96
Trade-off of Low Observables and ( L / D )MaxTrade-off of Low Observables and ( L / D )Max
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6
5
4
3
Body Planform Area
( Body Volume )2/3
( L / D ) M a x ,
( L i f t / D r a g ) M
a x Lower
Radar Cross
Section
TailoredWeapons
ConventionalWeapons
( circular
cross section )
Trade off of Low Observables and ( L / D ) Max Versus Volumetric Efficiency
Trade off of Low Observables and ( L / D ) Max Versus Volumetric Efficiency
2 4 6 8 10
Advantages:• ( L / D )Max
• Low RCS
Advantages:• Payload• Launch PlatformIntegration
Circular Cross Section
C / and Static Margin Define StaticCm / and Static Margin Define Static
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Δ C m / Δ α and Static Margin Define Static
Stability
Δ C m / Δ α and Static Margin Define Static
Stability
Cm
Statically Stable: ΔCm / Δα < 0,with xac behind xcg
δ1 δ2
Cm
Statically Unstable: ΔCm / Δα > 0,with xac in front of xcg
δ1
δ2
Non-oscillatoryConvergent
OscillatoryConvergent
t
Non-oscillatoryDivergent
OscillatoryDivergent
t
α α
α
Note: Statically unstable missi le requires high bandwidth autopilot.
Autopi lot negative rate feedback provides stabili ty augmentat ion.
xCG
x AC
xCG
x AC
Body Aerodynamic Center Is a Function of Angle Body Aerodynamic Center Is a Function of Angle
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y y g
of Attack, Nose Fineness, and Body Length
y y g
of Attack, Nose Fineness, and Body Length
0
1
2
3
4
5
0 20 40 60 80 100
Angle of Attack, Deg
D i s t a n c e t o B o d y A e r o d y n a
m i c
C e n t e r / L e n g t h o f N o s e total length of body /
length of nose = 1
total length of body /length of nose = 2
total length of body /
length of nose = 5total length of body /length of nose = 10
( x AC )B / lN = 0.63 ( 1 - sin2 α ) + 0.5 ( lB / lN ) sin2 α
Note: Based on slender body theory ( Pitts , et al ) and cross flow theory ( Jorgensen ) references. No flare.
( x AC )B = Location of body aerodynamic center, lN = length of nose, α = angle of attack, lB = total length of body.
Example:
Rocket Baseline Body
lB / lN = 143.9 / 19.2 = 7.49
α = 13 deg
( x AC )B / lN = 0.81
19.2143.9
Fl I St ti St bilit
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Based on Slender Body Theory:
( CNα )F = 2 [( dF / d )2 – 1 ]
( xac )F = xF + 0.33 lF [ 2 ( dF / d ) + 1 ] / [ ( dF / d ) + 1 ] ( CNα
)B = 2 per rad
( xac )B = 0.63 lN
ΣM = 0 at Aerodynamic Center. For a Body-Flare:
( CNα )B {[ xCG – ( x AC )B ] / d } + ( CNα )F [ xCG – ( x AC )F ] / d = - [( CNα )B + ( CNα )F ][( x AC – xCG ) / d ]
Static Margin for a Body-Flare
( x AC – xCG ) / d = - {( CNα)B {[ xCG – ( x AC )B ] / d } + ( CNα
)F {[ xCG – ( x AC )F ] / d }} /[( CNα
)B + ( CNα)F ]
Flare Increases Static Stability Flare Increases Static Stability
+M
+α
x = 0 ( xac )B
( CNα)B ( CNα )F
lBlN
( xac )F
xF
9
xCG
d dF
x AC
CNα = ( CNα )B + ( CNα )F
Fl I St ti St bilit ( t )Fl I St ti St bilit ( t )
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Example of Static Margin for THAAD ( Statically Unstable Missile )
( CNα )F = 2 [( 18.7 / 14.6 )2 – 1 ] = 2 [(1.28)2 – 1 ] = 1.28 per rad
( xac )F = 230.9 + 0.33 ( 12.0 )[ 2 ( 18.7 / 14.6 ) + 1 ] / [ ( 18.7 / 14.6 ) + 1 ] = 237.1 in
( xac )B = 0.63 ( 91.5 ) = 57.7 in
xCGLaunch = 146.9 in ( x AC – xCG )Launch / d = - { 2 {[ 146.9 – 57.7 ] / 14.6 } + 1.28 {[ 146.9 – 237.1 ] / 14.6 }}
/ [ 2 + 1.28 ] = - 0.41
Flare Increases Static Stability ( cont ) Flare Increases Static Stability ( cont )
9
( CNα)B
( xac )B = 57.7 91.5 146.9
14.6 18.7 in
( xac )F = 237.1230.9 242.9
( CNα )F
x AC = 140.9
CNα= ( CNα
)B + ( CNα )F
Tail Stabilizers Have Lower Drag While Flares Tail Stabilizers Have Lower Drag While Flares
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g
Have Lower Aero Heating and Stability Changes
g
Have Lower Aero Heating and Stability Changes
Type Stabilizer Drag Span Heating ΔCNα Tail ControlFlare ( e.g., THAAD )
Tails ( e.g., Standard Missile )
Note: Superior Good Average Poor –
– –
– –
Wi Si i T dWi Si i T d
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Wing Sizing Trades Wing Sizing Trades
Advantages of Small Wing / Strake / No Wing
• Range in high supersonic flight / high dynamic pressure
• Max angle of attack
• Launch platform compatibility
• Lower radar cross section
• Volume and weight for propellant / fuel
Advantages of Larger Wing
• Range in subsonic flight / low dynamic pressure• Lower guidance time constant*
• Normal acceleration*
• High altitude intercept*
• Less body bending aeroelasticity ( wing stiffens body )• Less seeker error due to dome error slope ( lower angle of attack )
• Less wipe velocity for warhead ( lower angle of attack )
• Lower gimbal requirement for seeker
*Based on assumption of aerodynamic control and angle of attack below wing stall
Most Supersonic Missiles AreWinglessMost Supersonic Missiles AreWingless
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Stinger FIM-92 Grouse SA-18 Grison SA-19 ( two stage ) Gopher SA-13
Starburst Mistral Kegler AS-12 Archer AA-11
Gauntlet SA-15 Magic R550 Python 4 U-Darter
Python 5 Derby / R-Darter Aphid AA-8 Sidewinder AIM-9X
ASRAAM AIM-132 Grumble SA-10 / N-8 Patr io t MIM-104 Starstreak
Gladiator SA-12 PAC-3 Roland ( two stage ) Crotale
Hellf ire AGM-114 ATACM MGM-140 Standard Missi le 3 ( three stage ) THAAD
Most Supersonic Missiles Are Wingless Most Supersonic Missiles Are Wingless
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
Wings, Tails, and Canards with Large Area and Wings, Tails, and Canards with Large Area and
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at High Angle of Attack Have High Normal Force at High Angle of Attack Have High Normal Force
0
1
2
3
4
0 30 60 90
M < 1.35, based o n s lender wing theory + Newtonian impact theory
M = 2, based on linear wing theory + Newtonian impact theory
M = 5, based on linear wing theory + Newtonian impact theory
( C N ) W i n g
S R E F / S W ,
W i n g N o r m a l F o r c
e C o e f f i c i e n t
f o r R o c k e t B
a s e l i n e
α’ = αW = α + δ , Wing Effective Angle of Attack for Rocket Baseline, Deg
⏐( CN )Surface ⏐ = [ 4⏐sin α’ cos α’⏐ / ( M2 – 1 )1/2 + 2 sin2α’ ] ( SSurface / SRef ), if M > { 1 + [ 8 / ( π A )]2 }1/2
⏐( CN )Surface ⏐ = [ ( π A / 2) ⏐sin α’ cos α’⏐ + 2 sin2α’ ] ( SSurface / SRef ), if M < { 1 + [ 8 / ( π A )]2 }1/2
Note: Linear wing theory appl icable if M > { 1 + [ 8 / ( π A )] 2 }1/2, slender wing theory appl icable if M < { 1 + [ 8 / ( π A )]2 }1/2, A = Aspect Rat io < 3, SSurface = Surface Planform Area, SRef = Reference Area
Example for Rocket BaselineWing
AW = 2.82
SW = 2.55 ft2
SRef = 0.349 ft2
δ = 13 deg, α = 9 degM = 2
{ 1 +[ 8 / ( π A )]2 }1/2 = 1.35
Since M > 1.35, use linear wingtheory + Newtonian theory
α’ = αW
= α + δ = 22°( CN )Wing SRef / SW = 4 sin 22°cos 22° / ( 22 – 1 )1/2 + 2 sin2 22°= 1.083
( CN )Wing = 1.08 ( 2.55 ) / 0.349 =7.91
Aerodynamic Center of a Thin Surface ( e.g.,Aerodynamic Center of a Thin Surface ( e.g.,
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Wing, Tail, Canard ) Varies with Mach Number Wing, Tail, Canard ) Varies with Mach Number
0
0.1
0.2
0.3
0.4
0.5
0 1 2 3 4 5
M, Mach Number
X A C / C M A C ,
S u r f a
c e N o n - d i m e n s i o n a l
A e r o d y n a
m i c C e n t e r
A = 1
A = 2 A = 3
Note: Based on linear wing theoryThin wing ⇒ M ( t / c ) << 1( x AC )Surface = Surface aerodynamic
center distance from leadingedge of ( c
MAC)SurfacecMAC = Mean aerodynamic chord
A = Aspect rat io = b2 / S
( x AC / cMAC )Surface = [ A ( M2 – 1 )1/2 – 0.67 ] / [ 2A ( M2 –1 )1/2 – 1 ], if M > ~ 2
( x AC / cMAC )Surface = 0.25, if M < ~ 0.7
Example: Rocket Baseline Wing
A = 2.82
cMAC = 13.3 in
( xMAC )Wing = 67.0 in
M = 2
( x AC / cMAC )Wing = 0.481
( x AC
)Wing
= 6.4 in from mac leadingedge = 73.4 in from nose tip
x AC
xMAC cMAC
Hinge Moment Increases with Dynamic Pressure Hinge Moment Increases with Dynamic Pressure
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and Effective Angle of Attack and Effective Angle of Attack
0
5000
10000
15000
20000
25000
30000
0 10 20 30
H M ,
E x a m p l e H i n g e M o
m e n t , i n - l b
q = 436 psf ( M = 0.8 ) q = 1242 psf ( M = 1.35 )
q = 2725 psf ( M = 2 ) q = 17031 psf ( M = 5 )
HM = NSurface ( x AC - xHL )Surface
α’ = αW = α + δ , Wing Effect ive Angle of Attack of Rocket Baseline, Deg
Note: Based on linear wingtheory, slender wing theory,and thin wing ( M ( t / c ) << 1 )
NSurface = Normal force on surface( two panels )
( x AC - xHL )W = distance fromsurface aerodynamic center tohinge line of surface
Example for Rocket BaselineWing Control
cmac = 13.3 in
xHL = 0.25 cmac
SRef = 0.349 ft2
SW = 2.55 ft2
δ = 13 deg, α = 9 degα’ = αW = α + δ = 22°
M = 2, h = 20k f t, q = 2725 psf
NW = [ CNW( SRef / SW )] qSW =
1.083 ( 2725 ) ( 2.55 ) = 7525 lb
x AC / cmac = 0.48
HM = 7525 ( 0.48 – 0.25 ) ( 13.3 )
= 23019 in – lb for two panels
NW
x H L
x A C
c m a c
Wings, Tails, and Canards Usually Have Greater Wings, Tails, and Canards Usually Have Greater
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Skin Friction Drag Than Shock Wave Drag Skin Friction Drag Than Shock Wave Drag
0
0.1
0.2
0.3
0.4
0 10 20 30 40 50
M / ( q cmac ) = 0.00001 ft / lb M / ( q cmac ) = 0.0001 ft / lb
M / ( q cmac ) = 0.001 ft / lb M / ( q cmac ) = 0.01 ft / lb
( CD0 )Surface,Friction = nSurface { 0.0133 [ M / ( q cmac )]0.2 } ( 2 SSurface / SRef ), q in psf, cmac in ft( CDO
)Surface,Wave = nSurface ( 1.429 / MΛLE2 ){( 1.2 MΛLE
2 )3.5 [ 2.4 / ( 2.8 MΛLE2 – 0.4 )]2.5 – 1 } sin2 δLE cos ΛLE
tmac b / SRef , based on Newtonian impact theory( CDO
)Surface = ( CDO)Surface,Wave + ( CDO
)Surface,FrictionnSurfaces = number of surface planforms ( cruciform = 2 )
q = dynamic pressure in psf
cmac
= length of mean aero chord in ft
γ = Specif ic heat ratio = 1.4
MΛLE= M cos ΛLE = Mach number ⊥ leading edge
δLE = leading edge section total angle
ΛLE = leading edge sweep angle
tmac = max thickness of macb = span
Example for Rocket Baseline Wing:
nW = 2, M = 2, h = 20k ft ( q = 2,725 psf ), cmac = 1.108ft, SRef = 50.26 in2, SW = 367 in2, δLE = 10.01 deg, ΛLE =45 deg, t
mac
= 0.585 in, b = 32.2 in, MΛLE
= 1.41 ( M = 2 )
M / ( q cmac ) = 2 / [ 2725 ( 1.108 )] = 0.000662 ft / lb
n SSurface / SRef = 2 ( 367 ) / 50.26 = 14.60
( CDO)Wing,Friction = 0.090
( CD0)Wing,Wave = 0.024
( CDO )Wing = 0.024 + 0.090 = 0.11
E x a m p l e ( C D 0
) S u r f a c e , F r i c t i o n
n SSurface / SRef
Examples of Wing, Tail, and Canard Panel Examples of Wing, Tail, and Canard Panel
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Geometry Alternatives Geometry Alternatives
Parameter
Variation x AC
Bending Moment / Frict ion
Supersonic DragRCS
Span Constraint
Stability & Control
Aeroelastic Stab.
λ = Taper ratio = cT / cR
A = Aspect rat io = b2 / S = 2 b / [( 1 + λ ) cR ]yCP = Outboard center-of-pressure = ( b / 6 ) ( 1 + 2 λ ) / ( 1 + λ )
cMAC = Mean aerodynamic chord = ( 2 / 3 ) cR ( 1 + λ + λ2
) / ( 1 + λ )
Note: Superior Good Average Poor
Based on equal surface area and equal span.Surface area often has more impact than geometry.
–
–
–
–
–
–
Triangle
( Delta )
Aft Swept LE
Trapezoid
Double
Swept LEBow Tie Rectangle
–
–
Examples of Surface Arrangement and Examples of Surface Arrangement and
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Aerodynamic Control Alternatives Aerodynamic Control Alternatives
Two Panels( Mono-Wing )
Three( Tri-Tail )
Four ( Cruciform ) Six* Eight*
Folded Wraparound Extended Balanced ActuationControl
Flap Control
Interdigitated In-line
Note: More than four tails are usually free-to-roll pi tch / yaw stabilizers, for low induced roll.
Most Missiles Use Four Control Surfaces with Most Missiles Use Four Control Surfaces with
C bi d Pit h / Y / R ll C t l I t ti
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Control Integ Control Surfaces Example Control Effect Cost Packaging
Pitch / Yaw 2 Stinger FIM-92
Pitch / Roll 2 ALCM AGM-86
Pitch / Yaw / Roll 3 SRAM
Pitch / Yaw / Roll 4 Adder AA-12
Pitch + Yaw + Roll 5 Kitchen AS-4
Pitch / Yaw + Roll 6 Derby / R-Darter
Combined Pitch / Yaw / Roll Control Integration Combined Pitch / Yaw / Roll Control Integration
Note: Superior Good Average Poor –
–
– –
–
–
–
–
There Are Many Flight Control Configuration There Are Many Flight Control Configuration
Alt ti
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Alternatives Alternatives
ControlControl Design Alternatives
Tail Cruciform ( 4 )Tri-tail ( 3 )Not Compressed
FoldedWraparoundSwitchblade
Canard AboveRolling Airframe ( 2 )
Wing Tail ( 3, 4, 6, 8 )Strake / Canard & TailIn Line with ControlsInterdigi tated with Controls
TVC or Reaction JetControl
Movable NozzleJet TabJet Vane
Axial PlateSecondary InjectionNormal Jet / JI
Spanwise Jet / JI
Fixed Surface Alternatives
WinglessWingStrake / Canard
In Line with ControlsInterdigi tated with ControlsNumber ( 2, 3, 4 )
Tail ( 3, 4, 6, 8 )Tail + WingIn Line with Controls
Interdigi tated with Controls
Tail ( 3, 4, 6, 8 )Tail + Canard / StrakeTail + Wing
Above
Tail Control Is Efficient at High Angle of AttackTail Control Is Efficient at High Angle of Attack
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Tail Control Is Efficient at High Angle of Attack Tail Control Is Efficient at High Angle of Attack
α
V∞
ΔCN
CN Trim
( assumed statically stable ) CN at δ = 0
CNCNegative δ
CNCat δ = 0
☺ Efficient Packaging
☺ Low Hinge Moment / Actuator Torque
☺ Low Induced Rolling Moment
☺ Efficient at High α
Decreased Lift at Low α if Statically Stable
c g
Tail Control Is More Effective Than Conventional
C d C t l t Hi h A l f Att k
Tail Control Is More Effective Than Conventional
C d C t l t Hi h A l f Att k
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Canard Control at High Angle of Attack Canard Control at High Angle of Attack
V∞
α
+ δ
• Assumed static stabili ty• Control surface local
angle of attack α’ = α + δ• Panel stalled at high α*
Conventional Canard Control
V∞
α
– δ
• Assumed static stabili ty• Control surface local
angle of attack α’ = α – δ• Panel not stalled at high α
Tail Control
α ~ Angle of Attack ( deg ) α ~ Angle of Attack ( deg )
C m
δ / ( C mδ )α
= 0 °
1.0
0
ConvenCanard
Control
Tail
Control☺
10 – 20° 20 – 30°
C lδ / ( C lδ )α = 0 ° 1.0
0
ConvenCanard
Control
Tail
Control☺
10 – 15° 15 – 30°
Ø = 0°
*Note: Additional forward fixed surfaces ( such as Python 4 ) in front of movable canards alleviate stallat high α. Free-to-rol l tails ( such as Python 4 ) alleviate induced roll from canard control at high α.
About 70%of Tail Control Missiles Also Have WingsAbout 70%of Tail Control Missiles Also Have Wings
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JASSM AGM-158 Maverick AGM-65 CALCM JSOW AGM-154
Tomahawk BGM-109 Taurus KEPD 350 Storm Shadow / Scalp Popeye AGM-142
Exocet MIM40 TOW2-BGM71D AMRAAM AIM-120 Sunburn SS-N-22
Standard RIM-66 / 67 RBS-70 / 90 Shipwreck SS-N-19 Super 530
Sea Dart ( two stage ) FSAS Aster R-37 ( AA-X-13 ) Mica
Adder AA-12 Rapier 2000 SD-10 / PL-12 Seawolf
About 70% of Tail Control Missiles Also Have Wings About 70% of Tail Control Missiles Also Have Wings
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
Tail Control Alternatives: Conventional Balanced
Actuation Fin Flap and Lattice Fin
Tail Control Alternatives: Conventional Balanced
Actuation Fin Flap and Lattice Fin
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Control Hinge
Type of Tail Control Effectiveness Drag Moment RCS
Balanced Actuation Fin ( Example: ASRAAM AIM-132 )
Flap ( Example: Hellfi re AGM-114 )
Lattice Fin ( Example: Adder AA-12 / R-77 )
Actuation Fin, Flap, and Lattice Fin Actuation Fin, Flap, and Lattice Fin
–
–
Note: Superior Good Average Poor –
Lattice Fins Have Advantages for Low Subsonic
and High Supersonic Missiles
Lattice Fins Have Advantages for Low Subsonic
and High Supersonic Missiles
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and High Supersonic Missiles and High Supersonic Missiles
Advantages
High control effectiveness atlow subsonic and high
supersonic Mach number Low hinge moment
Short chord length
DisadvantagesHigh RCS ( cavities, normalleading edges )
High drag at transonic Mach
number ( choked flow )
Low Subsonic Transonic Low Supersonic High Supersonic
☺ ☺
Conventional Canard Control Is Efficient at Low
Angle of Attack But Stalls at High Alpha
Conventional Canard Control Is Efficient at Low
Angle of Attack But Stalls at High Alpha
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Angle of Attack But Stalls at High Alpha Angle of Attack But Stalls at High Alpha
α
V∞
δΔCN
CN Trim ( assumed statically stable )
CN at δ = 0C
N C
☺ Efficient Packaging
☺ Simplified
Manufacturing☺ Increased Lift at Low α
if Statically Stable
Stall at High α if Statically Stable
Induced Roll
Note: = CNC at δ = 0°
= CNC at δ = δ
*Note: Addit ional forward f ixed surface infront of movable canard alleviates stall athigh α. Free-to-roll tails alleviate inducedroll at high α. Dedicated rol l controlsurfaces avoid rol l control saturation andsimplify autopilot design.
c g
Canard Control Missiles Are Wingless and Most
Are Supersonic
Canard Control Missiles Are Wingless and Most
Are Supersonic
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Are Supersonic Are Supersonic
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
Stinger FIM-92 Grouse SA-18 Grison SA-19 ( two-stage ) Gopher SA-13
Starburst Gauntlet SA-15 Mistral AIM-9L
Archer AA- 11 Magic R 550 Python 4 U-Darter
Python 5 Derby / R-Darter Aphid AA-8 Kegler AS-12
GBU-12 GBU-22 GBU-27 GBU-28
Missiles with Split Canards Have Enhanced
Maneuverability at High Angle of Attack
Missiles with Split Canards Have Enhanced
Maneuverability at High Angle of Attack
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Kegler AS-12 Archer AA-11 Aphid AA-8
Magic R 550 Python 4 U-Darter
Maneuverability at High Angle of Attack Maneuverability at High Angle of Attack
Note: Forward fixed surface reduces local angle-of-attack for movable canard, providing higher stall angle of attack. Forwardsurface also prov ides a fixed, symmetrical location for vortex shedding from the body.
Python 4 also has free-to-roll tails and separate roll control ailerons.
α’ ~ α α’ ~ δα
δΔCN
CN
C
Note: α’ = Local angle of attack
Wing Control Requires Less Body Rotation But
Has High Hinge Moment Induced Roll and Stall
Wing Control Requires Less Body Rotation But
Has High HingeMoment Induced Roll and Stall
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Has High Hinge Moment, Induced Roll and Stall Has High Hinge Moment, Induced Roll and Stall
δV
Δ CN ~ CN Trim
☺ Low Body α / Dome Error Slope
☺ Fast Response ( if skid-to-turn )
Poor Actuator Packaging
Large Hinge Moment
Larger Wing Size
Induced Roll
Wing Stall
( α small ) cg
Wing Control Missile Susceptible to High Vortex
Shedding
Wing Control Missile Susceptible to High Vortex
Shedding
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Shedding Shedding
Strong vortices from wing interact with tail
Source: Nielsen Engineering & Research ( NEAR ) web si te:
http://www.nearinc.com/near/project/MISDL.htm
Video of Vortices from DeltaWing at High Angle of Attack
Source: Universi ty of Notre Dame web site:http://www.nd.edu/~ame/facilities/SubsonicTunnels.html
Wing Control Missiles Are Old Technology Wing Control Missiles Are Old Technology
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Sparrow AIM-7: IOC 1956
Skyflash: IOC 1978
Alamo AA-10 / R-27: IOC 1980
HARM AGM-88: IOC 1983
Aspide: IOC 1986
Permission of Missile Index. Copyright 1997©Missile.Index All Rights Reserved
TVC and Reaction Jet Flight Control TVC and Reaction Jet Flight Control
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Liquid Injection Hot Gas Injection
Axial Plate Jet Tab Movable Nozzle
± 7°± 12°
± 7°± 15° ± 20°
Note: Jet vanes provide roll cont rol and shareactuators with aero contro l, but have reduced ISP
Reaction JetM∞ Jet Flow
Jet Vane*
± 10°
Note:
•TVC and reaction jet flight control provide
high maneuverability at low dynamic pressure•TVC usually has lower time constant andmiss distance than aero control
•Reaction jets usually have lower timeconstant and miss distance than TVC
•Reaction jets can be either impulse jets or
controlled duration jets Jet inter. Thrust Jet interaction
Most Tactical Missiles with TVC or Reaction Jet
Control Also Use Aero Control
Most Tactical Missiles with TVC or Reaction Jet
Control Also Use Aero Control
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Jet Vane + Aero Control :
Mica Sea Sparrow RIM-7 AIM-9X
Sea Wolf GWS 26 IRIS-T A-Darter Javelin
Jet Tab + Aero Control : Archer AA-11
Reaction Jet + Aero Control:
PAC-3
Movable Nozzle + Aero Control + Reaction Jet:
SM-3 Standard Missile Aster FSAF 15
Movable Nozzle + Reaction Jet:
THAAD
Reaction Jet:
LOSAT
Control Also Use Aero Control Control Also Use Aero Control
Example Video of TVC ( FSAF-15 and Javelin )
Skid-to-Turn Is the Most Common Maneuver Law Skid-to-Turn Is the Most Common Maneuver Law
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Skid-To-Turn ( STT )• Advantage: Fast response• Features
– Does not require roll commands from autopilot – Works best for axisymmetric cruciform missiles
Bank-To-Turn ( BTT )
• Advantage: Provides higher maneuverabili ty for planar wing, noncircular / lifting bodies, and airbreathers
• Disadvantages – Time to rol l – Requires fast ro ll rate – May have higher dome error slope
• Features – Roll attitude commands from autopilot – Small sideslip
Rolling Air frame ( RA )• Advantage: Requires only two sets of gyros /
accelerometers / actuators ( packaging for small missile )
• Disadvantages for aero control – Reduced maneuverabili ty for aero cont rol – Requires high rate gyros / actuators – Requires precision geometry and thrust alignment
• Features – Bias roll rate and roll moment
– Can use impulse steering ( e.g., PAC-3, LOSAT ) – Compensates fo r thrust offset
Step 1: Roll Unt ilWing ⊥ LOS
Step 2: Maneuver @ RollRate = 0 and Wing ⊥ LOS
Bias Roll Rate ( e.g., 3 Hz )
Maneuver w / o Rol l Command
Target
Target
Target
L O S
Target
Maneuver with Bias RollMoment
L O S
L O S
L O S
STT
BTT ( withPlanar Wing )
RA
Asymmetric Inlets Require Bank-to-Turn Maneuvering
Asymmetric Inlets Require Bank-to-Turn Maneuvering
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Examples of Twin Inlet Missiles wi th Bank-to-Turn
Twin Side Inlets Ramjet: ASMP
Twin Cheek Inlets Ducted Rocket: HSAD
Twin Cheek Inlets Ducted Rocket: Meteor
Examples of Single Inlet Missiles with Bank-to-Turn
Chin Inlet Ramjet: ASALM
Bottom Inlet Turbojet: BGM-109 Tomahawk
Bottom Inlet Turbojet: Storm Shadow / Scalp
Top Inlet Turbofan: AGM-86 ALCM
gg
Note: Bank-to-turn maneuvering maintains low sideslip for better inlet efficiency.
X Roll Orientation Is Usually Better Than + Roll Orientation
X Roll Orientation Is Usually Better Than + Roll Orientation
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Yaw Right
Fin 1
Fin 3
Roll Right
+ Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base
X Roll Orientation with Four Tail Surfaces Control of Pitch / Yaw / Roll, Looking Forward from Base
Roll Right
Note: + roll orientation usually has lower trim drag, less static stability and control effectiveness in pitch and yaw, andstatically unstable roll moment derivative ( Clφ > 0 ).X roll orientation has better launch platform compatibility , higher L / D, higher static stability and controleffectiveness in pitch and yaw, and statically stable roll moment derivative ( Clφ < 0 ).
4 1
3 2
Pitch Up Yaw Right
Pitch Up
Fin 2Fin 4 T r a i l i n g e d g e
d e f l e c t i o n
Trimmed Normal Force Is Defined at Zero
Pitching Moment
Trimmed Normal Force Is Defined at Zero
Pitching Moment
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gg
P i t c h i n g M o m e n t ,
C m
N o r m
a l F o r c e ,
C N
Angle of Attack ( Deg )
αTrim @ Cm = 0
δ = 0
δ = δ Trim for either statically stable tail
contro l or statically unstable canard control
δ = 0
δ = δ Max
δ = δ Trim for either statically unstable tailcontro l or statically stable canard control
Angle of At tack ( Deg )
Relaxed Static Margin Allows Higher Trim Angle
of Attack and Higher Normal Force
Relaxed Static Margin Allows Higher Trim Angle
of Attack and Higher Normal Force
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Note: Rocket BaselineXCG = 75.7 in.Mach 2
( α + δ )Max = 21.8 deg, ( CNTrim)Max
α / δ = 0.75, ( Static Margin = 0.88 Diam )
α / δ = 1.5, ( SM = 0.43 Diam )
α / δ = ∞, ( SM = 0 )
gg
( CN, Trim )max, MaxTrimmed NormalForce Coefficient of Rocket Baseline
0 4 8 12 16 20 24
16
12
8
4
0
( αTrim )max, Μax Trim Angle of Attack, deg
Tails Are Sized for Desired Static Margin Tails Are Sized for Desired Static Margin
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( CNα)B
( CNα )W
( CNα)T
( x AC )T
( x AC )B
( x AC )W
+M
+ α
x = 0
xCG
x = lB
x = lN
x AC
ΣM = 0 at aerodynamic center
( CNα)B {[ xCG – ( x AC )B ] / d } + ( CNα
)W {[ xCG – ( x AC )W ] / d } SW / SRef + ( CNα)T {[ xCG – ( x AC )T ] / d } ST / SRef
= - [( CNα)B + ( CNα
)W SW / SRef + ( CNα)T ST / SRef ] [( x AC – xCG ) / d ]
Static margin for a specified tail area is
( x AC – xCG ) / d = - {( CNα )B {[ xCG – ( x AC )B ] / d } + ( CNα )W {[ xCG – ( x AC )W ] / d } SW / SRef + ( CNα )T {[ x CG – ( x AC )T ] / d } ( ST / SRef )} /[(CNα)B + (CNα
)W SW / SRef + ( CNα)T ST / SRef ]
Required tail area for a specified static margin is
ST / SRef = ( CNα)B {[ xCG – ( x AC )B ] / d } + ( CNα
)W {[ xCG – ( x AC )W ] / d } ( SW / SRef ) + {[( CNα)B + ( CNα
)W SW / SRef ][( x AC – xCG ) / d ]}/ {( C
Nα)T
[( x AC
)T
– xCG
] / d - ( x AC
– xCG
) / d }
CNα
Larger Tail Area Is Required for Neutral Stability
at High Mach Number
Larger Tail Area Is Required for Neutral Stability
at High Mach Number
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0
1
2
3
0 1 2 3 4 5
M, Mach Number
( S T ) N e u t r a l / S R e f , N e
u t r a l S t a b i l i t y T a i l A r e a /
R e f e r e
n c e A r e a
(ST)Neutral / SRef = { (CNα)B [ xCG – (x AC)B ] / d + (CNα)W {[ xCG – (x AC)W ] / d } ( SW / SRef )} / {{[ (x AC)T – xCG ] / d } (CNα)T }
Assumptions fo r f igure:
•XCG ≈ l / 2, (X AC)B ≈ d, ( X AC )T ≈ l – d
•α < 6 deg, turbulent boundary layer
•(CN
α
)B
= 2 per rad
•(CNα)T = (CNα)W = 4 / [ M2 –1 ]1/2, if M> { 1 + [ 8 / ( π A )]2 }1/2
•(CNα)T = (CNα)W = π A / 2, if M < { 1 +[ 8 / ( π A )] 2 }1/2
Example Rocket Baseline:
l = 144 in, d = 8 in, SW = 2.55 ft2, SRef =0.349 ft2, AW = 2.82, (cMAC)W = 13.3 in,xMAC = 67.0 in from nose tip, burnout( xCG = 76.2 in from t ip ), Mmax = 3
(x AC)W = 0.49 ( 13.3 ) = 6.5 in fromleading edge of MAC
(x AC)W = 6.5 + 67.0 = 73.5 in f rom nose
{[ xCG – (x AC)W ] / l } ( SW / SRef ) = 0.14( forward wing )
(ST)Neutral / SRef = 1.69 provides neutralstability
(ST)Neutral = 1.69 ( 0.349 ) = 0.59 ft2
{ [ x C G – ( x A C
) W ] / l }
( S W / S R e f ) =
0
{ [ x C G – ( x A C ) W
] / l } (
S W / S R e f
) = 0. 2 5
( f o r w a
r d w i n g )
{ [ x C G – ( x A C
) W ] / l } ( S
W / S R e f
) = - 0. 2 5
( a f t w
i n g )
Stability and Control Derivatives Conceptual Design Criteria
Stability and Control Derivatives Conceptual Design Criteria
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zy
xC
lδr Clδa
zy
xCnδa
Cnδr
zy
xC
lφ Clδa
z y
xCmα
Cmδ
z y
xClβ Clδa
| Clδr / Clδa | < 0.3 ( Roll Due to Rudder Deflection ) | Clφ / Clδa | < 0.5 ( Roll Due to Roll Angle )
| Cnδa / Cnδr | < 0.2 ( Yaw Due to Aileron Deflection ) | Cmα / Cmδ | < 1 ( Pitch Due to α )
| Clβ / Clδa | < 0.3 ( Rol l Due to Sideslip ) | Cnβ / Cnδr | < 1 ( Yaw Due to Sideslip )
zy
x
Cnδr
Cnβ
Note: The primary control derivative ( larger bold font ) should be larger than the undesirable stability and control derivative.
Most of the Rocket Baseline Body Buildup Normal
Force Is Provided by the Wing
Most of the Rocket Baseline Body Buildup Normal
Force Is Provided by the Wing
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CN, Normal ForceCoefficient of
Rocket Baseline
15
10
5
0 0 5 10 15 20 25
α, Angle of Attack, Deg
Body + Wing + Tail
Body + Wing
Body
Note for figure: M = 2, δ = 0
( CN )Total = ( CN )Wing-Body-Tail ≅ ( CN )Body + ( CN )Wing + ( CN )Tail
Note: ( CD0)Total = ( CD0
)Wing-Body-Tail ≅ ( CD0)Body + ( CD0
)Wing + ( CD0)Tail
( Cm )Total = ( Cm )Wing-Body-Tail ≅ ( Cm )Body + ( Cm )Wing + ( Cm )Tail
Summary of Aerodynamics Summary of Aerodynamics
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Conceptual Design Prediction Methods of Bodies and Surfaces Normal force coefficient
Drag coefficient
Aerodynamic center / pitching moment coefficient / hinge moment
Design Tradeoffs Diameter
Nose fineness
Boattail
Lifting body versus axisymmetric body
Wings versus no wings
Tails versus flares
Surface planform geometry
Flight control alternatives Maneuver alternatives
Roll orientation
Static margin / time to converge or diverge
Tail sizing
Summary of Aerodynamics ( cont ) Summary of Aerodynamics ( cont )
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Stability and Control Design Criteria Static stability
Control effectiveness
Cross coupling
Body Buildup
New Aerodynamics Technologies Faceted / window / multi-lens domes
Bank-to-turn maneuvering
Lifting body airframe Forward swept surfaces
Neutral static margin
Lattice fins
Split canard control Free-to-rol l tails
Discussion / Questions?
Classroom Exercise
Aerodynamics Problems Aerodynamics Problems
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1. Missile diameter tradeoffs include consideration of seeker range, warheadlethality, structural mode frequency, and d___.
2. Benefits of a high f ineness nose include lower supersonic drag and lower r____ c____ s______.
3. Three contributors to drag are base drag, wave drag, and s___ f_______drag.
4. To avoid flow separation, a boatail or flare angle should be less than __ deg.
5. A lifting body is most ef ficient at a d______ p_______ of about 700 psf.
6. At low angle of attack the aerodynamic center of the body is on the n___.
7. Subsonic missi les often have w____ for enhanced range.
8. The aerodynamic center of the wing is between 25% and 50% of the m___
a__________ c____.9. Hinge moment increases with the local flow angle due to control surface
deflection and the a____ o_ a_____.
10. Increasing the surface area increases the s___ f_______ d___.
Aerodynamics Problems ( cont ) Aerodynamics Problems ( cont )
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11. Leading edge sweep reduces drag and r____ c____ s______.
12. A missile with six control surfaces, four surfaces providing combined pitch /yaw control plus two surfaces providing roll control, has an advantage of good c______ e____________.
13. A missile with two control surfaces providing only combined pitch / yawcontrol has advantages of lower c____ and good p________.
14. A tail control missile has larger trim normal force if it is statically u_______.
15. Lattice fins have low h____ m_____.
16. Split canards allow higher maximum angle of attack and higher m______________.
17. Two types of unconventional control are thrust vector control and r_______ j__ control.
18. The most common type of TVC for tactical missiles is j__ v___ control.
19. Three maneuver laws are skid to turn, bank to turn, and r______ a_______.
20. Bank to turn maneuvering is usually required for missiles with a single wing
or with a_________ inlets.
Aerodynamics Problems ( cont ) Aerodynamics Problems ( cont )
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21. A missile is statically stable if the aero center is behind the c_____ o_g______.
22. Tail stabilizers have low drag while a f____ stabilizer has low aero heatingand a relatively small shift in static stability.
23. If the moments on the missile are zero the missile is in t___.
24. Total normal force on the missi le is approximately the sum of the normalforces on the surfaces ( e.g., wing, tail, canard ) plus normal force on theb___.
25. Increasing the tail area increases the s_____ m________.
Outline Outline
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Introduction / Key Drivers in the Design Process Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples Development Process
Summary and Lessons Learned
References and Communication Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
Missile Concept Synthesis Requires Evaluation
of Alternatives and Iteration
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Yes
Establish Baseline
Weight
Trajectory
MeetPerformance?
Measures of Merit and ConstraintsNo
No
Yes
Resize / Alt Conf ig / Subsystems / Tech
Al t Mission
Al t Baseline
Define Mission Requirements
Aerodynamics
Propulsion
High Specific Impulse Is Indicative of Lower Fuel / Propellant Consumption
High Specific Impulse Is Indicative of Lower Fuel / Propellant Consumption
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Scramjet: ISP typicallyconstrained by thermal choking
Turbojet: ISP typically constrained by turbine temperature limit
Ramjet: ISP typically constrained bycombustor insulation temperature limit
Solid Rocket: ISP typically constrainedby safety
4,000
3,000
2,000
1,000
0 I S P ,
S p e c i f i c I m p u l s e
, T h r u s t / ( F u e l o r P r o p e l l a n t
W e i g h
t F l o w R a t e ) , S
0 2 4 6 8 10 12
Mach Number
Ducted Rocket
Cruise Range Is Driven by L/D, sp , Velocity, and Propellant or Fuel Weight Fraction
Cruise Range Is Driven by L/D, sp , Velocity, and Propellant or Fuel Weight Fraction
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Typical Value for 2,000 lb Precision Strike Missi le
Note: Ramjet and Scramjet miss iles booster propellant for Mach 2.5 to 4 take-over speed not included in WP
for cru ise. Rockets require thrust magnitude control ( e.g., pintle, pulse, or gel motor ) for effective cruise.Max range for a rocket is usually a semi-ballistic flight profile, instead of cruise flight. Multiple stages maybe required for rocket range greater than 200 nm.
R = ( L / D ) Isp V In [ WL / ( WL – WP )] , Breguet Range Equation
Parameter
L / D, Lift / DragIsp, Specific Impulse
V AVG , Average Velocity
WP / WL, Cruise Propellant or
Fuel Weight / Launch WeightR, Cruise Range
103,000 s
1,000 ft / s
0.3
1,800 nm
51,300 s
3,500 ft / s
0.2
830 nm
31,000 s
6,000 ft / s
0.1
310 nm
5250 s
3,000 ft / s
0.4
250 nm
Solid RocketHydrocarbon FuelScramjet Missile
Liquid FuelRamjet Missile
Subsonic TurbojetMissile
Solid Rockets Have High Acceleration Capability Solid Rockets Have High Acceleration Capability
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1,000
100
10
1
0 1 2 3 4 5
RamjetTMax = (π / 4 ) d2 ρ0 V0
2 [( Ve / V0 ) -1 ]
Solid RocketT
Max= 2 P
c A
t= m
.V
e
M, Mach Number
( T / W ) M a x ,
( T h r u s t / W e i g h t ) M a x
Note:Pc = Chamber pressure, At = Nozzle throat area, m
.= Mass flow rate
d = Diameter, ρ0 = Free stream densi ty, V0 = Free stream velocity,V
e= Nozzle exit veloc ity ( Turbojet: V
e~ 2,000 ft / s, Ramjet: V
e~ 4,500 ft / s, Rocket: V
e~ 6,000 ft / s )
TurbojetTMax = (π / 4 ) d2 ρ0 V0
2 [( Ve / V0 ) -1 ]
Turbojet Nomenclature Turbojet Nomenclature
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0
Free Stream
1
Inlet Entrance
3
Compressor Exit
2
Compressor Entrance4
Turbine Entrance
Inlet Compressor Combustor Turbine Nozzle
5
Turbine Exit
High Temperature Compressors Are Required to
Achieve High Pressure Ratio at High Speed
High Temperature Compressors Are Required to
Achieve High Pressure Ratio at High Speed 2 ( γ - 1 ) / γ
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0
1000
2000
3000
0 1 2 3 4
M0, Free Stream Mach Number
T 3 ,
C o m p r e s
s o r E x i t T e m p e r a t u r e ,
p3 / p2 = 1
p3 / p2 = 2
p3 / p2 = 5
p3 / p2 = 10
T3 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M0 }( p3 / p2 ) 3 3
γ0 = 1.4, γ3 ≈ 1.29 + 0.16 e-0.0007 T3
Note: Ideal in let; ideal compressor; low subsonic,isentropic flow
Example:M0 = 2, h = 60k ft ( T0 = 398 R )
p3 / p2 = 5 ⇒ T3 = 1118 R, γ3 = 1.36
T3 = Compressor exit temperature in Rankine, T0 = free stream temperature in Rankine, γ = specific heat
ratio, M0 = free stream Mach number, p3 = compressor exit pressure, p2 = compressor entrance pressure
T3
High Turbine Temperature Is Required for High
Speed Turbojet Missiles
High Turbine Temperature Is Required for High
Speed Turbojet Missiles
( / ) f /
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0
1000
2000
3000
4000
5000
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
f / a, Fuel-to-Air Ratio
T 4 , T u r b o j e t
T u r b i n e T e m p e
r a t u r e ,
T3 = 500 R
T3 = 1000 R
T3 = 2000 R
T3 = 4000 R
T4 ≈ T3 + ( Hf / cp ) f / a, T in Rcp4
≈ 0.122 T40.109, cp in BTU / lb / R
Example:
M0 = 2, h = 60K ft ( T0 = 398 R ),p3 / p2 = 5 ⇒ T3 = 1118 R
RJ-5 fuel ( Hf = 14,525 BTU / lb ),cp = 0.302 BTU / lb / R , f / a =0.067 ( stochiometric ) ⇒ T4 =1118 + ( 14525 / 0.302 ) 0.067 =4,340 R
T4 = Turbojet turbine entrance temperature in Rankine, T3 = compressor exit temperature in Rankine,
Hf = heating value of fuel, cp = specific heat at constant pressure, f / a = fuel-to-air ratio
T4
Turbine Material Temperature Limit Is a
Constraint for a High Speed Turbojet Missile
Turbine Material Temperature Limit Is a
Constraint for a High Speed Turbojet Missile
T t C t i d I f M hT bi M t i lM Sh t
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Slightly Constrained Turbojet
Moderately Constrained Turbojet
Moderately Constrained Turbojet
Highly Constrained Turbojet
Very Highly Constrained Turbojet, Air Turbo Rocket, Turbo Ramjet
Very Highly Constrained Turbojet, Air Turbo Rocket, Turbo Ramjet
Temperature Constrained
Turbines for Mach 4 Cruise
≈ 1,500 sCeramic Matrix Composites4,000R
≈ 2,000 sRhenium Alloys4,500R
≈ 2,500 sTungsten Alloys5,000R
≈ 1,200 sSingle Crystal Nickel Aluminides
≈ 3,500R
≈ 1,000 sTitanium Aluminides ( lighter weight than nickel super alloys )
≈ 3,000R
≈ 1,000 sNickel Super Alloys3,000R
ISP for Mach4 Cruise
Turbine MaterialMax ShortDuration Temp
Note: Constrained turbojet for Mach 4 cruise imposes a limit on turbine temperature that is less than ideal. Constraintscould consis t of a combination of:
• Constraint on compressor pressure ratio to limi t turb ine temperature
• Constraint on fuel-to-air ratio to limit turbine temperature
• Use of afterburner to limit turbine temperature
Turbin -Based Missiles Are Capable of Subsonic
to Supersonic Cruise
Turbin -Based Missiles Are Capable of Subsonic
to Supersonic Cruise
T b j t
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Turbojet
Turbo Ramjet
Air Turbo Rocket
Regulus II
Firebee II
SS-N-19 Shipwreck
SR-71
Compressor Pressure Ratio for Maximum Thrust
Turbojet Is Limited by Turbine Temperature
Compressor Pressure Ratio for Maximum Thrust
Turbojet Is Limited by Turbine Temperature
( p3 / p2 )@Tmax {( T4 / T0 )1/2
/ { 1 + [( 0 1 ) / 2 ] M02
}}γ4
/ ( γ4
- 1 )
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1
10
100
0 0.5 1 1.5 2 2.5 3 3.5 4
M0, Mach Number
( p 3 / p 2 ) @ T m a x
T4 = 2000 R T4 = 3000 R
T4 = 4000 R T4 = 5000 R
Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974
( p3 / p2 )@Tmax ≈ {( T4 / T0 ) / { 1 + [( γ0 - 1 ) / 2 ] M0 }} 4 4
Assumptions: Ideal tu rbojet ( isentropic in let , compressor, turbine, nozzle; low subsonic and constant p ressurecombustion; exit pressure = free stream pressure )
Example:
M0 = 2.0, h = 60k ft (T0 = 390 R ) , T4 = 3,000 R,γ4 = 1.31
( p3 / p2 )@Tmax = {{ ( 3000 / 390 )1/2 / { 1 + [ ( 1.4 -1 ) / 2 ] 2.02 }} 1.31/ ( 1.31 – 1 ) = 6.31
Note:
T0
= Free stream temperature
T4 = Turbine entrance temperature
γ = Specific heat ratio
Turbojet Thrust Is Limited by Turbine Maximum
Allowable Temperature
Turbojet Thrust Is Limited by Turbine Maximum
Allowable Temperature
TId lM / ( p0 A0 ) = ( 0 M0 / a0 ) ( T / m )Id lM Note:
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0
5
10
15
20
0 1 2 3 4
M0, Mach Number
T m a x / [ ( p 0 ) (
A 0 ) ] , N o n d i m e n s i o n a l M a x i m u m
T h r u s t
T4 = 2000 R T4 = 3000 R
T4 = 4000 R T4 = 5000 R
R
a m j e t ( p 3
/ p 2 = 1 )
Example: M0 = 2, h = 60 k ft ( T0 = 390 R, p0= 1.047 psi ), T4 = 3,000 R, γ4 = 1.31, ( p3 /
p2 )@Tmax = 6.31, p2 = 8.19 psi , p3 = 51.7 psi, A0 = 114 in2, T2 = 702 R, T3 = 1133 R, γ3 =1.36
T5t= 2569 R, γ5 = 1.32, p5t
= 23.0 psi , Ve =4524 ft / s, ( T / m
.)IdealMax = 2588 ft / s,
TIdealMax / p0 A0 = 7.49
TIdealMax = 7.49 ( 1.047 ) ( 114 ) = 894 lb
TIdealMax / ( p0 A0 ) = ( γ0 M0 / a0 ) ( T / m . )IdealMax
Assumption: Ideal turbojet
Note:
( T / m.)IdealMax = Ve – V0
Ve = { 2 cp T5t[ 1 – ( p0 / p5t
)( γ5 - 1 ) / γ5 ]}1/2
T5t≈ T4 – T3 + T2
T3
≈ T2
( p3
/ p2
)( γ3 - 1 ) / γ3
T2 ≈ T0 { 1 + [( γ0 - 1 ) / 2 ] M02 }
p5t≈ p4 ( T5 / T4 )γ4 / ( γ4 - 1 )
p4 = p3
p2 ≈ p0 { 1 + [( γ0 - 1 ) / 2 ] M02 }γ0 / ( γ0 - 1 )
p0 = Free stream static pressure
A0 = Free stream flow area into in let
T4 = Turbine entrance temperature
Turbojet Specific Impulse Decreases with
Supersonic Mach Number
Turbojet Specific Impulse Decreases with
Supersonic Mach Number
( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = TIdealMax T0 / [( p0 A0 0 M0 ) ( T4 T3 )]
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0
0.2
0.4
0.6
0.8
0 1 2 3 4M0, Mach Number
( I S P ) I d e a l ( g
c ) ( c p ) ( T 0 ) / [ ( a 0 )
( H f ) ] ,
N o n d i m e n s i o n a l I d e a l S p e c i f i c I m p
u l s e
T4 = 2000 R T4 = 3000 R
T4 = 4000 R T4 = 5000 R
( ISP )Ideal@Tmax gc cp T0 / ( a0 Hf ) = TIdealMax T0 / [( p0 A0 γ0 M0 ) ( T4 – T3 )] Assumptions: Ideal turbojet ( isentropic inlet, compressor, turbine, nozzle; flow, low subsonic, constant pressure combustion;exit pressure = free stream pressure), max thrust
Example:
M0 = 2, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s), RJ-5 fuel ( Hf = 14,525 BTU / lbm ), T4 =
3,000 R, cp = 0.293 BTU / lbm / R, γ0 = 1.4Calculate ( ISP )Ideal@Tmax
gc cp T0 / ( a0 Hf ) =0.559
( ISP )Ideal@Tmax = 0.559 ( 968 ) ( 14525 ) / [ 32.2( 0.293 ) ( 390 )] = 2136 s
Note:gc = Gravitational constant = 32.2
cp = Specific heat at constant pressure
T0 = Free stream temperature
a0 = Free stream speed of sound
Hf = Heating value of fuel
TIdealMax = Ideal maximum thrust
γ = Specific heat ratio
T4 = Combustor exit temperature
T3 = Compressor exit temperature
R a m j e t ( p 3 / p
2 = 1 )
Tactical Missile Ramjet Propulsion Alternatives Tactical Missile Ramjet Propulsion Alternatives
Liquid Fuel Ramjet
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Rocket Boost Inboard Profile
Ramjet Sustain Inboard Profi le
Liquid Fuel Ramjet
Solid Fuel Ramjet
Solid Ducted Rocket
Boost
Sustain
Boost
Sustain
Note:Booster PropellantFuel
High Specific Impulse for a Ramjet Occurs Using
High Heating Value Fuel at Mach 3 to 4
High Specific Impulse for a Ramjet Occurs Using
High Heating Value Fuel at Mach 3 to 4
( ISP
)Ideal
gc
cp
T0
/ ( a0
Hf
) = { M0
{{( T4
/ T0
) / { 1 + [( γ0
- 1 ) / 2 ] M0
2 }}1/2 - 1 } / {{ 1 + [( γ0
- 1 ) / 2 ] M0
2 } {( T4
/ T0
) / {1 + [( 0 - 1 ) / 2 ] M0
2 }} – 1 }
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0
0.2
0.4
0.6
0 1 2 3 4 5M0, Free Stream Mach Number
( I S P ) I d e a l ( g c
) ( c p ) ( T 0 ) / [ ( a 0 ) ( H f ) ] ,
N o n d i m e n s i o n a l I d e a l S p e c i f i c I m
p u l s e
T4 / T0 = 3 T4 / T0 = 5
T4 / T0 = 10 T4 / T0 = 15
p1 + [( γ0 1 ) / 2 ] M0 }} 1 }
Assumptions: Ideal ramjet , isentropic inlet and nozzle, low subsonic and constant pressure combustion, ex it pressure = freestream pressure, φ ≤ 1
Example for Ramjet Baseline:
M = 3.5, h = 60k ft ( T0 = 390 R, a0 = 968 ft / s ),RJ-5 fuel ( H
f
= 14,525 BTU / lbm ), T4
= 4,000 R,cp = 0.302 BTU / lbm / R, γ0 = 1.4
Calculate ( ISP )Ideal gc cp T0 / ( a0 Hf ) = { 3.5 {{(4000 / 390 ) / { 1 + [( 1.4 - 1 ) / 2 ] 3.52 }} 1/2 - 1 } / {{1 + [( 1.4 - 1 ) / 2 ] 3.52 } { ( 4000 / 390 ) / { 1 + [(1.4 - 1 ) / 2 ] 3.52 }} – 1 } = 0.372
( ISP )Ideal = 0.372 ( 968 ) ( 14525 ) / [ 32.2 ( 0.302 ) (
390 ) = 1387 s
Note:
gc = Gravitational constant = 32.2
cp = Specific heat at constant pressure
T0 = Free stream temperature
a0 = Free stream speed of sound
Hf = Heating value of fuel
γ = Specific heat ratio
T4 = Combustor exit temperature
Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974
High Thrust for a Ramjet Occurs from Mach 3 to
5 with High Combustion Temperature
High Thrust for a Ramjet Occurs from Mach 3 to
5 with High Combustion Temperature
TIdeal / ( p0 A0 ) = 0 M0
2
{{[ T4 / T0 ] / { 1 + [( 0 - 1 ) / 2 ] M0
2
}}1/2
- 1 }
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0
5
10
15
20
25
0 1 2 3 4 5M0, Free Stream Mach Number
T / [ P H I ( p 0 )
( A 0 ) ] , N o n d i m i m e n s i o n a l
T h r u s t
T4 / T0 = 3 T4 / T0 = 5
T4 / T0 = 10 T4 / T0 = 15
T / ( φ p A ) γ M {{[ T / T ] / { 1 [( γ 1 ) / 2 ] M }} 1 } Assumptions: Ideal ramjet, isentropic inlet and nozzle, low subsonic and constant pressurecombustion, exit pressure = free stream pressure, φ ≤ 1
Note: T4 and T0 in R Example for Ramjet Baseline:
M0 = 3.5, α = 0 deg, h = 60k ft ( T0 = 390 R, p0 =
1.047 psi ), T4 = 4,000 R, ( f / a ) = 0.055, φ =0.82, A0 = 114 in2, γ0 = 1.4
TIdeal / ( φ p0 A0 ) = 1.4 ( 3.5 )2 {{[ 4000 / 390 ] / { 1+ [( 1.4 – 1 ) / 2 ] ( 3.5 )2 }} 1/2 – 1 } = 12.43
TIdeal = 12.43 ( 0.82 ) ( 1.047 ) ( 114 ) = 1216 lb
Note:
( T )Ideal = Ideal thrus t
p0 = Free stream static pressure
A0 = Free stream flow area into inlet
γ0 = Free stream specific heat ratio
M0 = Free stream Mach number T4 = Combustor exit temperature
T0 = Free stream temperature
φ = Equivalence ratio = fuel-to-air ratio /stochiometric fuel-to-air ratio
Source: Ashley, H., Engineering Analysis of Flight Vehicles, Dover Publications, Inc., New York, 1974
Ramjet Combustor Temperature Increases with
Mach Number and Fuel Flow
Ramjet Combustor Temperature Increases with
Mach Number and Fuel Flow
T4 T0 { 1 + [( 0 - 1 ) / 2 ] M02
} + ( Hf / cp ) ( f / a )
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0
2000
4000
6000
0 1 2 3 4 5
M0, Free Stream Mach Number
T 4 , C o m b u s t o r E x
i t T e m p e r a t u r e f o r
R J - 5
F u e l , R a n k i n e
f / a = 0.01 f / a = 0.03 f / a = 0.05 f / a = 0.067
Example:
•M0 = 3.5
•h = 60k ft ( T0 = 390 R )
•RJ-5 fuel ( Hf = 14,525 BTU / lb / R )
•f / a = 0.055
•γ0 = 1.4
•cp = 0.122 T0.109 BTU / lbm / R.
Note: cp ≈ 0.302 +/- 5% if 2500 R < T < 5000 R
•Then T4 = 390 { 1 + [( 1.4 – 1 ) / 2 ] ( 3.5 )2
} +[( 14525 ) / ( 0.302 )] 0.055 = 3,991 R
Note: ( f / a )φ = 1
≈ 0.067 for stochiometric combustion of li quid hydrocarbon fuel, e.g., RJ-5.
T ≈ T { 1 [( γ 1 ) / 2 ] M } ( H / c ) ( f / a ) Assumptions: Low subsonic combust ion. No heat t ransfer through in let ( isentropicflow ). φ ≤ 1.
T4 = combustor exit temperature in Rankine, T0 = free stream temperature in Rankine,γ = specific heat ratio, M0 = free stream Mach number, Hf = heating value of fuel, cp =specific heat at constant pressure, f / a = fuel-to-air ratio.
Ramjet Combustor Entrance Mach Number
Should Be Low, to Avoid Thermal Choking
Ramjet Combustor Entrance Mach Number
Should Be Low, to Avoid Thermal Choking ( M
3
)TC
= {{ - b + [ b2 – 4 γ3
2 ]1/2 } / ( 2 γ3
2 )}1/2
b = 2 + ( T / T )( 1 + )2 / {( 1 + 0 2 M 2 )[ 1 + ( – 1 ) / 2 ]}
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0
0.1
0.2
0.3
0.4
0 1 2 3 4 5
M0, Free Stream Mach Number
( M 3 ) T C ,
C o m
b u s t o r E n t r a n c e M
a c h
N u m b e r w i t h T h e r m a l C h o k i n
g
T4t / T0 = 3 T4t / T0 = 5
T4t / T0 = 10 T4t / T0 = 15
b = 2 γ3 + ( T4t/ T0 )( 1 + γ4 )2 / {( 1 + 0.2 M0
2 )[ 1 + ( γ4 – 1 ) / 2 ]}
Assumptions: Constant area combust ion, [( γ 3 – 1 ) / 2 ] M32 << 1, isentropic inlet
Example:
M0 = 2, h = 60k ft ( T0 = 390 R ), T4t= 4,000 R, γ0 = 1.4
γ4 = 1.29 + 0.16 e-0.0007 ( 4000 ) = 1.300
T0t= ( 1 + 0.2 M0
2 ) T0 = 702 R
γ 3 = 1.29 + 0.16 e-0.0007 ( 702 ) = 1.388
b = 2 ( 1.388 ) + ( 4000 / 390 )( 1 + 1.300 )2 / {( 1 + 0.2( 22 )[ 1 + ( 1.300 – 1 ) / 2 ]} = - 24.211
( M3 )TC = {{ 24.211 + [( -24.211 )2 – 4 ( 1.3882 )]1/2 } / [ 2 ( 1.3882 )]}1/2 = 0.204
Note:
( M3 )TC = Combustor entrance Mach number withthermal choking ( M4 = 1 )
γ3 = Specific heat ratio at combustor entranceM0 = Free stream Mach number
T4t= Combustor exit total temperature
T0 = Free stream static temperature
γ4 = Specific heat ratio in combust ion
A Ramjet Combustor with a Low Entrance Mach
Number Requires a Small Inlet Throat Area
A Ramjet Combustor with a Low Entrance Mach
Number Requires a Small Inlet Throat Area
AIT / A3 = [( + 1 ) / 2 ]( γ + 1 ) / [ 2 ( γ - 1 )] M3 {[ 1 + ( - 1 ) / 2 ] M32 }-( γ + 1 ) / [ 2 ( γ - 1 )] = ( 216 / 215 ) M3 ( 1 + M32 / 5 )-3
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0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
( A )IT / A3, Inlet Throat Area to Combusto r Area Ratio
M 3 ,
C o m b u s t o r E n
t r a n c e M a c h N u m b e
r
[( γ ) ] {[ ( γ ) ] } ( ) ( ) Assumptions: Isentropic in let , MIT = 1, γ = 1.4
Note:
AIT = Inlet throat area
A3 = Combustor entrance areaM3 = Combustor entrance Mach number
γ = Specific heat ratio
Example:
Ramjet Baseline
AIT = 41.9 in2
A3 = 287 in2
AIT / A3 = 41.9 / 287 = 0.1459
Assume sonic flow ( M = 1 ) at AIT
M3 = 0.085M3 = 0.085 < ( M3 )TC = 0.204
Typical Ramjet Has Nearly Constant Pressure
Combustion
Typical Ramjet Has Nearly Constant Pressure
Combustion
Assume Rayleigh Flow, with Heat Addition at
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y g , Constant Area
Negligible Friction
Pressure Loss in Combustor is Given by p
4
/ p3
= ( 1 + γ3
M3
2 ) / ( 1 + γ4
M4
2 )
Mach Number Increase in Combustor Is Given by T4t
/ T0 = [( 1 + γ3 M32 ) / ( 1 + γ4 M4
2 )]2 ( M4 / M3 )2 { 1 + [( γ4 – 1 ) / 2 ] M42 } / { 1 + [( γ3 – 1 ) / 2 ] M3
2 }
From Prior Example
M0 = 2, h = 60k ft ( T0 = 390 R ), T4t= 4,000 R, γ0 = 1.4, γ4 = 1.300, and γ 3 = 1.388
Assume Ramjet Baseline with Sonic Inlet Throat
AIT / A3 = 41.9 / 287 = 0.1459 ⇒ M3 = 0.085
Solving Above Equations
M4
= 0.304
p4 / p3 = 0.902
Assumption of Nearly Constant Pressure Combustion Is Reasonably Accurate
10% error
Minimum Length for the Combustor Is a
Function of Combustion Velocity
Minimum Length for the Combustor Is a
Function of Combustion Velocity
( l ) = t V
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0.1
1
10
100 1000 10000
Vcomb, Combustion Velocity, ft / s
M i n i m u m C
o m b u s t o r L e n g
t h ,
f t
tcomb = 0.001 s
tcomb = 0.002 s
tcomb = 0.004 sExample for tcomb = 0.002 s and
Subsonic Combustion Ramjet:
•Vcomb = 200 ft / s
•( lcomb
)min
= 0.002 ( 200 ) = 0.4 ft
Example for tcomb = 0.002 s andScramjet:
•Vcomb = 3,000 ft / s
•( lcomb )min = 0.002 ( 3000 ) = 6.0 ft
( lcomb )min = tcomb Vcomb
Ramjet Engine / Booster Integration Options Ramjet Engine / Booster Integration Options
I t l R k t R j t ( IRR )
FuelBoost PropellantLow Cruise Drag ( Modern Ramjets )
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Integral-Rocket Ramjet ( IRR ) Af t Drop-of f Booster
Podded Drop-off Booster Forward Booster
Podded Ramjet
Podded Ramjet, Aft Drop-off Booster
Podded IRR
p
Source: Kinroth, G.D. and Anderson, W.R., “ RamjetDesign Handbook,” CPIA Pub. 319, June 1980
g ( j )
High Cruise Drag
Ramjet Engine / Booster Integration Trades Ramjet Engine / Booster Integration Trades
a g g l i t y
l i t ySelection Factors
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Superior Above Average Average Below average
L e n g t h
D i a m e t e r
W e i g h t
E j e c t a b l e s
C r u i s e D r a
C a r r y D r a g
C o s t
C y c l e
C o m p a t i b i
I n l e t
C o m p a t i b i
Source: Kinroth , G.D. and Anderson, W.R., “ Ramjet Design Handbook,” CPIA Pub. 319, June 1980
Integral Rocket – Ramjet ( IRR )
Af t Booster ( Drop-off )
Forward Booster
Podded Booster ( Drop-off )
Podded Ramjet
Podded IRR
Podded Ramjet Af t Booster ( Drop-off )
–
–
–
–
–
– –
–
– – – –
–
–
–
–
–
–
Ramjets with Internal Boosters and No Wings
Have Low Drag
Ramjets with Internal Boosters and No Wings
Have Low Drag
1 2
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1.2
0.8
0.4
0
2 3 4 5
M, Mach Number
CD0= DO / ( q SREF ), Zero-Lift Drag
Coefficient
Note:Nose Fineness Ratio ≥ 2.25Nose Bluntness Ratio ≤ 0.20
• IRR
• Af t Drop Off Booster
• Forward Booster
• Podded Drop Off Booster
With Wings
Without Wings• IRR
• Af t Drop-of f Booster
• Forward Booster
• Podded Drop-off Booster
• Podded Ramjet
• Podded IRR• Podded Ramjet, Aft Drop
Off Booster
Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980
CD0
Sketch
Ramjet Inlet Options Ramjet Inlet Options
PlacementType Inlet
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Nose
Source: Kinroth, G.D. and Anderson, W.R., “ Ramjet Design Handbook,” CPIA Pub. 319, June 1980.
Nose-full axisymmetric
Af t-crucifo rm ( four ) two d imensional
Af t unders ide-belly mounted two dimensional
Af t unders ide-ful l ax isymmetri c
Af t-twin cheek-mounted two dimensional
Cruciform Two-dimensional
Underslung Two-dimensional
Underslung Axisymmetric
Twin Two-dimensional
Under Wing Axisymmetric
Af t Cruciform Axisymmetric
Forward Cruciform Axisymmetric
Chin
In planar wing compression field-twin axisymmetric
Af t-c ruci form ( four ) axisymmetric
Forward in nose compression field-cruciform ( four )axisymmetric
Forward underside in nose compression field-partial axisymmetric
Ramjet Inlet Concept Trades Ramjet Inlet Concept Trades
e t y n g
s t d d t y
Selection Factorse y
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Superior Above Average Average Below average
Source: Kinroth, G.D. and Anderson, W.R., “Ramjet Design Handbook,” CPIA Pub. 319, June 1980
–
C a r r i a g e
E n v e l o p e
A l p h a
C a p a b i l i t
W e i g h t
D r a g
W a r h e a d
S h r o u d i n
i n l e t C o s
P r e f e r r e d
S t e e r i n g
P r e f e r r e d
C o n t r o l
P r i m e
M i s s i o n
S u i t a b i l i t
Note:BTT = Bank to TurnSTT = Skid to TurnW = Wing C = CanardT = Tail
STT W, C ATS, STA
BTT T ATS, ATA, STA – – STT T ATS, ATA, STA
STT T ATS
BTT T ATS, ATA, STA –
BTT T ATS, ATA, STA
– BTT T ATS
– BTT T ATS, ATA, STA
STT T ATS
Type Inlet P r e s s u r e
R e c o v e r y
–
–
–
–
United Kingdom
Current Supersonic Air-breathing Missiles Have Either a Nose Inlet or Axisymmetric Aft Inlets
Current Supersonic Air-breathing Missiles Have Either a Nose Inlet or Axisymmetric Aft Inlets
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Sea Dart GWS-30
France
ASMP ANS
Russia
AS-17 / Kh-31 Kh-41 SS-N-22 / 3M80
SA-6 SS-N-19 SS-N-26
China
C-101 C-301
Taiwan
Hsiung Feng III
India
BrahMos
• Af t in lets have lower inlet volume and do not degrade lethali ty of fo rward located warhead.
• Nose Inlet may have higher f low capture, pressure recovery, smaller carriage envelope, and lower drag.
Shock on Inlet Cowl Lip Prevents Spillage Shock on Inlet Cowl Lip Prevents Spillage
Inlet w/o External CompressionInlet Swallows 100% of the Free
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Stream Flow
External Compression Required for Efficient Pressure Recovery if MachNumber > 2 and Inlet Start at LowSupersonic Mach number
External Compression Inlet ( wi thSpillage )
Shocks Converge Outside Inlet Lip( Results in Spillage Air )
External Compression Inlet ( w/o
Spillage )Inlet Swallows 100% of the FreeStream Flow
Shocks Converge at Inlet Lip ( InletCaptures Maximum Free Stream
Flow )
Shocks
Spillage
Shocks
Shock Wave Angle Increases with Deflection
Angle and Decreases with Mach Number
Shock Wave Angle Increases with Deflection
Angle and Decreases with Mach Number tan ( α + δ ) = 2 cot θ
2D
( M2 sin2 θ2D
– 1 ) / [ 2 + M2 ( γ + 1 – 2 sin2 θ2D
)] , for 2D flow, perfect gas
Note: θ2D = 2D shock wave angle, M = Mach number, α = angle of attack, δ = body deflection angle, γ = specific heatratio 0 81
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0
10
20
30
40
50
0 5 10 15 20
Alpha + Delta, Deflectio n Angle, Degrees
T h e t a , 2
D S h o c
k W a v e A n g l e @ G a m m a =
1 . 4 , D e g r e e s
Mach 2 ( Deltamax = 23 deg ) Mach 3 ( Deltamax = 34 deg )
Mach 5 ( Deltamax = 41 deg )
ratio, θconical ≈ 0.81 θ2D
Example for Ramjet Baseline:
δ = 17.7 deg, M = 3.5, α = 0 deg, γ = 1.4
⇒ θ2D = 32 deg
θconical ≈ 0.81 θ2D = 0.81 ( 32 ) = 26 deg
δ
θ
α
Approximate est imate of θ:
θ2D ≈ μ + α + δ = sin-1
( 1 / M ) + α + δθconical ≈ 0.81 θ2D = 0.81 [ sin-1 ( 1 / M ) +α + δ ]
Capture Efficiency of an Inlet Increases with Mach
Number
Capture Efficiency of an Inlet Increases with Mach
Number ( A0 / Ac )conical = ( h / l ) ( 1 + δ M + αM ) / [( 1 – 0.23δM + αM )( δ + h / l )] , conical nose with forward inlet
( A0 / Ac )2D = ( h / l ) ( 1 + δ M + αM ) / [( 1 + αM )( δ + h / l )] , 2D nose with forward in let
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0
0.2
0.4
0.6
0.8
1
0 1 2 3 4 5
M, Mach Numb er
A 0 / A c , B a s e l i n e R a m j e t I n l e t C a p t u r e
E f
f i c i e n c y
Alpha = 0 Deg Alpha = 10 Deg
Ac
A0 s tream l ine s t r e a m l i n e
oblique shock
h inlet
nose body
δ
s t r e a m l i n e s tream l ine
Note: A0 / Ac ≤ 1, AC = inlet capture area, A0 = free stream flow area, δ = defection angle in rad, h = inlet height, l =distance from nose tip to inlet
α
Example for baseline ramjet ( conicalnose )
h = 3 in
l = 23.5 in
h / l = 0.1277
AC
= 114 in2
δ = 17.7 deg ( 0.3089 rad )
M = 3.5, α = 0 deg
A0 / Ac = 0.81 ⇒ A0 = 92 in2
Spillage = Ac - A0 = 114 - 92 = 22 in2
Isentropic Compression Allows Inlet Start at
Lower Mach Number
Isentropic Compression Allows Inlet Start at
Lower Mach Number AIT / A0 = 1.728 ( MIE )start [ 1 + 0.2 ( MIE )start
2 )-3, Assumptions: 2-D in let , Isentropic f low through in let ( n = ∞ ), γ = 1.4
AIT / A0 = ( MIE )start {[ 0.4 ( MIE )start2 + 2 ] / [ 2.4 ( MIE )start
2 ]3.5 }{[2.8 ( MIE )start2 – 0.4 ] / 2.4 }2.5 {[ 1.2 / ( 1 + 0.2 (
MIE ) t t2 ]}3 Assumptions: 2-D inlet s ingle normal shock ( n = 1 ) = 1 4
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0
1
2
3
4
0 0.2 0.4 0.6 0.8 1
AIT / A0
( M ) I E , I n
l e t E n t r a n c e S t a r t M a c h
N
u m b e r
Inlet Start for Isentro pic Compression
Inlet Start for Single Normal Shock
MIE )start ]} , Assumptions: 2 D inlet, s ingle normal shock ( n = 1 ), γ = 1.4
Note: AIT = inlet throat area, A0 = free stream flow area, ( MIE )start = inlet entrance start Mach number, γ = specific heatratio, n = number of shocks
Example for ramjet baseline
AIT = 0.29 ft2
Ac = 114 in2 = 0.79 ft2 ⇒ AIT / Ac = 0.367
Process:
1. Assume ( MIE )start
2. Compute capture efficiency AIT / A0
3. Compute ( MIE )start and compare withassumed ( MIE )start
4. Iterate unti l convergence
Limit for isentropic compression
- From Prior Figure, A0 / Ac = 0.53- Compute AIT / A0 = ( A IT / Ac ) / ( A0 / Ac ) =
0.367 / 0.53 = 0.69 ⇒ ( MIE )start = 1.8
Ramjet baseline has mixed compressionwith n = 5. Actual inlet start Machnumber is ( MIE )start > 1.8
n = 1n = ∞
Forebody Shock Compression Reduces the Inlet
Entrance Mach Number
Forebody Shock Compression Reduces the Inlet
Entrance Mach Number ( MIE )2D = {{ 36 M0
4 sin2 θ2D - 5 [ M02 sin2 θ2D - 1 ][ 7 M0
2 sin2 θ2D + 5 ]} / {[ 7 M02 sin2 θ2D - 1 ] [ M0
2 sin2 θ2D + 5 ]}}1/2
tan ( α + δ ) = 2 cot θ2D ( M02 sin2 θ2D – 1 ) / [ 2 + M0
2 ( 2.4 – 2 sin2 θ2D )]
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0
1
2
3
4
0 10 20 30 40
Alpha + Delta, Local Angle of At tack at Inlet Entrance, Deg
( M ) I E ,
I n l e t E n t r a n c e M a c h N u m b e r
M0 = 2 M0 = 3 M0 = 5
Assumptions: 2D flow, perfect gas, γ = specific heat ratio = 1.4
Note: MIEt= inlet entrance Mach number, M0 = free stream Mach number, θ = oblique shock angle, α = angle of attack, δ = bodydeflection angle
Example for ramjet baseline
δ = 17.7 deg
( MIE )start = 1.8 ( from prior example )
Compute M0 = 2.55
Note: Ramjet baseline forebody isconical, not 2D
Optimum Forebody Deflection Angle(s) for Best
Pressure Recovery Increases with Mach Number
Optimum Forebody Deflection Angle(s) for Best
Pressure Recovery Increases with Mach Number
First External Shock
Second External Shock
Note: δTotal = Total deflection angle,δ1 = 1st deflection angle, δ2 = 2nd
deflection, δ3 = 3rd deflection.
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0
20
40
60
0 1 2 3 4
M0, Free Stream Mach Number
O p t i m u m T o t a l D e
f l e c t i o n A n g l e ,
D e g
n = 1 n = 2 n = 3 n = 4 Isentropic Compression
δ1
Second External Shock
δ2
3
Optimum deflection angle providesequal loss in total pressure acrosseach shock wave.
Optimum deflection angles arenearly equal for M > 4.
Reference: “ Technical Aerodynamics Manual,” North American Rockwell Corporation , DTIC AD 723823, June 1970.
Example: Optimum forebody deflection angles for double wedge ( n = 3 ) at Mach 2: δ1 = 10.4 deg, δ2= 11.2 deg ⇒ δtotal = 10.4 + 11.2 = 21.6 deg
δTotal
10.4, 11.2
15.0, 18.816.1, 22.1
7.6, 8.2, 8.2
11.1, 13.0, 15.5
12.1, 15.2, 19.4
Oblique Shocks Prior to the Inlet Normal Shock
Are Required to Satisfy MIL-E-5008B
Oblique Shocks Prior to the Inlet Normal Shock
Are Required to Satisfy MIL-E-5008B
1
e ( l Sh k )
MIL-E-5008B Requirement: ptInlet / pt0 = 1 – 0.075 ( M – 1 )1.35
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0.01
0.1
0 1 2 3 4 5
M, Mach Number
P t I n l e t / p t 0 ,
I n l e t T o t a
l P r e s s u r e
R a t i o
n = 1 ( Normal Shock )
n = 2 ( 1 Optimum ObliqueShock + Normal Shock )
n = 3 ( 2 Opt ObliqueShocks + Normal Shock )
n = 4 ( 3 Opt ObliqueShocks + Normal Shock
Ideal Isentropic Inlet
MIL-E-5008B
Source for Optimum 2D Shocks: Oswatitsch, K.L., “Pressure Recovery for Missiles with Reaction Propulsion at HighSupersonic Speeds”, NACA TM - 1140, 1947.
Example: MIL-E-5008B requirement for Mach 3.5 ( ptInlet/ p t0
= ηinlet = 0.74 ) can be satisf ied only if there are morethan three oblique shocks prior to inlet normal shock.
Note: 2D flow assumed
ptInlet= Inlet total pressure
pt0 = Free stream total pressure
High Density Fuels Provide Higher Volumetric Performance but Have Higher Observables
High Density Fuels Provide Higher Volumetric Performance but Have Higher Observables
Type FuelVolumetricPerformance,BTU / in3
LowObservables
Density,lb / in3
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Turbine ( JP-4, JP-5, JP-7, JP-8, JP-10 ) ~ 0.028 559
Liquid Ramjet ( RJ-4, RJ-5, RJ-6, RJ-7 ) ~ 0.040 581
HTPB ~ 0.034 606
Slurry ( 40% JP-10 / 60% carbon ) ~ 0.049 801
Solid Carbon ( graphite ) ~ 0.075 1132
Slurry ( 40% JP-10 / 60% aluminum ) ~ 0.072 866
Slurry ( 40% JP-10 / 60% boron carbide ) ~ 0.050 1191
Solid Mg ~ 0.068 1200
Solid Al ~ 0.101 1300
Solid Boron ~ 0.082 2040
–
yp BTU / in3
Superior Above average Average Below average
Observables
–
–
–
–
–
lb / in
–
Ducted Rocket Design Implications Ducted Rocket Design Implications
Excess Fuel from Gas Generator ~ 30 % ⇒ Behaves more like a rocket ( higher burn rate, higher burn
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( g gtemperature, lower ISP )
~ 70 % ⇒ Behaves more like a ramjet ( higher ISP, lower burn rate, lower burn temperature )
Choice of Fuel Metal ( e.g., B, Al, Mg ) ⇒ Higher ISP, higher density, deposits, higher
observables
Carbon based ( e.g., C, HTPB ) ⇒ Lower observables, higher reliability,
lower ISP
Choice of Oxidizer AP ⇒ Higher burn rate, lower hazard, HCl contrail
Min Smoke ( e.g., HMX, RDX ) ⇒ Lower Observables, lower heating value,lower burn rate, hazardous
Thrust Magnitude Control Approaches Pintle or valve in gas generator throat
Retractable wires in grain
High Propellant Fraction Increases Burnout Velocity
High Propellant Fraction Increases Burnout Velocity
5000
Assumption: T >> D, T >> W sin γ, γ = constΔV = -gc Isp ln (1 - Wp / Wi)
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0
4000
3000
2000
1000
0 0.1 0.2 0.3 0.4 0.5
Example: Rocket BaselineWi,boost = WL = 500 lb, Wp, boost = 84.8 lbISP, boost = 250 sWP, boost / Wi = 84.8 / 500 = 0.1696
ΔV = -32.2 ( 250 ) ln ( 1 - 0.1696 ) = 1496 ft / s
ΔV, MissileIncremental
Burnout Velocity,
ft / s
WP / Wi, Propellant Weight / Initial Missi le Weight
Isp = 250 s
Isp = 200 s
High Specific Impulse Requires High Chamber
Pressure and Optimum Nozzle Expansion
High Specific Impulse Requires High Chamber
Pressure and Optimum Nozzle Expansion
ISP = cd {{[ 2 γ2 / ( γ - 1 )] [ 2 / ( γ + 1 )] ( γ + 1 ) / ( γ - 1 ) [ 1 – ( pe / pc ) ( γ - 1 ) / γ ]}1/2 + ( pe / pc ) ε - ( p0 / pc ) ε } c* / gc
T = w.p ISP = ( gc / c* ) pc At ISP
= {[ 2 / ( + 1 )]1 / ( γ - 1 ) [( -1 ) / ( + 1 )]1/2 } / {( p / p )1 / γ [ 1 - ( p / p ) ( γ - 1 ) / γ ]1/2 }
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200
250
300
0 10 20 30Nozzle Expansion Ratio
I s p ,
S p e c i f i c I m p
u l s e o f R o c k e t B a s e l i n e , s
pc = 300 psi pc = 1000 psi
pc = 2000 psi pc = 3000 psi
Note:ε = nozzle expansion ratiope = exit pressure
pc = chamber pressurep0 = atmospheric pressurew.
P = propellant weight f low rate At = nozzle throat area ( minimum, sonic, choked )γ = specific heat ratio = 1.18 in figurecd = discharge coefficient = 0.96 in figure
c* = characterist ic veloc ity = 5,200 ft / s in f igureh = 20k ft, p0 = 6.75 psi in figure
Example for Rocket Baseline:
ε = Ae / A t = 6.2 ⇒ pe / pc = 0.02488, A t = 1.81 in2
( pc )boost = 1769 psi, pe = 44 psi , ( ISP )boost = 257 s
( ISP )ε = 6.2 / ( ISP )ε = 1 = 257 / 200 = 1.29( T )boost = ( 32.2 / 5200 ) ( 1769 ) (1.81 )( 257 ) = 5096 lb
( pc )sustain = 301 psi , pe = 7.49 psi , ( ISP )sustain = 239 s
( ISP )ε = 6.2 / ( ISP )ε = 1 = 240 / 200 = 1.20
( T )sustain = ( 32.2 / 5200 ) ( 301 ) (1.81 )( 240 ) = 810 lb
ε {[ 2 / ( γ + 1 )] ( ) [( γ 1 ) / ( γ + 1 )] } / {( pe / pc ) [ 1 ( pe / pc ) ( ) ] }
High Propellant Weight Flow Rate Requires High
Chamber Pressure and Large Nozzle Throat
High Propellant Weight Flow Rate Requires High
Chamber Pressure and Large Nozzle Throat
100000
w.
p = gc pc At / c*
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100
1000
10000
100000
1 10 100
Propellant Weight Flow Rate, lb / s
( p c ) A t , C h a m
b e r P r e s s u r e x N o z z l e
T h
r o a t A r e a ,
l b
c* = 4800 ft / s
c* = 5200 ft / s
c* = 5600 ft / s
Rocket Baseline A t for Boost:
c* = 5200 ft / s
( pc )boost = 1,769 psi
w.
p = Wp / tb = 84.8 / 3.69 = 23.0 lb / s
pc At = c* w .p / gc = 5200 ( 23.0 ) / 32.2= 3,714 lb
At = 3714 / 1769 = 2.10 in2
Note: At = nozzle throat area, c* = characteristic velocity, w.
p = propellant weight flow rate, gc = gravitational constant,p
c
= chamber pressure
High Chamber Pressure Requires Large
Propellant Burn Area and Small Nozzle Throat
High Chamber Pressure Requires Large Propellant Burn Area and Small Nozzle Throat
600
a ,
i n 2
Ab
= gc
pc A
t/ ( ρc*r )
r = r pc=1000 psi ( pc / 1000 )n
Example Ab for Rocket
Baseline: At= 1.81 in2
= 0 065 lb / in3
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0
200
400
0 500 1000 1500 2000Pc, Rocket Baseline Motor Chamber Pressure, psi
A b ,
R o c k e t B a s e l i n e P r o p e l l a n t B u r n A r e a ρ = 0.065 lb / in3
n = 0.3
r pc = 1000 psi = 0.5 in / s
c* = 5,200 ft / s
Tatmosphere = 70 °F
For sustain ( pc = 301 psi ):
•r = 0.5 ( 301 / 1000 )0.3 = 0.35in / s
• Ab = 149 in2
For boost ( pc = 1,769 psi )
•r = 0.59 in / s
• Ab = 514 in2
Note: Ab = propellant burn area, gc = gravitation constant, At = nozzle throat area,ρ = density of propellant, c* = characteristic velocity,r = propellant burn rate, r pc=1000 psi = propellant burn rate at pc = 1,000 psi, pc = chamber pressure, n = burn rate exponent
Conceptual Design Sizing Process for a Rocket
Motor
Conceptual Design Sizing Process for a Rocket
Motor 1. Define Altitude and Required Thrust-time
New Value ( s )
2. Assume Propellant ( Characterist ic Velocity, Nominal) C
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Yes
4. Compute Propellant Weight Flow Rate and Propellant Used
No
NoYes
5. Determine Diameter and Length to Satisfy wp and Ae
OK?
OK?
OK?
Yes
New Value ( s )
No
Burn Rate, Burn Rate Exponent ), Chamber Pressure, Burn Area, and Nozzle Geometry ( Expansion Ratio, Throat Area )
3. Compute ISP andThrust
Example Web Cross Section / Volumetric Loading
~ 82% ~95% ~90%
Conventional Solid Rocket Thrust-Time Design Alternatives with Propellant Cross-Section
Conventional Solid Rocket Thrust-Time Design Alternatives with Propellant Cross-Section
l b )
Constant
Example Mission•≈ Cruise
Thrust Profile
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82% 95% 90%
End Burner Radial Slotted Tube~ 79%
~ 87%
~ 85%
~ 85%
T h r u s t (
Burning Time ( s )
Thrust
RegressiveThrust
ProgressiveThrust
Boost-Sustain
Boost-Sustain-Boost
Burning Time ( s )
Burning Time ( s )
Burning Time ( s )
Burning Time ( s )
T h r u s t ( l b
)
T h r u s t ( l b )
T h r u s t ( l b )
T h r u s t ( l b )
Medium Burn Rate Propellant
High Burn Rate PropellantNote: High thrus t and chamber pressure require large surface burn area.
•Dive at ≈constantdynamicpressure
•Climb at ≈constant
dynamicpressure
•Fast launch –≈ cruise
•Fast launch –≈ cruise – highspeed terminal
Production of Star Web Propellant.Photo Courtesy of BAE
Conventional Rocket Has Fixed Burn while Thrust Magnitude Control Can Vary Burn Interval
Conventional Rocket Has Fixed Burn while Thrust Magnitude Control Can Vary Burn Interval
Conventional Fixed Burn Interval ( Boost )
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End Burning
Conventional Fixed Burn Interval ( Boost – Sustain )
Radial BoostEnd Burning Sustain
Simultaneous Burning
1st Pulse: Radial Boost2nd Pulse: End Burning Sustain
Separate Burning ( Pulsed Motor )
1st Pulse: Radial Boost2nd Pulse: Radial Sustain / Boost
Separate Burning ( Pulsed Motor )
Concentric Radial BurningHigh Burn Rate Boost
Low Burn Rate Sustain
Radial Burning
Boost Propellant
Sustain Propellant
Pulse Motor TMC Variable Burn Interval ( Boost – Coast – Boost / Sustain - Coast )
Note: Each pulse increases motor cost approximately 40%.
Tactical Rocket Motor Thrust Magnitude Control
Alternatives
Tactical Rocket Motor Thrust Magnitude Control
Alternatives
Solid Pulse Motor
☺ High ISP
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SP
Limited Pulses
Solid Pintle Motor ☺ Continuously Select Up to
40:1 Variation in Thrust
☺ Reduce MEOP on Hot Day
Good ISP Only If Burn RateExponent n → 1
Bi-propellant Gel Motor
☺ High ISP
☺ Duty Cycle Thrust
☺ Insensitive Munition
Lower Max Thrust
Toxicity
Thermal or Mechanical Barriers
Pintle
Pressurization Gelled Oxidizer Gelled Fuel Combust ionChamber
Solid Rocket Propellant Alternatives Solid Rocket Propellant Alternatives
B
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250 - 260 0.062 0.1 - 1.5
Superior Above Average Average Below Average
• Min Smoke . No Al fuel or AP
oxidizer. Either Composite with
Nitramine Oxidizer ( CL-20, ADN,
HMX, RDX ) or Double Base. Very low
contrail (H2O).
• Reduced Smoke . No Al ( binder
fuel ). AP oxidizer. Low contrail ( HCl ).
• High Smoke . Al fuel. AP oxidizer.High smoke ( Al2O3).
–
ISP,Specific
Impulse, s
ρ,Density,lb / in3
BurnRate @
1,000 psi,in / s Safety Observables
– – –
–
Type
220 - 255 0.055 - 0.062 0.25 - 2.0
260 - 265 0.065 0.1 - 3.0
Steel is the Most Common Motor Case Material Steel is the Most Common Motor Case Material
VolumetricEffi i Weight
Airframe /Launcher
C tTypeTemper-
t IM
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Superior Above Average Average Below Average
Steel
Aluminum
Strip Steel /Epoxy Laminate
Composite
Titanium
–
Efficiency Weight Attachment Cost
–
Type
–
–
– –
– –
ature
–
IM
Heat Transfer Drives Rocket Nozzle Materials,
Weight, and Cost
Heat Transfer Drives Rocket Nozzle Materials,Weight, and Cost
HousingThroat
Exit Cone
Dome Closeout
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Throat
Rocket Nozzle Element High Heating ( High Chamber Pressure or Long Burn )⇒ High Cost / Heavy Nozzle
Low Heating ( Low Chamber Pressure or Short Burn ) ⇒ Low Cost / Light Weight Nozzle
♦ Housing Material Al ternat ives
♦ Steel ♦ Cellulose / Phenolic♦
Aluminum
♦ Throat Material Al ternatives
♦ Tungsten Insert♦ Rhenium Insert♦ Molybdenum Insert
♦ Cellulose / Phenolic Insert♦ Silica / Phenolic Insert♦ Graphite Insert♦ Carbon – Carbon Insert
♦ Exit Cone, Dome Closeout,and Blast Tube Material Al ternatives
♦ Silica / Phenol ic Insert♦ Graphite / Phenolic Insert♦ Silicone Elastomer Insert
♦ No Insert♦ Glass / Phenolic Insert
Summary of Propulsion Summary of Propulsion
Emphasis Turbojet propulsion
Ramjet propulsion
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Ramjet propulsion
Rocket propulsion
Conceptual Design Prediction Methods Thrust
Specific impulse
Design Trades
Turbojet turbine material, compressor ratio, and cycle Ramjet engine / booster / inlet integration
Ramjet fuel
Propellant burn area requirement
Nozzle throat area Nozzle expansion ratio
Rocket motor grain
Thrust magnitude control
Summary of Propulsion ( cont ) Summary of Propulsion ( cont )
Design Trades ( cont ) Solid propellant alternatives
Motor case material alternatives
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Nozzle materials
New Propulsion Technologies Hypersonic turbojet
Ramjet / ducted rocket
Scramjet
Combined cycle propulsion High temperature turbine materials
High temperature combustor
Oblique shock airframe compression
Mixed compression inlet Low drag inlet
High density fuel / propellant
Endothermic fuel
Summary of Propulsion ( cont ) Summary of Propulsion ( cont )
New Propulsion Technologies ( cont ) Solid rocket thrust magnitude control
High burn exponent propellant
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g p p p
Low observable fuel / propellant
Discussion / Questions? Classroom Exercise ( Appendix A )
Propulsion Problems Propulsion Problems
1. An advantage of turbojets compared to ramjets is s_____ thrust.2. The specific impulse of a turbojet is often limited by the maximum
allowable temperature of the t______.
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3. The specific impulse of a ramjet is often limited by the maximum allowable
temperature of the c________.4. Ducted rockets are based on a fuel-rich g__ g________.
5. A safety advantage of solid rocket propulsion over liquid propulsion is lesst_______.
6. A rocket boost to a take-over Mach number is required by ramjets ands________.
7. Parameters that enable the long range of subsonic cruise turbojet missilesare high lif t, low drag, available fuel volume, and high s_______ i______.
8. High thrust and high acceleration are achievable with s____ r_____propulsion.
9. In a turbojet the power to dr ive the compressor is provided by the t______.
Propulsion Problems ( cont ) Propulsion Problems ( cont )
10.The compressor exit temperature is a function of the flight Mach number and the compressor p_______ r____.
11. Compressor exit temperature, fuel heating value, and fuel-to-air ratio
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determine the turbojet t______ temperature.
12. Three types of turbine based propulsion are turbojet, turbo ramjet, and a__t____ r_____.
13. Mach number and fuel-to-air ratio determine the ramjet c________temperature.
14. An example of a ramjet with low drag and light weight is an i_______ r_____ramjet.
15. Russia, France, China, United Kingdom, Taiwan, and India are the onlycountries with currently operational r_____ missiles.
16. 100% inlet capture efficiency occurs when the forebody shock wavesintercept the i____ l__.
17. Excess air that does not flow into the inlet is called s_______ air.
Propulsion Problems ( cont ) Propulsion Problems ( cont )
18. Starting a ramjet inlet at lower supersonic Mach number requires a larger area of the inlet t_____.
19. Optimum pressure recovery across shock waves is achieved when the total
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pressure loss across each shock wave is e____.
20. The specific impulse and thrust of a ramjet are a function of the efficiencyof the combustor, nozzle, and i____.
21. High density fuels have high payoff for v_____ limited missiles.
22. The specific impulse of a ducted rocket with large excess fuel from the gas
generator can approach that of a r_____.23. High speed rockets require large p_________ weight.
24. At the throat, the flow area is minimum, sonic, and c_____ .
25. For an optimum nozzle expansion the nozzle exit pressure is equal to the
a__________ pressure.26. High thrust and chamber pressure are achievable through a large propellant
b___ area.
Propulsion Problems ( cont ) Propulsion Problems ( cont )
27. Three approaches to solid rocket thrust magnitude control are pulse motor,pintle motor, and g__ motor.
28. A high burn exponent propellant al lows a large change in thrust with only a
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small change in chamber p_______.
29. Three tradeoffs in selecting a sol id propellant are safety, observables, ands_______ i______.
30. A low cost motor case is usually based on steel or aluminum material whilea light weight motor case is usually based on c________ material.
31. Rockets with high chamber pressure or long burn time may require at_______ throat insert.
Outline Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
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y g
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,Conversion Factors, Syllabus )
Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration
Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration
Establish Baseline
Al t Mission
Alt Baseline
Define Mission Requirements
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Yes
Trajectory
MeetPerformance?
Measures of Merit and ConstraintsNo
No
Yes
Resize / Alt Conf ig / Subsystems / Tech
Al t Baseline
Aerodynamics
Propulsion
Weight
Designing Light Weight Missile Has High Payoff Designing Light Weight Missile Has High Payoff
Production cost
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Logistics cost
Size
Firepower
Observables
Mission flexibil ity
Expeditionary warfare
Flight Performance ( Range, Speed,Maneuverability ) Sensitive to Subsystem Weight
Flight Performance ( Range, Speed,Maneuverability ) Sensitive to Subsystem Weight
Dome - Seeker - Guidance and Propulsion Wings Stabilizers
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High Sensitivity Low Sensitivity - Minor Sensitivity
Control -
Warhead Insulation FlightControl
Power Supply
Structure DataLink -
Missile Range is a Function of Launch Weight,Propellant Weight, and Specific Impulse
Missile Range is a Function of Launch Weight,Propellant Weight, and Specific Impulse
1000
ΔV ≈ -gc Isp ln ( 1 - WPropellant / Wi )
R ≈ V2 sin ( 2θi ) / gc
Assumptions:
θI = Launch Incidence Angle = 45 deg for maxrange
Thrust Greater Than Drag and Weight
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10
100
100 1000 10000
Wi, Example Initial Launch Weight, lb
R m a
x , M a x i m u m R a n g e , n m
Sing le-Stag e Miss ile Two-Stag e Missile
Flat, Non-rotating Earth
For Two-Stage Missi le with ( Wi )Min : ΔV1 = ΔV2
Example: Two-Stage Missi le with Min imumWeight and Rmax = 200 nm = 1.216 x 106 ft
Assume ISP = 250 sec, WPayload = 500 lb, WInert =0.2 WPropellant
V = [( 32.2 ) ( 1.216 x 106 )]1/2 = 6251 ft / sΔV1 = ΔV2 = V / 2 = 3125 ft / s
Wi,SecondStage = WPayload + WInert + WPropellant = 814 lb
Wi, FirstStage = WInert + WPropellant = 85 + 427 = 512 lb
Wi = Wi,FirstStage + Wi,SecondStage = 1326 lbCompare: Single-Stage Missile, R = 200 nm
ΔV = 6251 = - 32.2 ( 250 ) ln [ 1 – WPropellant / (WPropellant + 0.2 WPropellant + 500 )] ⇒ Wp = 767 ⇒Wi = 1420 lb
Missile Weight Is a Function of Diameter and Length
Missile Weight Is a Function of Diameter and Length
1000
10000
W e i g h t , l b
WL = 0.04 l d2
Units: WL( lb ), l ( in ), d ( in )
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10
100
1000
100 1000 10000 100000 1000000
ld2, Missile Length x Diameter2, in3
W L ,
M i s s i l e L a u
n c h W
FIM-92 SA-14 Javelin RBS-70 Starstreak Mistral HOT Trigat LR
LOCAAS AGM-114 Roland RIM-116 Crotale AIM-132 AIM-9M Magic 2Mica AA-11 Python 3 AIM-120C AA-12 Skyflash Aspide AIM-9P
Super 530F Super 530D AGM-65G PAC-3 AS-12 AGM-88 Penguin III AIM-54C
Arm at Sea Dart Sea Eagle Kormoran II AS34 AGM-84H MIM-23F ANS
MM40 AGM-142 AGM-86C SA-10 BGM-109C MGM-140 SSN-22 Kh-41
Most Subsystems for Tactical Missiles Have a Density of about 0.05 lb / in 3
Most Subsystems for Tactical Missiles Have a Density of about 0.05 lb / in 3
Guidance: Flight Control : Warhead: Propellant: Data Link:
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Guidance:0.04 lb / in3
Flight Control :0.04 lb / in3
Warhead:0.07 lb / in3
Propellant:0.06 lb / in3
Structure and Motor Case:0.10 ( Al ) to 0.27 ( steel ) lb / in3
Aero Surfaces:
0.05 ( bui lt-up Al ) to 0.27 ( solidsteel ) lb / in3
Data Link:0.04 lb / in3
Dome Material:0.1 lb / in3
Modeling Weight, Balance, and Moment-o -Inertia Is Based on a Build-up of Subsystems
Modeling Weight, Balance, and Moment-o -Inertia Is Based on a Build-up of Subsystems
Example Missile Configuration EngineInlet SectionWith Fuel
Wing SectionWith Fuel
FuelPl
Nose G&C Warhead
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Model
Structure and Subsystems Engine Structure and Subsystems
Warhead and Structure Fuel
Inlet Structure and Subsystems Aero Surfaces
Legend Assume Uniform Weight Distribut ion For a Given Segment
+x
Inlet
Plug
+z
Nose G&C Warhead
xCG = Σ ( xsubsystem1 Wsubsystem1 + xsubsystem2 Wsubsystem2 + … ) / Wtotal
IY = Σ [ ( Iy,subsystem1 )local + Wsubsystem1 ( xsubsystem1 - xCG )2 / gc + ( Iy,subsystem2 )local + Wsubsystem2 ( xsubsystem2 - xCG )2 / gc + … ]
Moment-o -Inertia Is Higher for High Fineness Ratio Body
Moment-o -Inertia Is Higher for High Fineness Ratio Body
100
L o c a l M o m e n
C y l i n d e r
C o n e
( Iy,cylinder )local = [ W d2 / gc ] [ ( 1 / 16 ) + ( 1 / 12 ) ( l / d )2 ]
( Iy,cone )local = [ W d2 / gc ] [ ( 3 / 80 ) + ( 3 / 80 ) ( l / d )2 ]
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0.01
0.1
1
10
0 10 20 30
l / d, Length / Diameter
( I y , l o c a l ) g / ( W
d 2 )
, N o n d i m e n s i o n a l Y
a w
o f I n e r t i a
Example for Ramjet Baseline at Launch ( xcg = 8.04 ft )
Assume missi le can be approximated as a conical nose-cyl inder
For the cone, d = 1.25 ft, l / d = 1.57, Wcone = 15.9 lb, xcg,cone = 1.308 ft
For the cyl inder, l / d = 7.22, d = 1.698 ft, Wcylinder = 2214 lb, xcg,cylinder = 8.09 ft
Iy = ( Iy,cone )local + Wcone ( xcg,cone - xCG )2 / gc + ( Iy,cylinder )local + Wcylinder ( xcg,cylinder -xCG )2 / gc
( Iy,cone )local = [ 15.9 ( 1.25 )2 / 32.2 ] [ 0.0375 + 0.0375 ( 1.57 )2 ] = 0.10 slug-ft2
( Iy,cylinder )local = [ 2214 ( 1.698 )2 / 32.2 ] [ 0.0625 + 0.0833 ( 7.22 )2 ] = 872 slug-ft2
Iy = 0.10 + 22.4 + 872 + 0.16 = 895 slug-ft2
Structure Design Factor of Safety Is Greater for Hazardous Subsystems / Flight Conditions
Structure Design Factor of Safety Is Greater for Hazardous Subsystems / Flight Conditions
3.0
Pressure Bott le ( 2.50 / 1.50 )Ground Handling Loads ( 1.50 / 1.15 )
Captive Carriage and Separation Flight Loads ( 1.50 / 1.15 )
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2.0
1.0
0
FOS,Factor of Safety
( Ultimate / Yield )
Note:• MIL STDs include envi ronmental ( HDBK-310, NATO STANAG 4370, 810F, 1670A ), strength and rigid ity ( 8856 ), and captivecarr iage ( 8591 ).•The entire environment ( e.g., manufactur ing, transpor tation, storage, ground handling, captive carriage, launch separation,post-launch maneuvering, terminal maneuvering ) must be examined for driving conditions in structure design.•FOS Δ for castings is expected to be reduced in future as casting technology matures.•Reduction in required factor of safety is expected as analysis accuracy improves wi ll result in reduced miss ile weight / cost.
Motor Case ( MEOP ) ( 1.50 / 1.10 )
Free Flight Loads ( 1.25 / 1.10 )
Δ Castings ( 1.25 / 1.25 )
Δ Fittings ( 1.15 / 1.15 )
Thermal Loads ( 1.00 / 1.00 )
Structure Concepts and Manufacturing Processes for Low Parts Count
Structure Concepts and Manufacturing Processes for Low Parts Count
Structure Manufacturing Process AlternativesComposites Metals
GeometryAl t t i
Vacuum Assist
VacuumBag /
HighSpeedCompression Filament Thermal
StructureConcept
Al t t iStrip
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Al ternat ivesRTM
g Autoclave
pMachine
pMold Wind Pultrusion Form FormingCast
MonocoqueIntegrally HoopStiffened
IntegrallyLongitudinalStiffened
Solid
Sandwich
Axisymmetr ic Ai rf rame
Surface
Lifting Body Ai rf rame
Al ternat ives
MonocoqueIntegrally HoopStiffened
IntegrallyLongitudinalStiffened
StripLaminate
Note: Manufacturing process cost is a function of recurring cost ( unit material, unit labor ) and non-recurring cos t ( tooling ).
Note: Very Low Parts Count Low Parts Count Moderate Parts Count High Parts Count –
–
–
Low Parts Count Manufacturing Processes for Complex Airframes
Low Parts Count Manufacturing Processes for Complex Airframes
Vacuum Assisted RTM
Resin Pump
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Filament Wind
Pultrusion ………………………………….
Metal CastingMold Cavity
Riser
Pour Cup Vent
Parting Line
p3D Fiber Orientation
2D Fiber Orientation ( 0-±45-90 deg )Helical wind versusradial w ind
Tactical Missile Airframe Material Alternatives Tactical Missile Airframe Material Alternatives
Tension( σTU / ρ )
Aluminum 2219
MaterialTypeBucklingStability
( σBuckling / ρ )
MaxShort – Life
Temp
ThermalStress
Joining Cost Weight
MetallicIncreasing
– –
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Superior Above Average Average Below Average –Note:
Steel PH 15-7Mo
Titanium 6Al-4V
S994 Glass /Epoxy and S994Glass / Polyimide
Glass or Graphite ReinforceMolding
Graphite / Epoxyand Graphite
Polyimide
IncreasingCost
CompositeIncreasingCost
–
–
– –
–
–
Strength –Elasticity of Airframe Material Alternatives Strength –Elasticity of Airframe Material Alternatives
400
Glass Fiber w / o Matrix
Kevlar Fiber w / o Matrix
Graphite Fiber w / o Matrix
Note:• High strength fibers are:
– Very small d iameter – Unidirectional
Hi h d l f
σ
t = P / A = E ε
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Aluminum Al loy ( 2219-T81 )
300
200
100
0
σt, Tensile Stress,103 psi
0 1 2 3 4 5
ε, Strain, 10-2 in / in
Titanium Alloy ( Ti-6Al-4V )
Very High Strength Stainless Steel( PH 15-7 Mo, CH 900 )
( 400 – 800 Kpsi )
E, Young’s modulus of elasticity, psiP, Load, lbε, Strain, in / in A, Area, in2
Room temperature
– High modulus of elasticity
– Very elastic – No yield before failure – Non forgiving failure
• Metals: – Ductile,
– Yield before failure – Al low adjacent st ructure
to absorb load – Resist crack formation – Resist impact loads – More forgiving failure
High Strength Stainless Steel( PH 15-7 Mo, TH 1050 )
Structural Efficiency at High Temperature of Short Duration Airframe Material Alternatives Structural Efficiency at High Temperature of Short Duration Airframe Material Alternatives
10.0
12.0
g t h /
Graphite / Epoxy( ρ = 0.065 lb / in3 )0-±45-90 Laminate
Graphite / Polyimide ( ρ = 0.057 lb / in3 ), 0-±45-90 Laminate
Ti3 Al ( ρ = 0.15 lb / in3 )
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200 400 600 800 1,0000
Short Duration Temperature, ° F
8.0
6.0
4.0
2.0
0
σ T U /ρ ,
U l t i m
a t e T e n s i l e S t r e n g
D e
n s i t y ,
1 0 5 I n . Ti-6Al-4V Annealed Titanium ( ρ = 0.160 lb / in
3
)PH15-7 Mo Stainless Steel ( ρ = 0.277 lb / in3 ). Note:Thin wall steel susceptible to buckling.
Graphite
Glass
2219-T81 Aluminum
( ρ = 0.101 lb / in3 )
Chopped EpoxyComposites,Random Orientation( ρ = 0.094 lb / in3 )
3 ( )
Hypersonic Missiles without External Insulation Require High Temperature Structure
Hypersonic Missiles without External Insulation Require High Temperature Structure
F
2,000 r =
1
r =
0 . 8
r =
0 . 9
Tr = T0 ( 1 + 0.2 r M2 )
( Tmax )Nickel Alloys ( e.g., Inconel, Rene,Hastelloy, Haynes )
( Tmax )Titanium Aluminide ≈ 2,500 °F )
( Tmax )Single Crystal Nickel Aluminides ≈ 3,000 °F( Tmax )Ceramic Matrix Composit e ≈ 3,500 °F
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M, Mach Number
T r ,
R e c o v e
r y T e m p e r a t u r e ,°
•••
•
•
•1,500
1,000
500
010 2 3 4 5 6
Note:
• γ = 1.4
• Tr = Recovery Temperature, R
• T0 = Free stream temperature, R
• Tmax = Max temperature capabili ty
• No external insulation assumed
• r is recovery factor • h = 40k f t ( TFree Stream = 390 R )• Stagnation r = 1
• Turbulent boundary layer r = 0.9• Laminar boundary layer r = 0.8• Short-duration flight ( less than
30 m ), but with thermal soak
( Tmax )Graphite Polyimide
( Tmax ) Al Al loy
( Tmax )Steel
( Tmax )Ti Alloy•
( Tmax )Graphite Epoxy
Structure / Insulation Trades for Short Duration Flight Structure / Insulation Trades for Short Duration Flight
Example Structure / Insulation Concepts Mach Tmax k c ρ α
Increasing
Hot Metal Structure ( e.g., Al ) withoutInsulation 600 0.027 0.22 0.101 0.000722
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Hot Metal Structure ( e.g., Al ) 600 0.027 0.22 0.101 0.000722
Cold Metal Structure ( e.g., Al ) 600 0.027 0.22 0.101 0.000722
Internal Insulation ( e.g., Min-K ) 2000 0.0000051 0.24 0.012 0.00000106
Note:• Tactical missiles use passive thermal protection ( no active cooling )• Small thickness allows more propellant / fuel for diameter const rained missi les ( e.g., VLS launcher )• Weight and cost are application specific• Tmax = max temp capability, ° F; k = thermal conduct ivi ty, BTU / s / ft2 / ° F / ft; c = specific heat or thermal
capacity, BTU / lbm / ° F; ρ = density, lbm / in3; α = thermal dif fusivi ty = k / ( ρ c ), ft2 / s
Self-insulating Composite Structure( e.g., Graphite Polyimide ) 1100 0.000109 0.27 0.057 0.00000410
Ext Insulation ( e.g., Micro-Quartz Paint ) 1200 0.0000131 0.28 0.012 0.00000226
Internal Insulation ( e.g., Min-K ) 2000 0.0000051 0.24 0.012 0.00000106
External Insulation Has High Payoff for Short Duration Flight
External Insulation Has High Payoff for Short Duration Flight
1,000
900
800 F 4.0
Example Airf rame Temperature wi th No ExternalInsulator – Steel Airf rame Selected.
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800
700
600
500
400
300
200
1000
E x a m p l e T e m p e r a t u r e °
0 2 4 6 8 10 12 14
1.0
2.0
3.0
MachNumber
Time After Launch ~ s
Mach
Note: Short Range Air-to-Air MissileLaunch ~ 0.9 Mach at 10k ft Alt itude
Atmosphere ~ Hot Day ( 1% Risk ) Mi l-HDBK-310
Example Airf rame Temperature with 0.012 in Insulator – Aluminum Ai rf rame Acceptable for Short Duration.
Bulk Ceramics• Melt
Graphites• Burn• ρ ~ 0.08 lb / in3
• Carbon / Carbon
6,000
5,000
Medium Density PhenolicComposites
• Char • ρ ~ 0.06 lb / in3
• Nylon Phenolic, Silica
Phenolic Composites Are Good Insulators for High Temperature Structure and Propulsion Phenolic Composites Are Good Insulators for High Temperature Structure and Propulsion
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Melt• ρ ~ 0.20 lb / in3
• Zirconium Ceramic,Hafnium Ceramic
Tmax, MaxTemperatureCapability,
R
4,000
3,000
2,000
00 1 2 3 4
Insulation Effic iency, Minutes To Reach 300° F at Back Wall
1,000
Note: Assumed Weight Per Unit Area of Insulator / Ablator = 1 lb / ft2
Porous Ceramics• Melt• Resin Impregnated• ρ ~ 0.12 lb / in3
• Carbon-SiliconCarbide
y o e o c, S caPhenolic, Glass
Phenolic, CarbonPhenolic, GraphitePhenolic
Low DensityComposites
• Char
• ρ ~ 0.03 lb / in3
• Micro-QuartzPaint, Glass-Cork-Epoxy,Silicone Rubber
Plastics
• Sublime• Depolymerizing• ρ ~ 0.06 lb / in3
• Teflon
A “Thermally Thin” Surface ( e.g., Metal Airframe ) Has Uniform Internal Temperature A Thermally Thin Surface ( e.g., Metal
Airframe ) Has Uniform Internal Temperature
1000
r e R a t e f o r
/ s e c
( dT / dt )t = 0 = ( Tr - Tinitial ) h / ( c ρ z )
T = Tr – ( Tr – Tinitial ) e – h t / ( c ρ z )
h = k NNU / x
Thermally thin ⇒ h ( z / k )surface < 0.1
Example for Rocket Baseline Airf rame:
Aluminum skin w/o external insulationc = 0.215 BTU / lb / R, ρ = 0.10 lb / in3 = 172.8 lb / f t3,z = 0.16 in = 0.0133 ft, k = 0.027 BTU / s / f t2 / R / ft
Assume Mach 2 sustain f light, 20k f t al ti tude ( T0 =447 R , k = 3.31 x 10-6 BTU / s / ft2 / R / ft ), Turbulentb d l 1 6 ft
x = 1.6 ft
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1
10
100
0 1 2 3 4 5 6
M, Mach Number
d T / d
t , I n i t i a l S k i n T e m p e r
a t u r
R o c k e t B a s e l i n e , D e g F /
h = sea level h = 20K ft h = 50K ft h = 80K ft
Note: No external insulation; thermally thin struc ture ( uniform internal temperature ); “ Perfect” insulation behind airframe; 1-Dheat transfer; Turbulent boundary layer; Radiation neglected; dT / dt = Temperature rate, R / s; Tr = Recovery ( max )temperature, R; h = Convection heat transfer coeffic ient, BTU / s / ft2 / R; c = Specific heat, BTU / lb / R; ρ = Densi ty, lb / ft3; z =Thickness, ft; k = Conduct ivi ty, BTU / s / ft2 / R / ft; Re = Reynolds number; NNU = Nusselt number
boundary layer, x = 1.6 ft
Rex = ρ0 M a0 x / μ0 = 12.56 x 106
NNU = 0.0271 Re0.8 = 12947
h = k NNU / x = 0.0268 BTU / s / ft2 / R
Test: h ( z / k )surface = 0.0132 < 0.1 ⇒ thermally thin
Calculate Tr
= T0
[ 1 + 0.2 r M2 ] = 447 [ 1 + 0.2 ( 0.9 )( 2 )2 ] = 769 R
At t = 0, Assume Tinitial = 460 R, or 0° F
( dT / dt )t = 0 = ( 769 - 460 ) ( 0.0268 ) / [( 0.215 )(172.8 ) ( 0.01333 )] = 17°F / s
At a sustain time t = 10 s, T = 769 - ( 769 – 460 ) e –
0.0268 ( 10 ) / [ 0.215 ( 172.8 ) ( 0.0133 )]
= 589 R, or 129° F
Reference: Jerger, J.J.,Systems Preliminary Design Principles of Guided Missile Design,D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960
A “Thermally Thick” Surface ( e.g., Radome ) Has a Large Internal Temperature Gradient
A “Thermally Thick” Surface ( e.g., Radome ) Has a Large Internal Temperature Gradient
1
[ T ( z, t ) - Tinitial ] / [ Tr – Tinitial ] = erfc { z / [ 2 ( α t )1/2 ] } – e( h z / k ) + h2 α t / k2erfc { z / [ 2 ( α t )1/2 ] + h ( α t )1/2 / k }
[ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 - eh2
α t / k2
erfc [ h ( α t )1/2 / k ] Appl icable fo r thermal ly th ick sur face: z / [ 2 ( α t )1/2 ] > 1
Example: Rocket Baseline Radome
z = 0.25 in = 0.0208 ft, k = 5.96 x 10-4 BTU / s / ft / R,
= 1 499 x 10-5 ft 2 / s1T ) i n i t i a l ] X = 1.6 ft
k= 0
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0
0.5
0.1 1 10 100
Note: T ( z,t ) ∼ ( T )initial; 1-D heat transfer; Radiation neglected; Turbulent boundary layer; Tr = Recovery temperature, R; h =Heat transfer coeffic ient, BTU / ft2 / s / R; k = Thermal conduct ivity o f material, BTU / s / ft2 / R / ft ; α = Diffusivity o f material,ft 2 / s; zmax = Thickness of material, ft; erfc = Complementary error function
α = 1.499 x 10 5 ft 2 / s
Mach 2, 20k ft alt ( T0 = 447 R ), Turbulent boundary layer,x = 19.2 in = 1.6 ft, t = 10 s, Tr = 769 R, Tinitial = 460 R
⇒ h = 0.0268 BTU / s / ft ⇒ ( h / k )( α t )1/2 = 0.491
Test: z / [ 2 ( α t )1/2 ] = 0.0208 / { 2 [ 1.499x10-5 ( 10 )]1/2 } =0.849 < 1 ⇒ not quite thermally thick
Inner wall ⇒ h z / k = 0.935[ T ( 0.0208, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.0608
T ( 0.0208, 10 ) = 479 R ( Note: Tinner ≈ Tinitial )
Surface ⇒ h z / k = 0
[ T ( 0, 10 ) - Tinitial ] / [ Tr – Tinitial ] = 0.372
T ( 0, 10 ) = 575 R
Reference: Jerger, J.J.,Systems Preliminary Design Principles of Guided Missile Design,D. Van Nostrand Company, Inc., Princeton, New Jersey, 1960
( h / k )( α t )1/2
h z
/ k
= 1
0 0
h z /
k 1
0
h z /
k = 1
h z / k =
0 . 1
[ T ( z , t
) - ( T ) i n i t i a l ] / [ ( T ) r – ( T
h z / k
Internal Insulation Temperature Can Be Predicted Assuming Constant Flux Conduction
Internal Insulation Temperature Can Be Predicted Assuming Constant Flux Conduction
1
[ T ( z, t ) – Tinitial ] / [ T ( 0, t ) – Tinitial ] = e- z2 / ( 4 α t ) – ( π / α t )1 / 2 ( z / 2 ) erfc { z / [ 2 ( α t )1/2 ]}
Appl icable for thermally thick surface: z / [ 2 ( α t )1/2
] > 1 Example for Rocket Baseline Air frame Insulation:
0.10 in Min-K Internal Insulation behind 0.16 in aluminumSkin
X = 1.6 fti t i a
l ]
Aluminum
Min K
0.16 in
0 10 in
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0
0.5
0.1 1 10 100
Note: 1-D conduction heat transfer, Radiation neglected, Constant heat flux input, T ( z,t ) = Inner temperature of insulationat time t, Tinitial = Initial temperature, T ( 0, t ) = Outer temperature of insulation at time t, α = Diffusivity o f insulation material,ft 2 / s; zmax = Thickness of insulation material, ft; erfc = Complementary error function
Assume M = 2, 20k f t alt , x = 1.6 ft , Tinitial = 460 R, t = 10 s,zMin-K = 0.10 in = 0.00833 ft , αMin-K = 0.00000106 ft2 / s, k =5.96 x 10-4 BTU / s / f t, h = 0.0268 BTU / s / f t
Test: z / [ 2 ( α t )1/2 ] = 0.00833 / {2 [ 0.00000106 ( 10 )]1/2} =1.279 > 1 ⇒ thermally thick
( α t )1/2 / z = [ 0.00000106 ( 10 ) ] 1/2 / 0.00833 = 0.3907
[ TMin-K ( 0.0217, 10 ) – 460 ] / [ TMin-K ( 0, 10 ) – 460 ] = 0.0359
Assume ( Tinner )aluminum = ( Touter )Min-K
From prior example, ( Tinner )aluminum = 569 R at = 10 s
Then, ( Touter )Min-K = 569 R at t = 10 s
Compute, ( Tinner )Min-K = 460 + ( 569 – 460 ) 0.0338 = 460 + 4= 464 R
Reference: Carslaw, H. S. and Jaeger, J. C.,Conduction of Heat in Solids, Clarendon Press, 1989
( α t )1/2 / z
[ T ( z , t ) –
T i n i t i a l ] / [ T ( 0 ,
t ) –
T i n i Min-K 0.10 in
z
A Sharp Nose Tip / Leading Edge Has High Aerodynamic Heating
A Sharp Nose Tip / Leading Edge Has High Aerodynamic Heating
0.4
0.5
0.6
r a n s f e r C o e f f f o r
0 k f t , B T U / f t 2 / s / R
hr = NNUr kr / dNoseTip
NNUr = 1.321 RedNoseTip0.5 Pr 0.4
Example for Rocket Baseline Nose Tip:
Assume M = 2, 20k f t alt , stagnation ( Tr = 805R ) for a sharp nose tip ( e.g., 1% blunt )
dNoseTip / dRef = 0.01 ⇒ dNoseTip = 0.01 ( 8in ) = 0.08 in = 0.00557 ft
R V d / 3 39 104
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0
0.1
0.2
0.3
0 1 2 3 4 5 6
M, Mach Number
h r , S t a g n a t i o n H e a
t T
R o c k e t B a s e l i n e a t h = 2 0
1% Bluntness 2% Bluntness
5% Bluntness 10% Bluntness
Note: 1-D conduction heat transfer; Laminar boundary layer; Stagnation heating; Radiation neglected; hr = Convectionheat transfer coefficient fo r stagnation recovery, BTU / s / ft2 / R; NNUr
= Nusselt number for stagnation recovery; kr = Ai r thermal conductivi ty at s tagnat ion recovery ( total ) temperature, BTU / s / ft / R; dNoseTip = Nose tip diameter, ft;RedNoseTip = Reynolds number based on nose tip diameter, Pr = Prandtl number
RedNoseTip = ρ0 V0 dNoseTip / μr = 3.39 x 104
NNUr = 223
hr = 0.1745 BTU / ft2 / s / R
Outer surface temperature after 10 s heatingin sustain flight ( M = const, Tr = const ):
[ T ( 0, t ) - Tinitial ] / [ Tr – Tinitial ] = 1 – eh2αt / k2
erfc { h ( α t )1/2 / k }
[ T ( 0, 10 ) - 460 ] / [ 805 – 460 ] = 1 – e [( 0.1745 )2
( 1.499 x 10-5 ) ( 10 ) / ( 5.96 x 10-4 )2 ] erfc { ( 0.1745 ) [1.499 x 10-5 ( 10 )]1/2 / ( 5.96 x 10-4 )]} = 0.845
T ( 0, 10 ) = 460 + 345 ( 0.845 ) = 752 R
Reference: Allen, J. and Eggers, A. J., “A Study of the Motion and Aerodynamic Heating of BallisticMissiles Entering the Earth’s Atmosphere at High Supersonic Speeds”, NACA Report 1381, April 1953.
Tactical Missile Radiation Heat Loss Is Usually Small Compared to Convective Heat Input
Tactical Missile Radiation Heat Loss Is Usually Small Compared to Convective Heat Input
10
100QRad = 4.76 x 10
-13
ε T4
QRad in BTU / ft2 / s, T in R
Example: Ramjet Baseline
Assume:
•Titanium skin wi th emissivity =
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0.01
0.1
1
10
0 1 2 3 4 5 6
Cruise Mach Numb er
Radiation Heat
Flux at
Equilibrium
Temperature,
BTU / ft2 / s
Emissivity = 0.1 Emissivity = 1
•Titanium skin wi th emissivity ε =
0.3•Long duration ( equilib rium )heating at Mach 4
•h = 80k ft , T0 = 398 R
•Turbulent boundary layer ( r =0.9 ) ⇒ T = Tr = T0 ( 1 + 0.2 r M2 ) =
1513 R
Calculate:
QRad = 4.76 x 10-13 ( 0.3 ) ( 1513 )4
= 0.748 BTU / ft2 / s
Design Concerns for Localized Aerodynamic Heating and Thermal Stress
Design Concerns for Localized Aerodynamic Heating and Thermal Stress
Body JointsH t i il h ll
Flare / Wedge Corner FlowShock wave – boundary layer
interaction
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Hot missile shellCold frames or bulkheadsCauses premature buckling
IR Domes / RF RadomesLarge temp gradients due to low thermal conduct ionThermal st ress at attachmentLow tensile strengthDome fails in tension
Leading Edges
Hot stagnation temperature on leading edgeSmall radius prevents use of external insulationCold heat sink material as chord increases in thickness
leads to leading edge warpShock wave interaction with adjacent body structure
Separated FlowHigh heating at reattachment
Note: σTS
= Thermal stress from restraint in compression or tension = α E ΔT
α = coefficient of thermal expansion, E = modulus of elasticity, ΔT = T2 – T1 = temperature difference.
Example: Thermal Stress for Rocket Baseline Pyroceram Dome, α = 3 x 10-6, E = 13.3 x 106 psi
Assume M = 2, h = 20k f t alt , t = 10 s. Based on prior figure, ΔT = TOuterWall – TInnerWall = 102 R
Then σTS = 3 x 10-6 ( 13.3 x 106 ) ( 102 ) = 4,070 psi
Examples of Aerodynamic Hot Spots Examples of Aerodynamic Hot Spots
Nose Tip
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Leading Edge
Flare
Tactical Missile Body Structure Weight Is about 22% of the Launch Weight
Tactical Missile Body Structure Weight Is about 22% of the Launch Weight
1000
W e i g h t , l b
Hellf ire ( 0.22 )
Sidewinder ( 0.23 )
Sparrow ( 0 18 )
WBS
/ WL≈ 0.22
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10
100
100 1000 10000
WL, Launch Weight, lb
W B S , B
o d y S t r u c t u r e
W Sparrow ( 0.18 )
Phoenix ( 0.19 )
Harpoon ( 0.29 )
SM 2 ( 0.20 )
SRAM ( 0.21 )
ASALM ( 0.13 )
SETE ( 0.267 )
Tomahawk ( 0.24 )
TALOS ( 0.28 )
Example for 500 lb missile
WL = 500 lb
WBS = 0.22 ( 500 ) = 110 lb
Note: WBS includes all load carry ing body structure. If motor case, engine, or warhead case carry externalloads then they are included in WBS. WBS does not include tail, wing, or other surface weight.
Body Structure Thickness Is Based on Considering Many Design Conditions Body Structure Thickness Is Based on Considering Many Design Conditions
Structure Design Conditions That May Drive Air frame Thickness
Manufacturing
Transportation
Carriage
Launch
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Fly-out Maneuvering
Contributors to Required Thickness for Cylindrical Body Structure
Minimum Gage for Manufacturing: t = 0.7 d [( pext / E ) l / d ]0.4. t ≈ 0.06 in i f pext ≈ 10 psi
Localized Buck ling in Bending: t = 2.9 r σ / E
Localized Buckling in Ax ial Compression: t = 4.0 r σ / E
Thrust Force: t = T / ( 2 π σ r )
Bending Moment: t = M / ( π σ r 2 )
Internal Pressure: t = p r / σ
High Risk ( 1 ), Moderate Risk ( 2 ), and Low Risk ( 3 ) Estimates of Required Thickness1. t = FOS x Max ( tMinGage , tBuckling,Bending , tBuckling,AxialCompression , t AxialLoad , tBending , tInternalPressure )
2. t = FOS x ( t2MinGage + t2
Buckling,Bending + t2Buckling,AxialCompression + t2
Ax ialLoad + t2Bending + t2
InternalPressure )1/2
3. t = FOS x ( tMinGage + tBuckling,Bending + tBuckling,AxialCompression + t AxialLoad + tBending + tInternalPressure )
Localized Buckling May Be A Concern fo Thin Wall Structure
Localized Buckling May Be A Concern fo Thin Wall Structure
0.1
S t r e s s
Bending
Axial Compression
σBuckling,Bending
/ E ≈ 0.35 ( t / r )
σBuckling,AaxialCcompression / E ≈ 0.25 ( t / r )
Note: Thin wall cylinder with local buckling
σBuckling / E = Nondimensional buckling stress
Buckling stress in bending
r t
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0.0001
0.001
0.01
0.001 0.01 0.1
t / r, thickness / radius
N o n d i m e
n s i o n a l B u c k l i n g
σBucklingBending= Buckling stress in bending
σBucklingAxialCompression = Buckling st ress in axialcompression
E = Young’s modulus of elasticity
t = Air frame thickness
r = Air frame radiusMin thickness for fab and handling ≈ 0.06 in
Example for Rocket Baseline in Bending:
4130 steel motor case, E = 29.5 x 106 psi
σyield = 170,000 psi
t = 0.074 in, r = 4 in
t / r = 0.0185
σBuckling,Bending / E ≈ 0.35 ( 0.0185 ) = 0.006475σbuckling,Bending ≈ 191,000 psiσbuckling,Bending ~ σyield
Note: Actual buckling stress can vary +/- 50%, depending upon typicalimperfections in geometry and the loading.
Process for Captive and Free Flight Loads Calculation
Process for Captive and Free Flight Loads Calculation
Free Flight
Maneuver Per Design Requirements
Captive Flight
Max Aircraft Maneuver Per MIL-A-8591
Carriage Load
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Weight loadof bulkhead
section
Ai r LoadObtainedBy WindTunnel
Ai r Load
Weight loadof bulkhead
section
Ai r Load
Note: MIL-A-8591 Procedure A assumes max air loads combine with max g forces regardless of angle of attack.
Example of αmax Calculated by MIL-A-8591 UsingProcedure A fo r F-18 Aircraft Carriage:
αmax = 1.5 nz,max Wmax / ( CLα q SRef )aircraft
αmax = 1.5 ( 5 ) ( 49200 ) / [ 0.05 ( 1481 ) ( 400 )] =12.5 deg
Maximum Bending Moment Depends Upon Load Distribution
Maximum Bending Moment Depends Upon Load Distribution
Example for Rocket Baseline:
c = 4, ejection load
l = 144 in
⇒
N = 10,000 lb ( 20 g )
⇒ MB = 360,000 in-lb
Max Bending
MB = N l / c
C = 8 for uniform loading
C = 7.8 for linear loading
Total Coefficient C Length l
w = load per unit length
0 l = length
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Moment MB
C 7.8 for li near loading
C = 6 for linear loading to center
C = 4 for load at center ( e.g., ejection load )
6
440,00030,000
20,000
4 1 3
2 5
100
200
1,000,000
2,000,000
5,0004,0003,000
2,000
1,000
500
400300
200
100
500,000400,000300,000200,000
100,000
LoadN
g
8 7.8100,000
50,000
10,000
50,00040,00030,00020,000
10,000
5,0004,0003,0002,000
1,000
500400300200
100
w
0 l
w
0 l
l0
N = Normal Force
l / 2
10
C = 1 for load at end ( e.g., contro l force )
N = Normal Force
l0
l
1
Bending Moment May Drive Body Structure Weight
Bending Moment May Drive Body Structure Weight
A = 2 π r tIz = IY = π r 3 t
r
tt
MB
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Example for Rocket Baseline:• Body has circular cross section• 2219-T81 aluminum skin ( σult = 65,000 psi )• r = 4 in• Ejection load = 10,000 lb ( 20 g )• M
B= 360,000 in ⋅ lb
• FOS = 1.5• t = 360,000 ( 1.5 ) / [ π ( 4 )2 ( 65,000 )] = 0.16 in
t = MB ( FOS ) / [ π r 2 σMax ] Note / Assumptions:
Thin cylinder
Circular cross section
Solid skin
Longitudinal strength
Axial load stress and thermalstress assumed small comparedto bending moment st ress
σ = MB r / IZ = MB r / (π r 3 t )
= MB / (π r 2 t )
Tactical Missile Propellant Weight Is about 72%of Rocket Motor Weight
Tactical Missile Propellant Weight Is about 72%of Rocket Motor Weight
10000
g h t , l Hellf ire ( 0.69 )
Sidewinder ( 0.61 )
WP / WM ≈ 0.72
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10
100
1000
10 100 1000 10000
WM, Total Motor Weight, lb
W P ,
P r o p e l l a n t W e i
Sparrow ( 0.64 )Phoenix ( 0.83 )
ASALM ( 0.86 )
SM-2 ( 0.76 )
SRAM ( 0.71 )TALOS ( 0.66 )
Example for Rocket BaselineWM = 209 lb
WP = 0.72 ( 209 ) = 150 lb
Note: WM includes propellant, motor case, nozzle, and insulation.
Increased propellant fraction if:
High volumetric loading
Composite case
Low chamber pressure
Low flight loads
Short burn time
Motor Case Weight Is Usually Driven By Stress from Internal Pressure
Motor Case Weight Is Usually Driven By Stress from Internal Pressure
Assume motor case is axisymmetric, wi th a front ellipsoid domeand an aft cylinder body
Motor CaseCylinder σt t = - 0∫
π/2p r sinθ dθ
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With metals – the material also reacts body bending
In composite motor designs, extra ( longitudinal ) fibers must usually beadded to accommodate body bending
HoopStress
Motor Dome
EllipsoidLongitudinalStress
p p
( σt )Longitudinal Stress
= [ 2 + ( a / b )
2
] p ( a b )
1/2
/ ( 6 t )
If a = b ( hemi dome of radius r ),then ( σt )Longitudinal Stress = p r / ( 2 t )
( σt )Hoop Stress = p r / t
Case Dome Nozzle
Case Cylinder
2 a
b
A Composite Motor Case Is Usually Lighter Weight
A Composite Motor Case Is Usually Lighter Weight
Calculate Maximum Effective Operating Pressure ( Burst Pressure )
pburst = pBoost, Room Temp x eπk Δ T x ( Design Margin for Ignition Spikes, Welds, Other Design Uncertainty )
Assume Rocket Motor Baseline: diameter = 8 in., length = 55 in, ell ipsoid dome a / b = 2, pBoost,RoomTemp =1769 psi, πk = ( Δp / ΔT ) / pc = 0.14% / °F
Assume Hot day T = 160° F ⇒ eπk ΔT = e0.0014 ( 160 - 70 ) = 1.134. Uncertainty factor is 1.134, 1σ
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Assume a 3σ uncertainty design margin is provided by, pburst ≈ 1769 x ( 1.134 )3 = 2,582 psi
Assume Ultimate Factor of Safety FOS = 1.5
Rocket Baseline Steel Case ( σt )ult = 190,000 psi
tHoop
= ( FOS ) x pburst x r / σt = 1.5 x 2582 x 4.0 / 190,000 = 0.082 in
tDome = ( FOS ) x pburst x ( a b )1/2 x [ 2 + ( a / b )2 ] / ( 6 σt ) = 1.5 x 2582 x [ 4 x 2 ]1/2 x [ 2 + ( 2 )2 ] / [ 6 x 190,000 ]= 0.058 in
Weight = WCylinder + WDome = ρ π d tHoop l + ρ ( 2 π a b ) tDome = 30.8 + 0.8 = 31.6 lb for steel case
Try Graphite Fiber at σt = 450,000 psi Ultimate, Assume 60% Fiber / 40% Epoxy Composite
tHoop = 1.5 x 2582 x 4.0 / [ 450,000 ( 0.60 )] = 0.057 in radial f ibers for internal pressure load
tDome = 0.041 in, for internal pressure load
Weight = 11.1 lb for composite case ( w/o insulation, attachment, aft dome, and body bending f iber )
Must also add about 0.015 in of either longitudinal fibers or helical wind to counteract body bending load
A Low Aspect Ratio Delta Wing Allows Lighter Weight Structure
A Low Aspect Ratio Delta Wing Allows Lighter Weight Structure
2
3
WSurface σmax1/2 / [ ρ S Nmax
1/2 ] = [ A ( 1 + 2 λ )]1/2
WSurface = ρ S tmac
troot = [ FOS Nmax A ( 1 + 2 λ ) / σmax,]1/2
Assumption: Uni form loading
Note:
Surface is 2 panels ( Cruci form wing has 4 panels )
WSurface = Surface weight sized by bending moment
ρ = Density
σmax = Maximum allowable ( ultimate ) stress
tmac = Thickness of mean aero chord cmac - d i m e n s i o n a l W e i g h t
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0
1
0 1 2 3
A, Aspect Ratio
Taper Ratio = 0 Taper ratio = 0.5 Taper Ratio = 1
troot = Thickness of root chord c root
Nmax = Maximum load
A = Aspect rat io
λ = Taper ratio
Example for Rocket Baseline Wing ( 2219-T81
Aluminum ): A = 2.82, λ = 0.175, cr = 19.4 in, σmax =σul t = 65k psi
Assume M = 2, h = 20k f t, α + δ = 22 deg
From prior example, Nmax = 7525 lb
Calculate troot = [ 1.5 ( 7525 ) ( 2.82 ) [ 1 + 2 ( 0.175 ) /65000 ]1/2 = 0.813 in
troot / croot = 0.813 / 19.4 = 0.0419 = tmac / cmac
tmac = 0.0419 ( 13.3 ) = 0.557 in
Wwing σmax1/2 / [ ρ S Nmax
1/2 ] = [ A ( 1 + 2 λ )]1/2.= 1.95
Wwing = 20.6 lb for 1 wing ( 2 panels )
W S u r f a c eσ m a x
1 / 2
/ (ρ
S N m a x
1 / 2 ) , N o n
Seeker Dome
Material
Density( g / cm3 )
DielectricConstant
MWIR /LWIR
Bandpass
TransverseStrength( 103 psi )
ThermalExpansion( 10-6 / ο F )
Erosion,Knoop ( kg
/ mm2 )
Max Short -Duration
Temp ( ο F )
RF-IR Seeker
Zinc Sulfide( ZnS )
4.05 8.4 18 4 350 700
Zinc Selenide 5.16 9.0 8 4 150 600
Dome Material Is Driven by the Type of Seeker and Flight Environment
Dome Material Is Driven by the Type of Seeker and Flight Environment
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( ZnSe)Sapphire /Spinel
3.68 8.5 28 3 1650 1800
Quartz / FusedSilica ( SiO2)
2.20 3.7 8 0.3 600 2000
Silicon Nitride( Si3N4)
3.18 6.1 90 2 2200 2700
Diamond ( C ) 3.52 5.6 400 1 8800 3500RF Seeker
Pyroceram 2.55 5.8 25 3 700 2200Polyimide 1.54 3.2 17 40 70 400IR Seeker
Mag. Fluoride( MgF2)
3.18 5.5 7 6 420 1000
Alon( Al23O27N5)
3.67 9.3 44 3 1900 1800
Germanium( Ge )
5.33 16.2 15 4 780 200
Superior Above Average Average Below Average - Poor
-
--
- --
--
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Missile Electrical Power Supply Alternatives Missile Electrical Power Supply Alternatives
Power SupplyMeasure of Merit
C t
Storage Life
Thermal BatteryLithium BatteryGenerator
W = WE E + WP P
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Voltage Stabil ity
0.31.51.4WP, Weight / Power ( kg / kW )
0.01250.00120.0007WE, Weight /Energy
( kg / kW-s )
Cost
Superior Above Average Average Below Average
Example for Thermal battery: If E = 900 kW–s, P = 3 kW ⇒ W = WEE + WPP = 0.0125 ( 900 ) + 0.3 ( 3 ) = 12.2 kg
Note: Generator provides highest energy with l ight weight for long time of fl ight ( e.g., cruise missile ).
Lithium battery provides nearly constant voltage suitable for electronics. Relatively high energy with light weight.
Thermal battery provides highest power with light weight ( may be required for actuators ).
Electromechanical Actuators Are Light Weight and Reliable
Electromechanical Actuators Are Light Weight and Reliable
HydraulicCold Gas PneumaticEMMeasure of Merit
Up to 1000Up to 600Up to 800Rate ( deg / s )
0.00340.00500.0025WT, Weight / Stall Torque ( lb /in-lb )
W = WT TS
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Superior Above Average Average Below Average
Reliability
Cost
Up to 60Up to 20Up to 40Bandwidth ( Hz )
Note:
• Actuation system weight based on four actuators.
•Cold gas pneumatic actuation weight includes actuators, gas bot tle,valves, regulator, and supply lines.
•Hydraulic actuation weight includes actuators, gas generator or gasbottle, hydraulic reservoir, valves, and supply lines.
•Stall torque ≈ 1.5 maximum hinge moment of s ingle panel.
Example weight for rocket baseline hydraulic actuation at Mach 2, 20k ft alt , α = 9 deg, with max control deflection of wing ( δ= 13 deg ) ⇒ Hinge moment of one panel = 11,500 in-lb. TS = 1.5 ( 11500 ) = 17,250 in-lb ⇒ W = WTTS = 0.0034 ( 17250 ) = 59 lb
Schematic of Cold Gas Pneumatic Actuation
Examples of Electromechanical Actuator Packaging
Examples of Electromechanical Actuator Packaging
Canard ( Stinger ) ……………
Tail ( AMRAAM )
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Tail ( AMRAAM ) …………………………………………………………………
Jet Vane / Tail ( Javelin ) ……
Movable Nozzle ( THAAD ) ……………………………………………………………
Summary of Weight Summary of Weight
Conceptual Design Weight Prediction Methods and WeightConsiderations Missile system weight, cg, moment of inertia
Factors of safety
Aerodynamic heating
St t
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Structure
Dome
Propulsion
Insulation
Power supply
Actuator
Manufacturing Processes for Low Parts Count, Low Cost
Precision castings Vacuum assisted RTM
Pultrusion / Extrusion
Filament winding
Summary of Weight ( cont ) Summary of Weight ( cont )
Design Considerations
Airframe materials
Insulation materials
Seeker dome materials
Thermal stress
Aerodynamic heating
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Aerodynamic heating
Technologies
MEMS
Composites
Titanium alloys
High density insulation
High energy and power density power supply
High torque density actuators
Discussion / Questions?
Classroom Exercise ( Appendix A )
Weight Problems Weight Problems
1. Propulsion system and structure weight are driven by f_____ o_ s_____
requirements.
2. For a ballistic range greater than about 200 nautical miles, a t__ s____ missileis lighter weight.
3. Tactical missile weight is proportional to v_____.
4 Subsystem d for tactical missiles is about 0 05 lb / in3
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4. Subsystem d______ for tactical missiles is about 0.05 lb / in3
5. Modeling weight, balance, and moment-of-inertia is based on a build-up of s_________.
6. Missile structure factor of safety for free flight is usually about 1.25 for ultimate loads and about 1.10 for y____ loads.
7. Manufacturing processes that can allow low parts count include vacuumassisted resin transfer molding of composites and c______ of metals.
8.Low cost airframe materials are usually based on aluminum and steel whi lelight weight airframe materials are usually based c________ materials.
9. Graphite f iber has high strength and high m______ o_ e_________.
Weight Problems ( cont ) Weight Problems ( cont )
10. The recovery factors of stagnation, turbulent boundary layer, and laminar
boundary layer are 1.0, 0.9, and ___ respectively.
11. The most popular types of insulation for temperatures greater than 4,000 Rare charring insulators based on p_______ composites.
12. Tactical missiles experience transient heating, and with increasing time
the temperature approaches the r temperature
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the temperature approaches the r_______ temperature.
13. The inner wall temperature is nearly the same as the surface temperaturefor a t________ t___ structure.
14. A thermally thick surface is a good i________.
15. A low conductivity structure is susceptible to thermal s_____.
16. The minimum gauge thickness is often set by the m____________ process.
17. A very thin wall structure is susceptible to localized b_______.
18. Ejection loads and flight control loads often result in large b______moment.
19. An approach to increase the tactical missile propellant / motor weightfraction over the typical value of 72% would be c________ motor case.
Weight Problems ( cont ) Weight Problems ( cont )
20. The required rocket motor case thickness is often driven by thecombustion chamber p_______.
21. A low aspect ratio delta wing has reduced w_____.
22. For low speed missi les, a popular infrared dome material is z___ s______.
23. A thermal battery provides high p
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23. A thermal battery provides high p____.24. The most popular type of actuator for tactical missiles is an
e________________ actuator.
Outline Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
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Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,Conversion Factors, Syllabus )
Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration
Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration
Establish Baseline Al t Mission
Al t Baseline
Define Mission Requirements
Aerodynamics
Propulsion
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Yes
MeetPerformance?
Measures of Merit and ConstraintsNo
No
Yes
Resize / Alt Conf ig / Subsystems / Tech
opu s o
Weight
Trajectory
Flight Envelope Should Have Large Max Range,Small Min Range, and Large Off Boresight
Off Boresight Flyout Envelope / Range
•Max•Min
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•Min
Forward Flyout Envelope / Range•Max•Min
Examples of Max / Min Range Limitations:
Fire Control System Range and Off Boresight
Seeker Range, Gimbal Angle, and Tracking Rate
Maneuver CapabilityTime of Flight
Closing Velocity
Conceptual Design Modeling Versus Preliminary Design Modeling
Conceptual Design Modeling Versus Preliminary Design Modeling
Conceptual Design Modeling
1 DOF [ Axial force ( CDO), thrust, weight ]
2 DOF [ Normal force ( CN ), axial force, thrust, weight ]
3 DOF point mass [ 3 aero forces ( normal, axial, side ),
CDO
CN
CN
C A
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3 O po ass [ 3 ae o o ces ( o a , a a , s de ),thrust, weight ]
3 DOF pitching [ 2 aero forces ( normal, axial ), 1 aero
moment ( pitching ), thrust, weight ]4 DOF [ 2 aero forces ( normal, axial ), 2 aero moments( pitching, roll ing ), thrust, weight ]
Preliminary Design Modeling
6 DOF [ 3 aero forces ( normal, axial, side ), 3 aeromoments ( pitching, rolling, yawing ), thrust, weight ]
CN Cm
C A
C A
C A
C A
Cl
ClCN Cm
CN Cm
CnCY
CY
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-DOF Simplified Equations of Motion Show Drivers for Configuration Sizing
-DOF Simplified Equations of Motion Show Drivers for Configuration Sizing
+ Normal Force
α << 1 rad
γ+ MomentV
+ Thrust
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Configuration Sizing Implication
Ιy θ.. ≈ Ιy α.. ≈ q SRef d Cmα
α + q SRef d Cmδδ High Control Effectiveness ⇒ Cmδ
>Cmα
, Iy small ( W small ), q large
( W / gc ) V γ. ≈ q SRef CNαα + q SRef CNδ
δ - W cos γ Large / Fast Heading Change ⇒ CN
large, W small, q large
( W / gc ) V. ≈ T - C A SRef q - CNα α2 SRef q - W sin γ High Speed / Long Range ⇒ Total
Impulse large, C A small, q small
δW
+ Axial Force
Note: Based on aerodynamic cont rol
1.00E+07
1.00E+08
u i s e
R a n g e ,
f t
For Long Range Cruise, Maximize V sp , L / D,and Weight Fraction of Fuel / Propellant
For Long Range Cruise, Maximize V sp , L / D,and Weight Fraction of Fuel / Propellant
R = ( V Isp ) ( L / D ) ln [ WBC / ( WBC - WP )] , Breguet Range Equation
l Rocketw i t h A x i
s y m m e t r i c A i r f r a m e
T y p i c a l R a m j e t w
i t h A x i s y m m e t r i c
A i r f r a m e
T y p i c a l S u b s o n i
c T u r b o j e t w i t h
W i n g
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1.00E+05
1.00E+06
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
WP / WBC, Propellant or Fuel Weigh t / Weigh t at Begin of Cruise
R ,
C r u
( V ISP )( L / D ) = 2,000,000 ft ( V ISP )( L / D ) = 10,000,000 ft
( V ISP )( L / D ) = 25,000,000 ft
Example: Ramjet Baseline at Mach 3 / 60k ft altR = 2901 ( 1040 ) ( 3.15 ) ln [ 1739 / ( 1739 - 476 )]= ( 9,503,676 ) ln [ 1 / ( 1 - 0.2737 )] = 3,039,469 ft= 500 nm
Note: R = cruise range, V = cruise veloci ty, ISP = specific impulse, L = lift, D = drag,WBC = weight at begin of cruise, WP = weight of propellant or fuel
T y p i c a l R o c k e t w
Efficient Steady Flight Is Enhanced by High L / D and Light Weight
Efficient Steady Flight Is Enhanced by High L / D and Light Weight
Steady Level Flight Steady Climb Steady Descent ( Glide )
T = DL = W
L
D T
W
γC
T – D
L
DT
W
V∞
γC VC
D – T
L
D
TW
γD
V
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SIN γD = ( D – T ) / W = VD / V∞
VD = ( D – T ) V∞/ WRD = Δh / tan γD = Δh ( L / D )
WγDVD
• Small Angle of At tack• Equilibrium Flight• VC = Velocity of Climb• VD = Velocity of Descent• γC = Flight Path Angle During Climb
• γD = Flight Path Angle During Descent• V∞ = Total Velocity• Δh = Incremental Altitude• RC = Horizontal Range in Steady Climb• RD = Horizontal Range in Steady Dive ( Glide )
Note:
Reference: Chin, S.S., “ Missile Configuration Design,”McGraw Hil l Book Company, New York, 1961
V∞T = W / ( L / D ) SIN γc = ( T – D ) / W = Vc / V∞
Vc = ( T – D ) V∞ / W
RC = Δh / tan γC = Δh ( L / D )
Flight Trajectory Lofting / Shaping Provides Extended Range
Flight Trajectory Lofting / Shaping Provides Extended Range
Altitude
Apogee or Cruise
Glide
Climb
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RangeRMAX
Rapid Pitch Up
Line-Of-Sight Trajectory
RMAX
Lofted Trajectory Design Guidelines for Horizontal Launch: – High thrust-to-weight ≈ 10 for safe separation – Rapid pi tch up minimizes time / propellant to reach efficient altitude – Climb at α ≈ 0 deg with thrust-to-weight T / W ≈ 2 and q ≈ 700 psf to minimize drag /
propellant – Apogee at q ≈ 700 psf, fol lowed by either ( L / D )MAX cruise or ( L / D )MAX glide
Small Turn Radius Using Aero Control Requires High Angle of Attack and Low Altitude Flight
Small Turn Radius Using Aero Control Requires High Angle of Attack and Low Altitude Flight
100000
1000000
o u s T
u r n R a d i u s , f t
RT = V / γ. ≈ 2 W / ( gc CN SRef ρ )
Assumption: Hor izontal Turn
Note for Example Figure:W = Weight = 2,000 lba / b = 1 ( circu lar cross section ), No wingsCN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 αl / d = Length / Diameter = 10
SRef = 2 ft2
C = 0 2
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1000
10000
0 5 10 15 20
Delta Alph a, Deg
R T , E x a m p l e I n s t a n t a n e o
h = sea level h = 20k ft h = 40k ft
h = 60k ft h = 80k ft
CDO= 0.2
( L / D )Max = 2.5q( L / D )Max
≈ 700 psf α( L / D )Max
= 15 degT( L / D )Max
= 740 lb
Example:
Δ α = 10 deg
CN = 0.94
h = 40k ft ( ρ = 0.000585 slug / ft3 )
RT = 2 ( 2,000 ) / [( 32.2 ) ( 0.94 ) ( 2 ) (0.000585 )] = 112,000 ft
Note: Require ( RT )Missile ≤ ( RT )Target, for small miss distance
High Turn Rate Using Aero Control Requires High Angle of Attack and High Velocity
High Turn Rate Using Aero Control Requires High Angle of Attack and High Velocity
10
15
20
, T u r n R a t e , d e g / s
γ.= gc CN ρ V SRef / ( 2 W ), rad / s
Assumption: Hor izontal Turn
Example for Lif ting Body at Alti tude h = 20,000 ft: Assume:• W = Weight = 2,000 lb• a / b = 1 ( circu lar cross section )• No wings• Negligib le tail lift• Neutral static stabilityC = sin 2 cos ( / 2 ) + 2 ( l / d ) sin2
n = 1 0 0 g
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0
5
10
0 1000 2000 3000
Veloc ity, ft / s
E x a m p l e G a m m a D o t
Alpha = 15 deg Alpha = 30 deg
Alpha = 90 deg
CN = sin 2 α cos ( α / 2 ) + 2 ( l / d ) sin2 α• SRef = 2 ft2
• l / d = Length / Diameter = 10• α = 15 deg• V = 2000 ft / s
Then:• N = Normal Force = CN q SRef
CN = sin [ 2 ( 15 )] cos ( 15 / 2 ) + 2 ( 10 ) sin2 ( 15 ) =0.50 + 1.34 = 1.835
q = Dynamic Pressure = 0.5 ρ V2 = 0.5 ( 0.001267 ) (2000 )2 = 2534 psf
N = 1.835 ( 2534 ) ( 2 ) = 9,300 lbN / W = 9300 / 2000 = 4.65 gγ.
= 32.2 ( 1.835 ) ( 0..001267 ) ( 2000 ) ( 2 ) / [ 2 ( 2000 )]= 0.0749 rad / s = 4.29 deg / s
For Long Range Coast, Maximize Initial Velocity and Altitude and Minimize Drag Coefficient
For Long Range Coast, Maximize Initial Velocity and Altitude and Minimize Drag Coefficient
0.6
0.8
1
V / Vi = { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t }
{[ gc ρ AVG SRef ( CD0 ) AVG ] / ( 2 W )} R = ln { 1 – [ gc2ρ AVG SRef ( CD0 ) AVG / ( 2 W )] [ sin γ ] t
2
+ {[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t }
Note: Based on 1 DOF coast
dV / dt = - gc CD0SRef q / W – gc sin γ
Assumptions:
• γ = constant
V / Vi @ γ = 0 deg
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0
0.2
0.4
0 0.5 1 1.5 2
Example for Rocket Baseline:
•W = WBO = 367 lb, SRef = 0.349 ft2, Vi = 2,151 ft / s , γ = 0 deg, ( CD0) AVG = 0.9, h = 20,000 ft ( ρ = 0.00127 slug / f t3 ), t = 10 s
•[( gc ρ SRef ( CD0) AVG Vi ) / ( 2 W )] t = {[ 32.2 ( 0.00127 ) ( 0.349 ) ( 0.9 ) ( 2151 )] / [ 2 ( 367 ) ]} 10 = 0.376
•V / Vi = 0.727 ⇒ V = 0.727 x 2151 = 1564 ft / s, { [( gc ρ SRef ( CD 0) AVG )] / ( 2 W )} R = 0.319 ⇒ Rcoast = 18,300 ft or 3.0 nm
[( g c ρ SRef CD0Vi ) / ( 2W )] t , Non-dimensional Coast Time
• α ≈ 0 deg
• D > W sin γ
V = velocity during coast
Vi = initial velocity ( begin coast )
R = coast range
Vx = V cos γ, Vy = V sin γ
Rx = R cos γ, Ry = R sin γ
{[ g c ρ AVG SRef (CD0) AVG ] / ( 2 W )} R
@ γ = 0 deg
For Ballistic Range, Maximize Initial Velocity,Optimize Launch Angle, and Minimize Drag For Ballistic Range, Maximize Initial Velocity,Optimize Launch Angle, and Minimize Drag
0 4
0.6
0.8
1
1.2
Vx / Vi = cos γi / { 1 + {[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t }
( Vy + gc t ) / Vi = sin γi / { 1 + {[ gc ρ AVG SRef ( CD
0 ) AVG Vi ] / ( 2 W )} t }
{[ gc ρ AVG SRef (CD0) AVG ] / ( 2 W cos γi )} Rx
= ln { 1 + [ gc ( ρ ) AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t }
{[ gc ρ AVG SRef (CD0) AVG ] / ( 2 W sin γi )} ( h – h i + gc t2 / 2 )
= ln { 1 + {[ gc ρ AVG SRef ( CD0 ) AVG Vi ] / ( 2 W ) t }
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0
0.2
0.4
0 0.5 1 1.5 2
Example for Rocket Baseline:
•W = 367 lb, SRef = 0.349 ft2, Vi = VBO = 2,151 ft / s, γi = 0 deg, ( CD0) AVG = 0.9, h i = 20,000 ft, ρ AVG = 0.00182 slug / ft3, t = 35 s
•[ gc ρ SRef ( CD0) AVG Vi / ( 2 W )] t = { 32.2 ( 0.00182 ) ( 0.349 ) ( 0.9 ) ( 2151 ) / [ 2 ( 367 ) ]} 35 = 1.821
•Vx / Vi = 0.354 ⇒ Vx = 762 ft / s, ( Vy + 32.2 t ) / Vi = 0.354 ⇒ Vy = - 1127 ft / s, {[ gc ρ SRef ( CD 0)] / ( 2 W cos γi )} Rx = 1.037 ⇒
Rx = 42,900 ft o r 7.06 nm, {[ g c ρ AVG SRef ( CD 0) AVG ] / ( 2 W sin γi )} ( h – h i + 16.1 t2 ) = 1.037 ⇒ h = 0 ft
{[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t, Non-dimensional Time
Assumptions: Thrust = 0, α = 0 deg, D > W sin γ, flat earth
Nomenclature: V= velocity dur ing ballistic f light, Vi = initialvelocity, Rx = horizontal range, h = altitude, hi = initial altitude,V
x
= horizontal velocity, Vy
= vertical velocity
High Propellant Weight, High Thrust, and Low Drag Provide High Burnout Velocity
High Propellant Weight, High Thrust, and Low Drag Provide High Burnout Velocity
0.3
0.4
0.5
0.6
0.7
S P ) ,
N o n d i m e n s i o n a l
m e n t a
l V e l o c i t y
ΔV / ( gc ISP ) = - [ 1 – ( D AVG / T ) – ( W AVG sin γ / T )] ln ( 1 - Wp / Wi )
Example for Rocket Baseline:
Assume γ = 0 deg
Assume Mi = 0.8, h = 20k ft
Wi = WL = 500 lb
For boost, WP = 84.8 lb
WP / WL = 0.1696
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0
0.1
0.2
0 0.1 0.2 0.3 0.4 0.5
Wp / Wi, Propellant Fraction
D
e l t a V / ( g I
I n c r e m
DAVG / T = 0 DAVG / T = 0.5 DAVG / T = 1.0
ISP = 250 s
TB = 5750 lb
Assume D = D AVG = 635 lb
D AVG / T = 0.110ΔV / [( 32.2 ) ( 250 )] = - ( 1 - 0.110 )ln ( 1 - 0.1696 ) = 0.1654
ΔV = ( 0.1654 ) ( 32.2 ) ( 250 ) =1331 ft / s
Note: 1 DOF Equation of Motion with α ≈ 0 deg, γ = constant, Wi = initial weight, W AVG = average weight, WP =propellant weight, ISP = specific impulse, T = thrust, Mi = init ial Mach number, h = altitude, D AVG = average drag,ΔV = incremental veloc ity , gc = gravitation constant, Vx = V cos γ, Vy = V sin γ, Rx = R cos γ, Ry = R sin γ
Note: R = ( Vi + ΔV / 2 ) tB, where R = boost range, Vi = initial velocity, tB = boost time
High Missile Velocity and Lead Are Required to Intercept High Speed Crossing Targets
High Missile Velocity and Lead Are Required to Intercept High Speed Crossing Targets
4
3 Note:Proportional Guidance
VM = Missi le Veloci tyVT = Target Veloci tyA = Target Aspect
VM VTL A
VM sin L = VT sin A, Proportional Guidance Trajectory
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VM / VT 2
00 10 20 30 40 50
L, Lead Angle, Deg
1
A = 90°
A = 45°
A Target AspectL = Missi le Lead Angle
≈Seeker Gimbal
Example:
L = 30 deg
A = 45 degVM / VT = sin ( 45° ) / sin ( 30° ) =
1.42
Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration
Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration
Establish Baseline Al t Mission
Al t Baseline
Define Mission Requirements
Aerodynamics
Propulsion
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Yes
MeetPerformance?
Measures of Merit and ConstraintsNo
No
Yes
Resize / Alt Conf ig / Subsystems / TechWeight
Trajectory
Summary of Flight Performance Summary of Flight Performance
Flight Performance Activi ty in Missile Design
Compute range, velocity, time-to-target, off boresight Compare with requirements
Discussed in This Chapter
Equations of motion Flight performance drivers
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Propulsion alternatives range comparison
Steady level flight required thrust
Steady climb and steady dive range prediction Cruise prediction
Boost prediction
Coast prediction
Ballistic flight prediction
Turn radius and turn rate predict ion
Target lead for proport ional homing guidance
Summary of Flight Performance ( cont ) Summary of Flight Performance ( cont )
Flight Performance Strongly Impacted by Aerodynamics
Propulsion
Weight
Discussion / Questions?
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Classroom Exercise ( Appendix A )
Flight Performance Problems Flight Performance Problems
1. Flight trajectory calculation requires input from aero, propulsion, and w_____.
2. Missi le flight envelope can be characterized by the maximum effective range,minimum effective range, and o__ b________.
3. Limitations to the missile effective range include the fire control system,seeker, time of flight, closing velocity, and m_______ capabili ty.
4. 1 DOF simulation requires modeling only the thrust, weight, and a____ f____.5 A 3 DOF simulation that models 3 aero forces is called p m simulation
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5. A 3 DOF simulation that models 3 aero forces is called p____ m___ simulation.
6. A simulation that includes 3 aero forces ( normal, axial, side ), 3 aero moments( pitch, roll, yaw ), thrust, and weight is called a _ DOF simulation.
7. The pitch angular acceleration θ.. is approximately equal to the second timederivative of the a____ o_ a_____.
8. Cruise range is a function of velocity, specific impulse, L / D, and f___ fraction.
9. If thrust is equal to drag and lift is equal to weight, the missi le is in s_____l____ flight .
10. Turn rate is a function of normal force, weight, and v_______.
Flight Performance Problems ( cont ) Flight Performance Problems ( cont )
11. Coast range is a function of initial velocity, weight, drag, and the t___ of flight.
12. Incremental velocity due to boost is a function of ISP, drag, and p_________weight fraction.
13. To intercept a high speed crossing target requires a high speed missile with ahigh g_____ angle seeker.
14. An analytical model of a rocket in co-altitude, non-maneuvering flight can bedeveloped by patching together the flight phases of boost and c
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developed by patching together the flight phases of boost and c____.
15. An analytical model of a rocket in a short range, off-boresight intercept can bedeveloped by patching the flight phases of boost and t___.
16. An analytical model of a guided bomb in non-maneuvering flight can bedeveloped from the flight phase of a steady d___.
17. An analytical model of an unguided weapon can be developed from theb________ flight phase.
18. An analytical model of a ramjet in co-altitude, non-maneuvering flight can bedeveloped by patching the flight phases of boost and c_____.
Outline Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
M f M it d L h Pl tf I t ti
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Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,Conversion Factors, Syllabus )
Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration
Missile Concept Synthesis Requires Evaluation of Alternatives and Iteration
Establish Baseline Al t Mission
Al t Baseline
Define Mission Requirements
Aerodynamics
Propulsion
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Yes
MeetPerformance?
No
No
Yes
Resize / Alt Conf ig / Subsystems / TechWeight
Trajectory
Measures of Merit and Constraints
Measures of Merit and Launch Platform Integration Should Be Harmonized
Measures of Merit and Launch Platform Integration Should Be Harmonized
Robustness
LethalityCost
Launch Platform
Integration /
Firepower
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Miss Distance
Carriage and
LaunchObservables
Other
SurvivabilityConsiderations
Reliability
Balanced Design
Tactical Missiles Must Be Robust Tactical Missiles Must Be Robust
RobustnessTactical Missiles Must Have Robust Capability to
Handle Adverse Weather
Clutter
Local Climate
Robustness
Lethal i ty
Miss Distance
Carriage andLaunch
Observables
Other
Survivability
Cons iderati ons
Reliability
Cost
Launch P latform
Integrati on /Fi repower
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Flight Environment Variation
UncertaintyCountermeasures
EMI / EMP
This Section Provides Examples of Requirements for Robustness
Adverse Weather and Cloud Cover Are Pervasive Adverse Weather and Cloud Cover Are Pervasive
0.6
0.8
1.0
Cloud Cover Over Ocean
CloudCover
Annual Average
Fraction of Cloud Cover North Atlantic
Descending Ai r
Rising Ai r Rising Ai r
Descending
South Pole
Region
NOAA satelli te imageof earth cloud cover
North PoleRegion
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0.0
0.2
0.4
85°N 65°N 45°N 25°N 5°N 0° 5°S 25°S 45°S 65°S 85°S
Over Land
Note: Annual Average Cloud Cover Global Average = 61%Global Average Over Land = 52%Global Average Over Ocean = 65%
Latitude Zone
Deserts ( Sahara,Gobi, Mojave )
Argentina, Southern Af rica and Austral ia
Descending Ai r
Reference: Schneider, Stephen H. Encyclopedia of Climate and Weather . Oxford University Press, 1996.
Radar Seekers Are Robust in Adverse Weather Radar Seekers Are Robust in Adverse Weather
Note:EO attenuation throughcloud at 0.1 g / m3 and 100m visibilityEO attenuation throughrain at 4 mm / hHumidi ty at 7.5 g / m3
Millimeter wave andmicrowave attenuationthrough cloud at 0.1gm / m3 or rain at 4 mm / h
1000
100
10
A T I O N ( d
B / k m )
H2O
O2, H2O
H2O
O2
O2
CO2
CO2
H2O, CO2
H2O
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3 cm 3 mm 0.3 mm 30 µm 3.0 µm
Increasing Wavelength
Increasing Frequency
Source: Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997
0.3 µm
gm / m3 or rain at 4 mm / h1
0.1
0.01
A T T E N U A
100 1 THz 10 100 1000
INFRAREDSUBMILLIMETER
10 GHz
MILLIMETER VISIBLE
H2O
2
H2O20° C1 ATM
EO sensors are ineffectivethrough cloud cover
Radar sensors have good tosuperior performancethrough c loud cover and rain
RADAR
X Ku K Ka Q V W Very Long Long Mid Short
O3
Radar Seekers Are Desirable for Robust Operation within the Troposphere Cloud Cover Radar Seekers Are Desirable for Robust Operation within the Troposphere Cloud Cover
40
30
h,Altitude
Cirrus ( 16 – 32k ft )
Cumulonimbus ( 2 – 36k ft )
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20
10
0
Altitude,103 ft
Note:•IR seeker may be able to operate “Under the Weather” at elevations less than 2,000 ft using GPS / INS midcourse guidance•IR attenuation through cloud cover greater than 100 dB per km. Cloud droplet size ( 0.1 to 50 μm ) causes resonance.•mmW has ~ 2 dB / km attenuation through rain. Typical rain drop size ( ∼ 4 mm ) is comparable to mmW wavelength.
Fog
Altocumulus ( 9 – 19k ft )
Cumulus ( 2 – 9k ft )Stratus ( 1 – 7k ft )
Al tostratus ( 8 – 18k ft )
Sensor Adverse
Weather
Impact
ATR / ATA
in Clutter
Range Moving
Target
Volume
Search
Time
Hypersonic
Dome
Compat.
Diameter
Required
Weight and
Cost
Maturity
• SAR
• Acti veImagingmmW
• Passive
ImagingmmW• Acti ve
Imaging IR- -
-
-
-
Precision Strike Missile Target Sensors Are Complemented by GPS / INS / Data Link Sensors
-
-
- -
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Note: Superior Good Below Average Poor
(LADAR)• Active Non-
image IR(LADAR)
• Active Non-image mmW
• PassiveImaging IR
• Acoust ic
• GPS / INS /
Data Link
-
-
-
--
--
-
-
Imaging Sensors Enhance Target Acquisition / Discrimination
Imaging Sensors Enhance Target Acquisition / Discrimination
Imaging LADAR Imaging Infrared SAR
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Passive Imaging mmW Video of Imaging Infrared Video of SAR Physics
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Example of Mid Wave –Long Wave IR Seeker Comparison ( cont )
Example of Mid Wave –Long Wave IR Seeker Comparison ( cont )
Next, Calculate LWIR Seeker Detection Range
RD = { ( IT )Δλ ηa Ao { D* / [( Δf p )1/2
( Ad )1/2
]} ( S / N )D-1
}1/2
, m ( IT )Δλ = ε Lλ ( λ2 - λ1 ) AT, W sr -1
Lλ = 3.74 x 104 / { λ5 { e[ 1.44 x 104 / ( λ TT )] – 1 }} , W cm -2 sr -2 μm-1
Assume λ = 10 μm, λ2 = 13 μm, λ1 = 7 μm, then
Lλ = 0.00310 W cm-2 sr -2 μm-1, ( IT )Δλ = 26.7 W sr -1
Assume Hg0.80Cd0.20Te detector at λ = 10 μm and 77 K ⇒ D* = 5 x 1010 cm1/2 Hz1/2 W-1
RD = { ( 26.7 ) ( 1 ) ( 0.01267 ) {( 5 x 1010 ) / [( 50 )1/2 ( 1.049 )1/2 ]} ( 5 )-1 }1/2 = 21,600 m
MWIR Seeker Versus LWIR Seeker Selection Depends Upon Target Temperature
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MWIR Seeker Versus LWIR Seeker Selection Depends Upon Target Temperature
0
5
10
15
0 500 1000 1500 2000
TT, Target Temperature, K
W a v e l e n g t h f o r M a x S p e c t r a l
R a d i a n c e ,
M i c r o n s
Subsonic Airframe
Mach 4 Air frame
Jet Engine
Rocket Plume
Flare
( λ )( Lλ )max= 2898 / TT, Wein’s Displacement Law, TT in K
M W I R
L W I R
Example: TT = 300 K
( λ )( Lλ )max= 2898 / TT
= 2898 / 300 = 10.0 μm
GPS / INS Provides Robust Seeker Lock-on in Adverse Weather and Clutter
GPS / INS Provides Robust Seeker Loc -on in Adverse Weather and Clutter •
4 8 0 P i x e l s
640 Pixels ( 300 m )
Target Image
175 m
Seeker Lock-on @ 850 m to go ( 1 pixel = 0.47 m )
3 m GPS / INS error ⇒ nMreq= 0.15 g, σ < 0.1 m
Seeker Lock-on @ 500 m to go ( 1 pixel = 0.27 m )
3 m GPS / INS error ⇒ nMreq= 0.44 g, σ < 0.1 m
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44 m88 m
Note: = Target Aim Point and Seeker Tracking Gate, GPS / INS Accuracy = 3 m, Seeker 640 x 480 Image, Seeker FOV = 20 deg, Proportional Guidance Navigation Ratio = 4, Velocity = 300 m / s, G&C Time Constant = 0.2 s.
Seeker Lock-on @ 250 m to go ( 1 pixel = 0.14 m )
3 m GPS / INS error ⇒ nMreq= 1.76 g, σ = 0.9 m
Seeker Lock-on @ 125 m to go ( 1 pixel = 0.07 m )
3 m GPS / INS error ⇒ nMreq= 7.04 g, σ = 2.2 m
Data Link Update at Seeker Lock-on Reduces Moving Target Error
Data Link Update at Seeker Lock-on Reduces Moving Target Error
100
1000
S e e k e r L
o c k - o n ,
VT = 1 m / s
VT = 10 m / s
VT 100 /
TESeekerLock-on
= [ TLE2 + ( VT
tLatency
)2 ]1/2
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10
0.1 1 10 100 1000
Target Latency at Seeker Lock-on, s
T a r g e t E
r r o r a t S VT = 100 m / s
VT = 1000 m / s
Note: tSeekerLock-on = Seeker Lock-on time, tUdate = Data Link Update Time, VT = Target Veloci ty, TLE = Target LocationError at Update = 10 m
Example:TLE = 10 mtSeekerLock-on = 100 stUdate = 90 sVT = 10 m / stLatency = tSeeker - tUdate = 100 – 90 = 10 s
TESeekerLock-on = [ TLE2
+ ( VT tLatency )2
]1/2
= { 102 + [ 10 ( 10 )]2 ]1/2
= 100.5 m
Optimum Cruise Is a Function of Mach Number,Altitude, and Planform Geometry
Optimum Cruise Is a Function of Mach Number,Altitude, and Planform Geometry
40
60
80
100
120
h ,
A l t i t u d
e ,
k f t
q = 200 psf
q = 500 psf
q = 1,000 psf
q = 2,000 psf
q = 5,000 psf
Ramjet
Scramjet
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0
20
40
0 1 2 3 4 5 6 7
M, Mach number
hq = 10,000 psf
q = 20,000 psf
Note:• U.S. 1976 Standard Atmosphere• For Efficient Cruise, ( L / D )Max for Cruising L ift ing Body Typically Occurs for 500 < q < 1,000 psf • ( L / D )Max for Cruise Miss ile with Low Aspect Ratio Wing Typically Occurs for 200 < q < 500 psf • q ≈ 200 psf lower limit for aero control
Note: q = 1 / 2 ( ρ V2 )Wingless Subsonic Turbojet
Subsonic Turbojet with Low Aspect Ratio Wing
Missile Guidance and Control Must Be Robust for Changing Events and Flight Environment Missile Guidance and Control Must Be Robust for Changing Events and Flight Environment
Booster ShutdownTransient at High Mach
Engine Start Transient Pitch-Over atHigh Alpha
Example High Performance Missi le Has• Low-to-High Dynamic Pressure
• Negative-to-Posi tive Static Margin• Thrust / Weight / cg Transients• High Temperature• High Thermal Load• High Vibration• High Acoustics
Level Out
Cruise
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Engine Shutdown
Transient
Air Launch at LowMach ( high α ) /
DeployCompressedCarriage Surfaces
Booster Ignition
Pitch-Up at High Alpha
Climb Terminal at HighDynamic Pressure
Dive
Precision Impactat α ≈ 0 Deg
Vertical Launch in Cross Wind ( high α )/ Deploy Compressed Carriage Surfaces
Pitch-Over at High Alpha
Design Robustness Requires Consideration of Flight Altitude
Design Robustness Requires Consideration of Flight Altitude
1
0 20 40 60 80 100
A l t i t u d e /
S e a L e v e l
Temperature Ratio
Troposphere Stratosphere
Troposphere ( h < 36,089 ft )
T / TSL
= 1 – 6.875 x 10-6 h, h in ft
p / pSL = ( T / TSL )5.2561
ρ / ρSL = ( T / TSL )4.2561
Stratosphere ( h > 36089 ft )
T = constant = 390 R
p / pSL = 0.2234 e - ( h – 36089 ) / 20807
ρ / ρSL = 0.2971 e - ( h – 36089 ) / 20807
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0.01
0.1
h, Geometr ic Altitude, kf t
C h a r a c t e r
i s t i c a t
C h a r a c t e r i s t i c a t
p
Pressu re Ratio
Density Ratio
Speed o f Sound Ratio
Note: TSL = Temperature at sea level, pSL = pressure at sea level, ρSL = density at sea level, cSL = speedof sound at sea level, h = altitude in ft .
U.S. Standard Atmosphere, 1976 – TSL = 519 R – pSL = 2116 lb / ft2
– ρSL
= 0.00238 slug / ft3
– cSL = 1116 ft / s
0.5
1
1.5
m S t a n d a r d A t m o s p h e r e Ratio: Cold-to-Standard
AtmosphereRatio: Hot-to-Standard Atmosphere
Ratio: Polar-to-Standard Atmosphere
Ratio: Tropic-to-Standard Atmosphere
( + 30 % )
( - 23% )
Design Robustness Requires Consideration of Cold and Hot Atmospheres
Design Robustness Requires Consideration of Cold and Hot Atmospheres
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0
0 5
Temp Density Speed of
Sound
V a r i a t i o n f r o
Note:
• Based on properties at sea level
•U. S. 1976 Standard Atmosphere: Temperature = 519 R, Density = 0.002377 slug / ft3, Speed of sound = 1116 ft / s
Design Robustness Is Required to Handle Uncertainty Design Robustness Is Required to Handle Uncertainty
0.5
1
N o r m a l i z e d P D F
Narrow Uncertainty ( e.g.,
SDD Flight Perfo rmance )
Broad Uncertain ty ( e.g.,Conceptual Design FlightPerformance )
Skewed Uncertainty ( e.g.,Cost, Weigh t, MissDistance )
Bimodal Uncertain ty ( e.g.,
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0
-20 -10 0 10 20
Typical % Error from Forecast Value
E x a m p l e Multi -mode Seeker Target
Location )
Uniform Bias Uncertainty( e.g., Seeker Aim PointBias )
Note for normal distribution: PDF = { 1 / [ σ ( 2 π )1/2 ]} e {[( x - μ ) / σ ]2 / 2 }
Counter-Countermeasures by Missile Enhance Design Robustness Counter-Countermeasures by Missile Enhance Design Robustness
Examples of CM ( Threat )
EOCM directed laser
flare
smoke
RFCM active radar
jammer
Examples of CCM ( Missile )
Imaging Seeker Multi-spectral / Multi-
mode Seeker
Temporal Processing
Hardened GPS / INS standoff acquisition
Integrated GPS / INS
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chaff
Decoy
Low Observables
Speed
Altitude
Maneuverability
Lethal Defense
directional antenna
pseudolite / differential
GPS
ATR / ATA
Speed
Altitude
Maneuverability Low Observables
Saturation
IIR ( I2R AGM-130 ) ………………………………………………
Two Color IIR ( Python 5 )
Acoustic - IIR ( BAT ) …………………………………………..
Examples of Countermeasure-Resistant Seekers Examples of Countermeasure-Resistant Seekers
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IIR – LADAR ( LOCAAS ) ………………………………………
ARH – mmW ( AARGM )
ARH - IIR ( Armiger ) …………………………………………….
TBM / TELs
OilRefineries
Naval
Armor
Transportation ChokePoints ( Bridges,Railroad Yards, TruckParks )
Counter Air Aircraft
C3II
Artillery
Air Defense ( SAMs,
AAA )
A Target Set Varies in Size and Hardness
Lethality
Robustness
Lethal i ty
Miss Dis tance
Carriage and
LaunchObservables
Other
SurvivabilityCons iderati ons
Reliability
Cost
Launch P latform
Integrati on /
Fi repower
Example of Precision Strike Target Set
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Parks )
Examples of Targets where Size and Hardness Drive Warhead Design/ Technology
•Small Size, Hard Target: Tank ⇒ Small Shaped Charge, EFP, or KE
Warhead
•Deeply Buried Hard Target: Bunker ⇒ KE / Blast Frag Warhead
•Large Size Target: Bui lding ⇒ Large Blast Frag WarheadVideo Example of Precis ion Str ike Targets
76% of Baghdad Targets Struck First Night of Desert Storm Were C 3 Time Critical Targets 76% of Baghdad Targets Struck First Night of Desert Storm Were C 3 Time Critical Targets Targets: 1. Directorate of Military Intelligence; 2, 5, 8,13, 34. Telephone switching stations; 3. Ministry of
Defense national computer complex; 4. Electrical transfer station; 6. Ministry of Defense headquarters; 7. Ashudad
highway bridge; 9. Railroad yard; 10. Muthenaairfield ( military
section ); 11. Air Force headquarters; 12. Iraqi Intelligence
Service; 14. Secret Police complex; 15. Army storage depot;
16. Republ ican Guard headquarters; 17. New presidentialpalace; 18. Electrical power station; 19. SRBM assembly
factory ( Scud ); 20. Baath Party headquarters; 21.Government conference center; 22 Ministry of Industry and
1
2
3
4
56
7
8
23
2425
2631
32
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Government conference center; 22. Ministry of Industry and
Military Production; 23. Ministry of Propaganda; 24. TV
transmitter; 25, 31. Communications relay stations; 26.Jumhuriya highway bridge; 27. Government Control Center
South; 28. Karadahighway bridge ( 14th July Bridge ); 29.
Presidential palace command center; 30. Presidential
palace command bunker; 32. Secret Police headquarters;
33. Iraqi Intelligence Service regional headquarters; 35.National Air Defense Operations Center; 36. Ad Dawrahoil
refinery; 37. Electrical power p lant
Source: AIR FORCE Magazine, 1 Apr il 1998
891011
12
13 1415 16
17
1819
20
2122
2426
27
28
2930
3233
3435
36
37
Anti-Fixed Surface Target Missiles ( large size, wings, subsonic, blast frag warhead )
AGM-154 Storm Shadow / Scalp KEPD-350 BGM-109 AGM-142
Anti-Radar Site Missiles ( ARH seeker, high speed or duration, blast frag warhead )
AGM-88 AS-11 / Kh-58 ARMAT Armiger ALARM
Anti-Ship Missiles ( large size, KE / blast frag warhead, and high speed or low altitude )
Type of Target Drives Precision Strike Missile Size, Speed, Cost, Seeker, and Warhead
Type of Target Drives Precision Strike Missile Size, Speed, Cost, Seeker, and Warhead
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MM40 AS-34 Kormoran AS-17 / Kh-31 BrahMos SS-N-22 / 3M80
Anti-Armor Missiles ( small size, hit-to-kill, low cost, shape charge, EFP, or KE warhead )
Hellfire LOCAAS MGM140 AGM-65 LOSAT
Anti-Buried Target Missiles ( large size, high fineness, KE / blast frag warhead )
CALCM GBU-28 GBU-31 Storm Shadow MGM-140Permission of Missile Index.
Examples of Light Weight Air Launched Multi- Purpose Precision Strike Weapons Examples of Light Weight Air Launched Multi- Purpose Precision Strike Weapons Weapon Fixed
SurfaceTargets(1)
Moving
Targets (2) Time
Critical
Targets (3)
Buried
Targets (4) Adverse
Weather (5) Firepower (6)
Example New Missile
AGM-65
Small Diameter Bomb
AGM-88
–
– –
– – –
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Hellfire / Brimstone /Longbow
LOCAAS –
–
Note:
Superior
Good
Average
Poor –
(1) – Multi-mode warhead desired. GPS / INS provides precision ( 3 m ) accuracy.
(2) - Seeker or high bandwidth data link required for terminal homing.
(3) - High speed with duration required⇒ High payoff of high speed / loiter and powered submunition.
(4) - KE penetration warhead required⇒ High impact speed, low drag, high density, long length.
(5) - GPS / INS, SAR seeker, imaging mmW seeker, and data link have high payoff.
(6) - Light weight required. Light weight also provides low cost
Blast Is Effective at Small Miss Distance Blast Is Effective at Small Miss Distance
100
1000
e s s u r e R a t i o t o U n d i s t u r b e d P r e s s u r
Δ p / p0 = 37.95 / ( z p01/3 ) + 154.9 / ( z p0
1/3 )2 + 203.4 / ( z p01/3 )3 + 403.9 / ( z p0
1/3 )4
z = r / c1/3
Note:
Based on bare sphere of pentolite ( Ec1/2 = 8,500 ft / s )
Δp = overpressure at distance r from explosion
p0 = undisturbed atmospheric pressure, psi
z = scaling parameter = r / c1/3
r = distance from center of explosion, ft
c = explosive weight , lb
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1
10
0 2 4 6 8 10
z ( p0 )1/3
D e l t a p / p 0 , O
v e r p r e
Reference: US Army Ordnance Pamphlet ORDP-2—290-Warheads, 1980
Example for Rocket Baseline Warhead:
c = 38.8 lbh = 20k feet, p0 = 6.8 psi
r = 10 ft
z = 10 / ( 38.8 )1/3 = 2.95
z p01/3 = 5.58
Δp / p0 = 13.36
Δp = 90 psi
Guidance Accuracy Enhances Lethality Guidance Accuracy Enhances Lethality
Rocket Baseline Warhead Against Typical Aircraft TargetPK > 0.5 if σ < 5 ft ( Δ p > 330 psi,fragments impact energy > 130kft-lb / ft2 )
PK > 0.1 if σ < 25 ft ( Δp > 24 psi,
fragments impact energy > 5k ft-lb / ft2 )
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Note: Rocket Baseline 77.7 lb warheadC / M = 1, spherical blast, h = 20k f t.
Video of AIM-9X Flight Test Missile Impact on Target( No Warhead )
Warhead Blast and Fragments Are Effective at Small Miss Distance Warhead Blast and Fragments Are Effective at Small Miss Distance
Hellf ire 24 lb shaped charge warheadfragments are from natural fragmenting case
2.4 mwitness
plate
Roland 9 kg explosively formed warheadmulti -projectiles are from preformed case
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Video of Guided MLRS 180 lb b last f ragmentation warhead
Maximum Total Fragment Kinetic Energy Requires High Charge-to-Metal Ratio Maximum Total Fragment Kinetic Energy Requires High Charge-to-Metal Ratio
0.2
0.3
0.4
o n - d i m e n s i o n
a l K i n e t i c E n e r g y
KE = ( 1 / 2 ) Mm Vf 2 = Ec Mc / ( 1 + 0.5 Mc / Mm )
Note:Based on Gurney EquationCylindr ical WarheadKE = Total Kinetic EnergyMm = Total Mass Metal FragmentsVf = Fragment Velocity
Ec = Energy Per Unit Mass ChargeMc = Mass of ChargeMwh = Mass of Warhead = Mm + Mc
L o w K E
H i g h K E
Example:
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0
0.1
0 0.5 1 1.5 2 2.5 3Mc / Mm, Charge-to-Metal Ratio
( K E / M w h ) / E c , N o
Reference: Carleone, Joseph (Editor), Tactical Missile Warheads (Progress in Astronautics and Aeronautics, Vol 155), AIAA, 1993.
Example:
Rocket Baseline Warhead
Mc = 1.207 slug
Mm = 1.207 slug
Mc / Mm = 1
Ec Mc = 52,300,000 ( 1.207 ) =63,100,000 ft -lb
KE = 63100000 / [1 + 0.5 ( 1 )]= 42,100,000 ft-lb
Multiple Impacts Are Effective Against Threat Vulnerable Area Subsystems Multiple Impacts Are Effective Against Threat Vulnerable Area Subsystems
0.4
0.5
0.6
0.7
0.8
0.9
1
r o b a b i l i t y o f K i l
Av / Atp = 0.1
Av / Atp = 0.5
Av / Atp = 0.9
PK = 1 - ( 1 - Av / Atp)nhits
Note:• Av = Target vulnerable area• Atp
= Target presented area
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0
0.1
0.2
0.3
0 5 10 15 20 25 30
nhits, Number of Impacts on Target
P
k ,
P p
Example:If Av / Ap = 0.1, nhits = 22 gives PK = 0.9
If Av / Ap = 0.9, nhits = 1 gives PK = 0.9
Small Miss Distance Improves Number of Warhead Fragment Hits Small Miss Distance Improves Number of Warhead Fragment Hits
20
40
60
80
100
N u m b e r o f F
r a g m e n t H i t s Wwh = 5 lb
Wwh = 50 lb
Wwh = 500 lb
Example for Rocket Baseline:
WWH = 77.7 lbMc / Mm = 1, Wm = 38.8 lb = 17,615 g
Average fragment weight = 3.2 g
nfragments = 17615 / 3.2 = 5505
nhits = nfragments [ AP / ( 4 π σ2 )]
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00 20 40 60 80 100
Sigma, Miss Distance, ft
N g
AP = Target presented area = 20 ft2
σ = Miss distance = 25 ft
nhits = 5505 { 20 / [( 4 π ) ( 25 )2 ]} = 14
Kinetic energy per square foot. = KE/ ( 4 π σ2 ) = 42100000 / [ 4 π ( 25 )2 ] =5,360 ft-lb / ft2
Note:• Spherical blast with uni formly distributed fragments• nhits = n fragments [ AP / ( 4 π σ2 )]• Warhead charge / metal weight = 1• Average fragment weight = 50 grains ( 3.2 g )• AP = Target presented area = 20 ft2
High Fragment Velocity Requires High Charge-to- Metal Ratio High Fragment Velocity Requires High Charge-to- Metal Ratio
4000
6000
8000
10000
m e n t V e l o c
i t y ,
f t / s
HMX Explosive
TNT Explosive
Note: Based on the Gurney equation for acylindrical warhead
HMX Explosive ( 2 EC )1/2 = 10,230 ft / s
TNT Explosive ( 2 EC )1/2 = 7,600 ft / sV = Fragment initial velocity ft / s
Vf = ( 2 Ec )1/2 [ ( Mc / Mm ) / ( 1 + 0.5 Mc / Mm )]1/2
Example:
Baseline Rocket Warhead
HMX E l i
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0
2000
0 1 2 3
Mc / Mm, Charge-to-Metal Ratio
V f , F r a g Vf = Fragment initial velocity , ft / s
Ec = Energy per uni t mass of charge, ft2
/ s2
Mc = Mass of chargeMm = Total mass of all metal fragmentsMwh = Mass of warhead = Mm + Mc
HMX Explosive
MC / Mm = 1Vf = 8,353 ft / s
P e r f o r a t i o n b y F r a g m e n t ( i n )
50 Grains( 3.2 g )
150 Grains ( 9.7 g )
.5
.375
.25
Small Miss Distance Improves Fragment Penetration Small Miss Distance Improves Fragment Penetration
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Note: Typical air-to-air missi le warhead
• Fragments init ial veloci ty 5,000 ft / s• Sea level• Average fragment weight 3.2 g• Fewer than 0.3% of the fragments weigh more than 9.7 g for nominal 3.2 g preformed warhead fragments• Small miss distance gives less reduction in f ragment velocity, enhancing penetration
2010 30 40 50 60 70 80 90 100 110 120
S t e e l P
.125
Miss Distance ( ft )
Hypersonic Hit-to-Kill Enhances Energy on Target for Missiles with Small Warheads
Hypersonic Hit-to-Kill Enhances Energy on Target
for Missiles with Small Warheads
3
4
5
6
7
8
9
a l E n e r g y o n
T a r g e t / W a r h e a d
C h a r g e E n e r g y
Weight o f missile /Weight o f charge = 20
Weight o f missile /Weight o f charge = 10
Weight o f
ET / EC = [( 1 / 2 ) ( WMissile / gc ) V2 + EC ( WC / gc )] / [ EC ( WC / gc )]
Example for Rocket Baseline:
WMissile = 367 lb
WC = 38.8 lb
WMissile / WC = 9.46
V = 2,000 ft / s
( 1 / 2 ) ( WMissile / gc ) V2 = 22.8 x 106 ft-lb )
EC ( WC / gc ) = 63.1 x 106 ft-lb
E / E = 1 36
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0
1
2
0 1000 2000 3000 4000 5000 6000
Missi le Clos ing Veloc ity, ft / s
E T / E C ,
T o t Weight o f
missile /
Weight o f charge = 5
Weight o f missile /Weight o f
charge = 2
Note: Warhead explosive charge energy based on HMX, ( 2 EC )1/2 = 10,230 ft / s.
1 kg weight at Mach 3 clos ing velocity has kinetic energy of 391,000 J ⇒ equivalent chemical energy of 0.4 lb TNT.
ET / EC = 1.36
Kinetic Energy Warhead Density, Length, and Velocity Provide Enhanced Penetration Kinetic Energy Warhead Density, Length, and Velocity Provide Enhanced Penetration
20
30
40
50
60
n e t r a t i o n / P e n e t r a t o r D i a m e t e r f o r
S t e e l o n C o n c r e t e
Note:V > 1,000 ft / s
l / d > 2Non-deforming ( high strength, sharp nose )
penetrator l = Penetrator lengthd = Penetrator diameter V = Impact velocity
ρP= Penetrator densityρT= Target densi tyσT= Target ultimate stress
Example for 250 lb Steel Penetrator l / d = 10
P / d = [( l / d ) – 1 ] ( ρP / ρT )1/2 + 3.67 ( ρP / ρT )2/3 [( ρT V2 ) / σT ]1/3
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0
10
20
0 1000 2000 3000 4000
V, Veloci ty, ft / s
P / d ,
T a r g e t P e n
l / d = 2 l / d = 5 l / d = 10
l / d = 10 l = 48 in ( 4 ft ) d = 4.8 in ( 0.4 ft ) Concrete target ρP = 0.283 lb / in3 ( 15.19 slug / f t3 ) ρT = 0.075 lb / in3 ( 4.02 slug / ft 3 ) V = 4,000 ft / s σT = 5,000 psi ( 720,000 psf )
P / d = [ 10 – 1 }( 15.19 / 4.02 )1/2 + 3.67 ( 15.19/ 4.02 )2/3 [ 4.02 ( 4000 )2 / 720000 ]1/3 = 57.3
P = ( 57.3 ) ( 0.4 ) = 22.9 ft
Source: Christman, D.R., et al, “Analysis of High-Velocity Projectile Penetration,” Journal of Applied Physics, Vol 37, 1966
Standard Missile 3 ( NTW ) PAC-3 THAAD
Examples of Kinetic-Kill Missiles Examples of Kinetic-Kill Missiles
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LOSAT LOSAT Video
CEP Approximately Equal to 1σ Miss Distance CEP Approximately Equal to 1σ Miss Distance
MedianTrajectory
Extreme MissileTrajectory
Missile Circu lar Error Probable ( 50%of shots within circle )
Missile 1σ Miss Distance ( 68%of shots within circle for anormal distribut ion of error )
Target
Presented Target Area
Miss DistanceRobustness
Lethality
Miss Distance
ObservablesSurvivability
Reliability
Cost
Launch Platform
Integration /Firepower
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Extreme MissileTrajectory
Hypothetical PlaneThrough Target
For a normal distribution of error:
Probability < 1σ miss distance = 0.68
Probability < 2σ miss distance = 0.95
Probability < 3σ miss distance = 0.997
Source: Heaston, R.J. and Smoots, C.W., “ Introduction to Precision Guided Munit ions,” GACIAC HB-83-01, May 1983.
A Collision Intercept Has Constant Bearing for a Constant Velocity, Non-maneuvering Target A Collision Intercept Has Constant Bearing for a Constant Velocity, Non-maneuvering Target
Example of Miss
( Line-of-Sight Angle Diverging )( Line-of-Sight Angle Rate L
.≠ 0 )
Example of Collision Intercept
( Line-of-Sight Angle Constant )( Line-of-Sight Angle Rate L
.= 0 )
Overshoot Miss
( LO S ) 1 > ( LO S )
0 ( LOS )1 = ( LOS )0t
t1
t2
t
t1
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Missile Target
Seeker Line-of-Sight
Missile Target
t0 t0
Seeker Line-of-Sight
Note: L = Missile Lead A = Target Aspect
AL L
A
A Maneuvering Target and Initial Heading Error
Cause Miss
A Maneuvering Target and Initial Heading Error
Cause Miss Target
Missile
CollisionPoint
+ZγM0
L
Maneuvering : d2Z + dZ + N’ Z = – N’ cos A 1 aT t2
A
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Target: τ
dt2 dt to – t t
o – t cos L 2
aT t
Initial HeadingError
: τ d2Zdt2
+ dZdt
+ N’ Zto – t
= – VM γM0
Note: to - t = 0 at intercept, causing discontinuity in above equations.
N’ = Effective navigation ratio = N [ VM / ( VM - VT cos A )]N = Navigation ratio = ( dγ / dt ) / ( dL / dt )τ = Missile time constant, VM= Velocity of missile, γM0
= Initial fl ightpath angle error of missile, to = Total time of fl ight, aT = Accelerationof target, VT = Velocity of target
Reference: Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design , D. Van NostrandCompany, Inc., Princeton, New Jersey, 1960
Missile Time Constant Causes Miss Distance Missile Time Constant Causes Miss Distance
τ is a measure of missile ability to respond totarget condition changes
τ equals elapsed time from input of targetreturn unti l missile hascompleted 63% or ( 1 – e-1 ) of correctivemaneuver ( t = τ )
τ also called “ rise time”
Contributions to time constant τ Control effectiveness ( τδ )
Control dynamics ( e.g., actuator rate ) ( τ . )
Input
Output
t i
Time
Timet i
63%
τ
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y ( g ) ( δ )
Dome error slope ( τDome ) Guidance and control filters ( τFilter )
Other G&C dynamics ( gyro dynamics,accelerometer, processor latency, etc )
Seeker errors ( resolution, latency, blind range,tracking, noise, glint, amplitude )
Approach to estimate τ τ = τδ + τδ
. + τDome
Acceleration Achieved Acceleration Commanded
= 1 – e- t / τ
Example for Rocket Baseline:
M = 2, h = 20k ft , coastτ = τδ + τδ
. + τDome
= 0.096 + 0.070 + 0.043 = 0.209 s
Time Constant τδ
for Control Effectiveness Is
Driven by Static Margin
Time Constant τδ
for Control Effectiveness Is
Driven by Static Margin
Assumptions for τδ Control surface deflection limited
Near neutral stability
Equation of motion is
α
..
= [ ρ V2
S d Cmδ / ( 2 Iy ) ] δMax
Integrate to solve for αMax
αMax= [ ρ V2 S d Cmδ/ ( 8 Iy ) ] δMax τδ
2
τδ is given by
αMax, δMax
– δMax
αMax
τδ / 2 τδ
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τδ = [ 8 Iy ( αMax / δMax ) / ( ρ V2
SRef d Cmδ )]1/2
Contributors to small τδ
Low fineness ( small Iy / ( SRef d ))
High dynamic pressure ( low altitude / highspeed )
Large Cmδ
Example for Rocket Baseline:
W = 367 lb, d = 0.667 ft, SRef = 0.349 ft2, Iy = 94.0 slug-ft2,
M = 2, h = 20k ft ( ρ = 0.001267 slug / ft3 ),
αMax= 9.4 deg, δMax
= 12.6 deg, Cmδ = 51.6 per rad,
τδ = { 8 ( 94.0 ) ( 9.4 / 12.6 ) / [ 0.001267 ( 2074 )2 ( 0.349 )( 0.667 ) ( 51.6 ) ]}1/2 = 0.096 s
Time Constant τδ
.
for Flight Control System Is Driven by Actuator Rate Dynamics Time Constant τ
δ
.
for Flight Control System Is Driven by Actuator Rate Dynamics
Assumptions for τδ.
Control surface rate limited ( δ.
= δ.
Max ) Near neutral stability
Equation of motion for δ.= +/- δ
.
Max
α...
= [ ρ V2 S d Cmδ / ( 2 Iy ) ] δ.
Max
Equation of motion for “ perfect” responseδ.= ∞, δ = δMax
α..
= [ ρ V2 S d Cmδ / ( 2 Iy ) ] δMax
τδ. is d ifference between actual response
to and “ perfect” ( ) response
α Max, δ Max α Max α Max
- δ Max
δ.
1
Example for Rocket Baseline.
τδ.τδ
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to αMax and perfect ( τδ ) response
Then
τδ. = 2 δMax / δ
.
Max
Note:Response for control rate limitResponse for no control rate limit
• δ.
Max= 360 deg / s, δ
Max= 12.6 deg
• τδ. = 2 ( 12.6 / 360 ) = 0. 070 s
| R | = 0.05 ( lN / d – 0.5 ) [ 1 + 15 ( Δ f / f ) ] / ( d / λ )
τDome = N’ ( VC / VM ) | R | ( α / γ.
)
α / γ.= α ( W / gc ) VM / { q SRef [ CNα
+ CNδ/ ( α / δ )]}
Substituting gives τDome = N’ W VC | R | / { gc q SRef [ CNα+ CNδ
/ ( α / δ )]}
Time Constant τDome for Radome Is Driven by Dome Error Slope Time Constant
τDome for Radome Is Driven by Dome Error Slope
0.03
0.02 E r r o r S l o p e ,
g
TangentOgiveDomeΔ f / f = 0.05
f / f = 0 02
Example for Rocket Baseline at M = 2, h = 20k ft, q =2725 psf
Assume VT = 1,000 ft / s, giving VC = 3,074 ft / s
Assume N’ = 4, f = 10 GHz or λ = 1.18 in, Δ f / f = 0.02
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0.01
0 | R |
@ d /λ
= 1
0 ,
R a d o m
e
D e g / D e g
0 1 2 3
lN / d, Nose Fineness
Faceted or WindowDome
Multi-lensDome
Δ f / f = 0.02
Δ f / f = 0Configuration data are lN / d = 2.4, d = 8 in, SRef = 0.349ft 2, W = 367 lb, CNα= 40 per rad, CNδ
= 15.5 per rad, α / δ= 0.75
Compute | R | = 0.05 ( 2.4 – 0.5 ) [ 1 + 15 ( 0.02 )] / ( 8 /1.18 ) = 0.0182 deg / deg
τDome = 4 ( 367 ) ( 3074 ) ( 0.0182 ) / [ 32.2 ( 2725 ) ( 0.349 )
( 40 + 15.5 / 0.75 )] = 0.043 s
High Initial Acceleration Is Required to Eliminate a Heading Error High Initial Acceleration Is Required to Eliminate a Heading Error
aM t0 / ( VM γM ) = N’ ( 1 – t / t0 ) N ’ – 2
aM t0 / ( VM γM ),Non-dimensional
Acceleration
6
4
2.5
3
4
6
Note: Proportional Guidanceτ = 0t0 = Total Time to CorrectHeading Error aM = Acceleration of MissileVM = Velocity of Missile
γM = Init ial Heading Error of MissileN’ = Effective Navigation Ratio
Example: Exoatmospheric Head-on Intercept, N’ = 4
Midcourse lateral error at t = 0 ( seeker lock-on ) =200 m, 1 σ
Rlock-on = 20000 m ⇒ γM = 200 / 20000 = 0.0100 rad
VM = 5000 m / s , VT = 5000 ⇒ t0 = Rlock-on / ( VM + VT ) =20000 / ( 5000 + 5000 ) = 2.00 s
aM t0 / ( VM γM ) = 4
aM = 4 ( 5000 ) ( 0.0100 ) / 2.00 ) = 100 m / s2
nM = 100 / 9.81 = 10.2 g
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2
00 0.2 0.4 0.6 0.8
t / t0, Non-dimensional Time1.0
N’ = 2
M g
Missile Minimum Range May Be Driven By 4 to 8 Time Constants to Correct Initial Heading Error Missile Minimum Range May Be Driven By 4 to 8 Time Constants to Correct Initial Heading Error
0.1
0.3
0.2
N’ = 3
N’ = 4
N’ = 6
Note: Proportional Guidance
( σHE )Max shown in figure is the envelope of adjoint solution( σHE )Max = Max miss distance ( 1 σ ) from heading error, ft
VM = Velocity of missile, ft / sγM = Init ial heading error , radt0 = Total time to correct heading error, sτ = Missile time constant, sN’ = Effective navigation ratio
Example: Ground Target, N’ = 4, = 0.2, GPS /
| ( σHE )Max / ( VM γM to ) |
σHE = VM γM t0 e-( t0 / τ ) j = 1∑N ’ – 1 { ( N’ - 2 )! [ - ( t0 / τ )] j / [( j – 1 )! ( N’ – j – 1 )! j! ]}
If N’ = 3, σHE = VM γM t0 e-( t0 / τ ) [ ( t0 / τ ) - ( t0 / τ )2 / 2 ]If N’ = 4, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - ( t0 / τ )2 + ( t0 / τ )3 / 6 ]
If N’ = 5, σHE = VM γM t0 e-( t0/ τ ) [( t0 / τ ) – ( 3 / 2 ) ( t0 / τ )2 + ( t0 / τ )3 / 2 – ( t0 / τ )4 / 24 ]If N’ = 6, σHE = VM γM t0 e-( t0 / τ ) [( t0 / τ ) - 2 ( t0 / τ )2 + ( t0 / τ )3 - ( t0 / τ )4 / 6 + ( t0 / τ )5 / 120 ]
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0.1
0
0 2 4 6 8tO / τ 10References:
•Donatelli, G.A., et al, “ Methodology for Predict ing Miss Distance for Air Launched Missi les,” AIAA-82-0364, January 1982•Bennett, R.R., et al, “ Analyt ical Determination of Miss Distances for Linear Homing Navigation ,” Hughes Memo 260, March 1952
Example: Ground Target, N 4, τ 0.2, GPS /
INS error = 3 m, Rlock-on = 125 m, γM = 3 / 125 =0.024 rad, VM = 300 m / s, t0 = 125 / 300 = 0.42 s
t0 / τ = 0.42 / 0.2 = 2.1, (σHE )Max / ( VM γM to ) = 0.12
( σHE )Max = 0.12 ( 300 ) ( 0.024 ) ( 0.42 ) = 2.2 m
Required Maneuverability Is about 3x the Target Maneuverability for an Ideal ( τ = 0 ) Missile Required Maneuverability Is about 3x the Target Maneuverability for an Ideal ( τ = 0 ) Missile
4
Assumptions:τ = 0
VM > VT
6
3
4
N’ = 2.5
N’ = 2 ∞↑
Wheret = Elapsed Timet0 = Time to TargetN’ = Effective Navigation Ratio
Missile-to-Target
nM
nT
,
nM / nT = [ N’ / ( N’ – 2 )] [ 1 – ( 1 – t / t0 )N ’ – 2 ]
Example:
τ = 0, N’ = 3, t / t0 = 1
⇒ nM / nT = 3
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2
00 0.2 0.4 0.6 0.8 1.0
t / t0, Non-Dimensional Time
4
6
Missile to Target
AccelerationRatio
Target Maneuvers Require 6 to 10 Time Constants to Settle Out Miss Distance Target Maneuvers Require 6 to 10 Time Constants to Settle Out Miss Distance
0 1
0.3
0.2
( σMAN )Max
gc nT τ2
N’ = 3
N’ = 4
Note: Proportional Guidance( σMAN )Max is the envelope of adjoint solu tion( σMAN )Max = Max miss ( 1 σ ) from target accel, ftnT = Target acceleration, ggc = Gravitation constant, 32.2τ = Missile time constant, s
σMAN = gc nT τ2 e-( t0 / τ ) j = 2∑N ’ – 1 { ( N’ - 3 )! [ - ( t0 / τ )] j / [( j – 2 )!
( N’ – j – 1 )! j! ]}If N’ = 3, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 ]If N’ = 4, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 6 ]If N’ = 5, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 3 + ( t0 /τ )4 / 24 ]If N’ = 6, σMAN = gc nT τ2 e-( t0 / τ ) [ ( t0 / τ )2 / 2 - ( t0 / τ )3 / 2 + ( t0 /τ )4 / 8 - ( t0 / τ )5 / 120 ]
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0.1
00 2 4 6 8tO / τ 10
N’ = 6N’ = Effective navigation ratioτ0 = Time of flight, s
References:
•Donatelli, G.A., et al, “ Methodology for Predict ing Miss Distance for Air Launched Missi les,” AIAA-82-0364, January 1982•Bennett, R.R., et al, “ Analyt ical Determination of Miss Distances for Linear Homing Navigation ,” Hughes Memo 260, March 1952
An Aero Control Missile Has Reduced Miss
Distance at Low Altitude / High Dynamic Pressure
An Aero Control Missile Has Reduced Miss
Distance at Low Altitude / High Dynamic Pressure
1
10
100
M a x i m u m M i s s D u e
t o M a n e u v e r i n g
T a r g e t , f t
h = SL
h = 20k f t
h = 40k f t
h = 60k f t
h = 80k f t
( σMan )Max = 0.13 gc nT τ2 @ N’ = 4, t0 / τ = 2Note: Proportional guidanceTarget maneuver init iated for max miss ( t0 / τ = 2 )
( σMan )Max in figure = Envelope of adjoint missdistanceτ = Missile time constant, sN’ = Effective navigation ratio = 4nT = Target acceleration, ggc = Gravitation constant = 32.2
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0.1
1
0 2 4 6 8 10
Target Maneuverability, g
R o c k e t B a s e l i n e
M
Example for Rocket Baseline at Mach 2, coasting
Assume:
• nT = 5g, VT = 1,000 ft / s, head-on intercept
•h = 20k ft ⇒ τ = 0.209 s
( σMan )Max = 0.13 ( 32.2 )( 5 )( 0.209 )2 = 0.9 ft•h = 80k ft ⇒ τ = 1.17 s
( σMan )Max = 0.13 ( 32.2 )( 5 )( 1.17 )2 = 28.7 ft
Glint Miss Distance Driven by Seeker Resolution,
Missile Time Constant, and Navigation Ratio
Glint Miss Distance Driven by Seeker Resolution,
Missile Time Constant, and Navigation Ratio
0.2
0.4
0.6
0.8
( b T ) R e s ,
N o n d i m e
n s i o n a l M i s s D i s t a n c
e
f r o m G l i n t @ 2 H z B a n d w i d t h
σGlint = KN’ ( W / τ )1/2
KN
’ = 0.5 ( 2 KN
’ = 4 )N’ / 4
KN’ = 4 = 1.206
W = ( bT )Res2 / ( 3 π2 B )
Note:Proportional guidance Adjo int miss distance
σGlint = Miss distance due to gl int noise, ftW = Glint no ise spectral density , ft2 / Hzτ = Missile time constant, sN’ = Effective navigation ratio( bT )Res = Target span resolut ion at seeker blind range, ftB = Noise bandwidth, Hz ( 1 < B < 5 Hz )
Example: Rocket Baseline at Mach 2, h= 20k ft altitude ⇒ τ = 0.209 s
Assume:
•N’ = 4
•B = 2 Hz
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0
0 0.2 0.4 0.6 0.8 1
Tau, Missi le Time Constant, s
S i g m a
/
N' = 3 N' = 4 N' = 6
•B = 2 Hz
•( bT )Res = b t = 40 ft ( radar seeker beamwidth resolution of target wing span )
Calculate:
W = ( 40 )2 / [ 3 π2 ( 2 )] = 27.0 ft2 / Hz
σGlint
/ ( bT
)Res
= KN
’ ( W / τ )1/2 / ( bt
)Res
= 1.206 ( 27.0 / 0.209 )1/2 / 40 = 0.343
σGlint = 0.343 ( 40 ) = 13.7 ftReference:Bennett, R.R., et al, “Analyt ical Determination of Miss Distances for Linear Homing Navigation,” Hughes Memo 260, March 1952
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Missile Carriage RCS and Launch Plume Are
Considerations in Launch Platform Observables
Missile Carriage RCS and Launch Plume Are
Considerations in Launch Platform Observables
Missile Carriage Alternatives Internal Carriage: Lowest Carriage RCS
Conformal Carriage: Low Carriage RCS
Conventional External Pylon or External Rail Carriage: High Carriage RCS
Plume Alternatives Min Smoke: Lowest Launch Observables ( H2O Contrail )
Reduced Smoke: Reduced Launch Observables ( e.g., HCl Contrail from APOxidizer )
Carriage and
Launch Observables
Robustness
Lethality
Miss Distance
ObservablesSurvivability
Reliability
Cost
Launch PlatformIntegration /Firepower
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High Smoke: High Launch Observables ( e.g., Al2O3 Smoke from Al Fuel )
Center Weapon Bay Best for Ejection Launchers
F-22 Bay Loadout: 3 AIM-120C, 1 GBU-32 F-117 Bay Loadout: 1 GBU-27, 1 GBU-10 B-1 Bay Loadout: 8 AGM-69
Video Side Weapon Bay Best for Rail Launchers
Examples of Weapon Bay Internal Carriage and
Load-out
Examples of Weapon Bay Internal Carriage and
Load-out
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AMRAAM Loading in F-22 Bay F-22 Side Bay: 1 AIM-9 Each Side Bay RAH-66 Side Bay: 1 AGM-114, 2 FIM-92, 4 Hydra 70 Each Side Bay
Minimum Smoke Propellant Has Low Observables Minimum Smoke Propellant Has Low Observables
High Smoke Example: AIM-7
Particles ( e.g., metal fuel ) at allatmosphere temperature.
Reduced Smoke Example: AIM-120
Contrail ( HCl from AP oxidizer ) at T < -10° Fatmospheric temperature.
Minimum Smoke Example: Javelin
Contrail (H2O ) at T < -35º Fatmospheric temperature.
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High Smoke Motor
Reduced Smoke Motor
Minimum Smoke Motor
High Altitude Flight and Low RCS Enhance
Survivability
High Altitude Flight and Low RCS Enhance
Survivability
100
1000
10000
100000
1000000
10000000
P t , R a d a r T r a
n s m i t t e d P o w e
r
R e q u i r e d f o
r D e t e c t i o n , W
Example for Pt= 50,000 W:
Not detected if:
h > 25k ft for σ = 0.001 m2
h > 77k ft for σ = 0.1 m2
Pt = ( 4 π )3 Pr R4 / ( Gt Gr σ λ2 ) Other SurvivabilityConsiderations
Robustness
Lethality
Miss Distance
ObservablesSurvivability
Reliability
Cost
Launch PlatformIntegration /Firepower
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0 20 40 60 80 100
h, Geometric Alt itude, kft
RCS = 0.1 m2 RCS = 0.01 m2 RCS = 0.001 m2
Note: Range Slant Angle = 20 deg, Gt = Transmitter Gain = 40 dB, Gr = Receiver Gain = 40 dB, λ = Wavelength = 0.03
m, Pr = Receiver Sensitivity = 10-14 W, σ = radar cross section ( RCS ) Based on Radar Range Equation with ( S / N )Detect = 1 and Unobstructed Line-of-Sight
Mission Planning and High Speed Enhance
Survivability
Mission Planning and High Speed Enhance
Survivability
0
1
2
x p ( V / R m a x ) , N o n - d i m e n s i o n a l T h r e a t
E x p o s u
r e T i m e
texp = 2 ( Rmax / V ) cos [ sin-1 ( yoffset / Rmax )] – treact
Example:
yoffset = 7 nm, Rmax = 10 nm = 60750 ft,y / R = 0.7, t = 15 s
R m a x treact V
texp V
Flyby
SAM
Siteyoffset
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0 0.2 0.4 0.6 0.8 1
yoffset / Rmax, Non-dimens ional Offset Distance from
Threat
t e
treac t ( V / Rmax ) = 0 treac t ( V / Rmax ) = 1.0
Note: Based on assumption of constant altitude, constant heading flyby of threat SAM site with an unobstructed line-of-sight. texp = exposure time toSAM threat, Rmax = max detection range by SAM threat, V = flyby veloci ty,yoffset = flyby offset, treact = SAM site reaction time from detection to launch
yoffset max react
If V = 1000 ft / s, t react ( V / Rmax ) = 0.247
•texp ( V / Rmax ) = 2 cos [ sin-1 ( 7 / 10 )] –15 ( 1000 / 60746 ) = 1.428 – 0.247 = 1.181
•texp = 1.181 ( 60746 / 1000 ) = 71.7 s
If V = 4000 ft / s, t react ( V / Rmax ) = 0.988
•texp ( V / Rmax ) = 0.440
•texp = 0.440 ( 60746 / 4000 ) = 6.7 s
Low Altitude Flight and Terrain Obstacles
Provide Masking from Threat
Low Altitude Flight and Terrain Obstacles
Provide Masking from Threat
500
1000
1500
2000
h m a s k ,
A l t i t u d e t h a t
M a s k s L i n e - o f - S i g h t
E x p o s u r e t o S u
r f a c e T h r e a t , f t
hmask = ( hmask )obstacle + ( hmask )earth = hobstacle ( Rlos / Robstacle ) + ( Rlos / 7113 )2
hmask = alti tude that allows obstacle and earth
curvature to mask exposure to surface threat LOS, ft
hobstacle = height of obs tacle above terrain, ft
Rlos = line-of-sight range to surface threat, ft
Robstacle = range from surface threat to obstacle, ft
Height of low hill or tall tree ≈ 100 ft
Height of moderate hill ≈ 200 ft
Height of high hill ≈ 500 ft
Height of low mountain ≈ 1000 ft
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0
0 10 20 30 40
Rlos, Line-of-Sight Range to Surface Threat, nm
Rlos ( hobstacle / Robstacle ) = 100 ft
Rlos ( hobstacle / Robstacle ) = 200 ftRlos ( hobstacle / Robstacle ) = 500 ft
Rlos ( hobstacle / Robstacle ) = 1000 ft
Example:hobstacle = 200 ft
Robstaacle = 5.0 nm = 30395 ft
Rlos = 10.0 nm = 60790 ft
Rlos ( hobstacle / Robstaacle ) = 60790 ( 200 /30395 ) = 400 ft
hmask = 200 ( 60790 / 30395 ) + ( 60790 /7113 )2 = 400 + 73 = 473 ft above terrain
Insensitive Munitions Improve Launch Platform
Survivability
Insensitive Munitions Improve Launch Platform
Survivability Critical Subsystems
Rocket motor or fuel tank
Warhead Severity Concerns Ranking of Power Output - Type
1. Detonation ( ~ 0.000002 s r ise time )
2. Partial detonation ( ~ 0.0001 s rise time )
3. Explosion ( ~ 0.001 s rise time )4. Deflagration or propulsion rise time ( ~ 0.1 s rise time )
5. Burning ( > 1 s )
Design and test considerations ( MIL STD 2105C )
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Fragment / bul let impact or blast Sympathetic detonation
Fast / slow cook-off fi re
Drop
Temperature Vibration
Carrier landing ( 18 ft / s sink rate )
Robustness
Lethality
Miss Distance
ObservablesSurvivability
Reliability
Cost
Launch PlatformIntegration /Firepower
High System Reliability Is Provided by High Subsystem Reliability and Low Parts Count High System Reliability Is Provided by High Subsystem Reliability and Low Parts Count
Typical Event /Subsystem
Rsystem ≈ 0.94 = R Arm X RLaunch X RStruct X R Auto XR Act X RSeeker X RIn Guid X RPS X RProp X RFuze X RW/H
Arm ( 0.995 – 0.999 )Launch ( 0.990 – 0.995 )
Structure ( 0.997 – 0.999 )
Autopi lot ( 0.993 – 0.995 )
Actuators ( 0.990 – 0.995 )
Seeker ( 0.985 – 0.990 )
Inertial Guidance ( 0.995 – 0.999 )
P S l ( 0 995 0 999 )
Reliability
Typical System Reliability
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Power Supply ( 0.995 – 0.999 )Propuls ion ( 0.995 – 0.999 )
Fuze ( 0.987 – 0.995 )
Warhead ( 0.995 – 0.999 )
0.90 0.92 0.94 0.96 0.98 1.00
Typical Reliability
Sensors, Electronics and Propulsion Drive
Missile Production Cost
Sensors, Electronics and Propulsion Drive
Missile Production Cost
Dome Seeker Guidance andControl
Propulsion•Rocket• Airbreather
Wings
Stabilizers
Warheadand Fuzing
AerothermalInsulation
FlightControl
Power Supply
Structure•Rocket• Airbreather
–
–
– – –
–
CostRobustness
Lethality
Miss Distance
ObservablesSurvivability
Reliability
Cost
Launch PlatformIntegration /Firepower
DataLink
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Very High( > 25% Production Cost )
–High( > 10% )
Moderate( > 5% )
Relatively Low( < 5% )
Note:System assembly and test ~ 10% production costPropulsion and structure parts count / cost of airbreathing missiles are higher than that of rockets
Sensors and Electronics Occupy a Large Portion
of a High Performance / High Cost Missile.
Sensors and Electronics Occupy a Large Portion
of a High Performance / High Cost Missile.
Example: Derby / R-Darter Missile
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Source: http://www.israeli-weapons.com/weapons/missile_systems/air_missiles/derby/Derby.html
Cost Considerations Cost Considerations
Life Cycle
System Development and Demonstration ( SDD )
Production
Logistics
Culture / processes
Relative Emphasis of Cost, Performance, Reliabil ity, Organization Structure
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Relaxed Mil STDs
IPPD
Profit
Competition
SDD Cost Is Driven by Schedule Duration and
Risk
SDD Cost Is Driven by Schedule Duration and
Risk
10
100
1000
10000
0 2 4 6 8 10 12 14
C S D D ,
S D D
C o s t i n M i l l i o n s
CSDD = $20,000,000 tSDD1.90, ( tSDD in years )
Example:
5 year ( medium risk ) SDD program
CSDD = $20,000,000 tSDD1.90
= ( 20,000,000 ) ( 5 )1.90
= $426,000,000
Low
Risk
SDD
High
Risk
SDD
Moderate
Risk
SDD
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0 2 4 6 8 10 12 14
tSDD, SDD Schedule Duration in Years
AGM-142 TOW 2 SLAM-ER MLRS LB Hellfire J ASSM Hellfire II
SLAM J DAM AGM-130 Harpoon ATACMS Tomahawk ESSM
AIM-120A J SOW HARM J avelin BAT PAC-3 PatriotNote: SDD required schedule duration depends upon risk. Should not ignore risk in shorter schedule.-- Source of data: Nicho las, T. and Rossi, R., “U.S. Missile Data Book, 1999,” Data Search Assoc iates, 1999 – SDD cost based on 1999 US$
Light Weight Missiles Have Low Unit Production
Cost
Light Weight Missiles Have Low Unit Production
Cost
100000
1000000
10000000
Javelin
Longbow Hellfire
AMRAAMMLRS
HARM
JSOW
Tomahawk
C1000th ≈ $6,100 WL0.758, ( WL in lb )
C
o s t o f M i s s i l e N u
m b e r 1 0 0 0 ,
U . S . $
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10000
10 100 1000 10000
Example:
2,000 unit buy of 100 lb missile:
C1000th ≈ $6,100 WL0.758 = 6100 ( 100 )0.758 =
$200,000
Cost of 2,000 miss iles = 2000 ( $200000 ) =$400,000,000
Note:-- Source of data: Nicholas, T. and Rossi, R., “U.S. Missi le Data Book, 1999,” Data Search Associates, 1999 – Unit product ion cost based on 1999 US$
C 1 0 0 0 t h , C
WL , Launch Weight, lb
Learning Curve and Large Production Reduce
Unit Production Cost
Learning Curve and Large Production Reduce
Unit Production Cost
0.1
1
/C 1 s t , C o s t o f U n i t x
/ C o s t o f F i r s t U n
i t
Javelin ( L = 0.764, C1st = $3.15M,Y1 = 1994 )
Long bow HF ( L = 0.761, C1st =$4.31M, Y1 = 1996 )
AMRAAM ( L = 0.738, C1st =$30.5M, Y1 = 1987 )
MLRS ( L = 0.811, C1st = $0.139M,Y1 = 1980 )
HARM ( L = 0.786, C1st = $9.73M,Y1 = 1981 )
JSOW ( L = 0.812, C1st = $2.98M,Y1 = 1997 )
Cx = C1st L log2x, C2x = L Cx , where C in U.S. 99$
Example:For a learningcurve coefficientof L = 80%, cost of uni t #1000 is 11%
the cost of the first
L = 1.0
L = 0.9
L = 0.8
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0.01
1 10 100 1000 10000 100000 1E+06
x, Number of Units Produced
C x / C Y1 1997 )
Tomahawk ( L = 0.817, C1st =$13.0M, Y1 = 1980 )
Source of data: Nicholas, T. and Rossi, R., “ U.S. Miss ile Data Book,1999,” Data Search Associates, 1999
Labor intensive learning curve: L < 0.8Machine intensive learning curve: L > 0.8 )
Contributors to the learning curve include:• More efficient labor • Reduced scrap• Improved processes
the cost of the firstunit L = 0.7
Low Parts Count Reduces Missile Unit
Production Cost
Low Parts Count Reduces Missile Unit
Production Cost
10
100
1000
10000
100000
1000000
P
a r t s C o u n t , H o u r s , o r C o s t ( U S
$ )
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0Parts Fasteners Circuit Cards Connectors Assembly /
Test Hours
Unit
Production
Cost ( US$ )
Current Tomahawk Tactical Tomahawk
Note: Tactical Tomahawk has superior flexibility ( e.g., shorter mission planning, in-flight retargeting, BDI / BDA,modular payload ) at lower parts count / cost and higher reliability. Enabling technologies for low parts count include:casting , pultrusion / extrusion, centralized electronics, and COTS.
Copperhead Seeker and Electronics Production Patriot Control Section Production
Video of Hellfi re Seeker and Electronics Production
Tactical Missile Culture Is Driven by Rate
Production of Sensors and Electronics
Tactical Missile Culture Is Driven by Rate
Production of Sensors and Electronics
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Peacetime Logistics Activity
•Contractor Post-production Engineering•Training Manuals / Tech Data Package•Simulation and Software Maintenance•Configuration Management
•Engineering Support•System Analysis•Launch Platform Integration•Requirements Documents•Coordinate Suppliers
•Storage Alternatives
•Wooden Round ( Protected )O R d ( H idi t T C i Sh k )
Logistics Cost Considerations Logistics Cost Considerations
Wartime Logistics Activity
•Deployment Alternatives• Ai rli ft
•Sealift•Combat Logistics
•Launch Platform Integration•Mission Planning•Field Tests•Reliability Data
•Maintainability Data•Effectiveness Data
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( )•Open Round ( Humidi ty, Temp, Corrosion, Shock )
•Reliability Maintenance•Surveillance•Testing
•Maintenance Al ternatives
•First level ( depot )•Two level ( depot, field )
•Disposal
y•Effectiveness Data•Safety Data
Simple: St inger More Sophisticated: Hawk and SLAMRAAM Complex: PAC-3
Very Complex: THAAD Video of Logistics Alternatives
Logistics Cost Lower for Simple Missile Systems Logistics Cost Lower for Simple Missile Systems
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Logistics Is Simpler for Light Weight Missiles Logistics Is Simpler for Light Weight Missiles
0
2
4
6
10 100 1000 10000
Missile Weight, lb
S u p p o r t P e r s o n n e l r e q u i r e d
f o r I n
s t a l l a t i o n
Support personnel f or installation with 50 lb lif t limit per person
Support personnel for installation with 100 lb lif t limit per person
Machine lift f or installation
Video of Simple Logistics fo r aLight weight Missile
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Predator ( 21 lb ) Sidewinder ( 190 lb ) Sparrow ( 500 lb ) Laser Guided Bomb ( 2,500 lb )
Small MEMS Sensors Can Provide Health
Monitoring, Reducing Cost and Weight
Small MEMS Sensors Can Provide Health
Monitoring, Reducing Cost and Weight
Micro-machined Electro-Mechanical Systems ( MEMS )
Small size / low cost semiconductor manufacturing process2,000 to 5,000 sensors on a 5 in sil icon wafer
Wireless ( RF ) Data Collection and Health Monitor ing
Distributed Sensors Over Missi le
Stress / strain
Vibration
Acoustics
Temperature
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pPressure
Reduced Logist ics Cost and Improved Reliabili ty
Health monitor ing
Reduced Weight and Production Cost
More Efficient Design
Missile Carriage Size, Shape, and Weight Are
Driven by Launch Platform Compatibility
Missile Carriage Size, Shape, and Weight Are
Driven by Launch Platform Compatibility
Surface Ships
CLS
~24” x 24”
263”
263”
~168”
3400 lb
3400 lb
~500 lb to3000 lb
~ 2 2 ” ~ 2 2
”
Fighters /Bombers /UCAVs
Rail /Ejection
VLS
Submarines
Launch Platform Integration / Firepower
Robustness
Lethality
Miss Distance
ObservablesSurvivability
Reliability
Cost
Launch PlatformIntegration /Firepower
22”
US Launch Platform Launcher Carriage Span / Shape Length Weight
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Ground
Vehicles158” 3700 lb
Helos
LaunchPods
Rail ∼13” x 13” 70” 120 lb
~ 2 8 ” ~ 2 8
”
Light Weight Missiles Enhance Firepower Light Weight Missiles Enhance Firepower
E, carry 1
C, carry 3
C, carry 1
E, carry 2
C, carry 2E, carry 3
E, carry 1
C, carry 1
E, carry 2
C, carry 2
5,000 lb
4,000 lb
3,000 lb
2,000 lb
1,000 lb
M a x S t r i k e
W e a p o n
W e i g
h t
C l e
a n
C L T a
n k
d T a n
k s
2 A I M
- 9
A G M - 8 8
2 A I M
- 9
C l e
a n
C L T a
n k
T a n
k s
2 A I M
- 9
A G M - 8 8
2 A I M
- 9
F-18 C / E
Inboard Asymmetric
Bring-Back Load Limit
Outboard AsymmetricBring-Back Load Limit
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+ C
+ 2 I n b d
+ C L T k + 2
+ C L T k + 2 A
+ 2 I n b d T k + 2
Configuration for Day Operationwith Bring-Back Load
+ C
+ 2 I n b d
+ C L T k + 2
+ C L T k + 2 A
+ 2 I n b d T k + 2
Configuration for Night Operationwith Bring-Back Load
Launch Envelope Limitations in Missile / Launch
Platform Physical Integration
Launch Envelope Limitations in Missile / Launch
Platform Physical Integration
Off BoresightSeeker field of regard ⇒ potential obscur ing from launch platform
Minimum Range
Launcher rail clearance and aeroelasticity ⇒ miss at min range
Helo rotor downwash ⇒ miss at min range
Safety
Launcher retention ⇒ potential inadvertent release, potential hang-fire
Launch platform local flow field α, β ⇒ potential unsafe separationL h l tf i t ti l f ti
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Launch platform maneuvering ⇒ potential unsafe separation
Handling qualities with stores ⇒ potential unsafe handling qualities
Launch platform bay / canister acoustics ⇒ missi le factor of safety
Launch platform bay / canister vibration ⇒ missile factor of safety
Store Separation Wind Tunnel Tests Are
Required for Missile / Aircraft Compatibility
Store Separation Wind Tunnel Tests Are
Required for Missile / Aircraft Compatibility
F-18 Store Compatibi lity Test in AEDC 16T AV-8 Store Compatibil ity Test in AEDC 4T
Types of Wind Tunnel Testing for Store Compatibility
- Flow field mapping with probe
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pp g p
- Flow field mapping with store
- Captive trajectory simulation
- Drop testing
Example Stores with Flow Field Interaction: Kh-41 + AA-10
Examples of Rail Launched and Ejection
Launched Missiles
Examples of Rail Launched and Ejection
Launched Missiles
Example Rail Launcher: Hellf ire / Brimstone Example Ejection Launcher: AGM-86 ALCM
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Video of Hellf ire / Brimstone Carriage / Launch Video of AGM-86 Carriage / Launch
Examples of Safe Store Separation Examples of Safe Store Separation
Laser Guided Bombs Drop from F-117
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AMRAAM Rail Launch from F-16 Video of Rapid Drop ( 16 Bombs ) from B-2
Examples of Store Compatibility Problems Examples of Store Compatibility Problems
Unsafe Separation Hang-Fire Store Aeroelastic Instability
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MIL-STD-8591 Aircraft Store Suspension and
Ejection Launcher Requirements
MIL-STD-8591 Aircraft Store Suspension and
Ejection Launcher Requirements
Store Weight / Parameter 30 Inch Suspension 14 Inch Suspension
♦ Weight Up to 100 lb Not Appl icable Yes
• Lug height ( in ) 0.75
• Min ejector area ( in x in ) 4.0 x 26.0
♦ Weight 101 to 1,450 lb Yes Yes
• Lug height ( in ) 1.35 1.00• Min lug well ( in ) 0.515 0.515
• Min ejector area ( in x in ) 4. 0 x 36.0 4.0 x 26.0
♦ Weight Over 1,451 lb Yes Not Appl icable
• Lug height ( in ) 1.35
• Min lug well ( in ) 1.080• Min ejector area ( in x in ) 4.0 x 36.0
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Ejection Stroke
Rail Launcher Forward Hanger Aft Hanger
LAU-7 Sidewinder Launcher 2.260 2.260
LAU 117 Maverick Launcher 1.14 7.23
MIL-STD-8591 Aircraft Store Rail Launcher
Examples
MIL-STD-8591 Aircraft Store Rail Launcher
Examples
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Note: Dimensions in inches.
• LAU 7 rail launched store weight and diameter limits are ≤ 300 lb, ≤ 7 in
•LAU 117 rail launched store weight and diameter limits are ≤ 600 lb, ≤ 10 in
Baseline AIM-120B AMRAAM
Compressed Carriage AIM-120C AMRAAM ( Reduced Span Wing / Tail )
Compressed Carriage Missiles Provide Higher
Firepower
Compressed Carriage Missiles Provide Higher
Firepower
17 5 in 17 5 in
Baseline AMRAAM: Loadout
of 2 AMRAAM per F-22 Semi-Bay
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17.5 in 17.5 in
12.5 in 12.5 in 12.5 in
Compressed Carriage AMRAAM: Loadout of 3 AMRAAM per F-22 Semi-Bay
Note: Alternative approaches to compressed carriage include surfaces with small span, folded surfaces, wraparound surfaces, and planar surfaces that extend ( e.g., switch blade, Diamond Back, Longshot ).
Video of Longshot Kit on CBU-97
Example of Aircraft Carriage and Fire Control
Interfaces
Example of Aircraft Carriage and Fire Control
Interfaces
WingWing Deploy
Safety Pin
Folding
Suspension
Lug
Fire Control /
Avionics
UmbilicalConnector
Flight Control
Access Cover Electrical
Safety Pin
Folding
SuspensionLug
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Example: ADM-141 TALD ( Tactical Air-Launched Decoy )Carriage and Fire Control Interfaces
Example of Ship Weapon Carriage and Launcher,
Mk41 VLS
Example of Ship Weapon Carriage and Launcher,
Mk41 VLS
8 Modules / Magazine Module Gas Management
Canister Cell Hatch
Cell
Before
Firing
Cell
After
Firing
Ship DeckExhaust Hatch
Missile Cover
Plenum
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Tomahawk Launch 8 Canister Cells / Module Standard Missi le Launch
Robustness Is Required for Carriage, Shipping,
and Storage Environment
Robustness Is Required for Carriage, Shipping,
and Storage Environment Environmental Parameter Typical Requirement Video: Ground / Sea Environment
Surface Temperature -60° F* to 160° F
Surface Humidity 5% to 100%
Rain Rate 120 mm / h**
Surface Wind 100 km / h steady***
150 km / h gusts****Salt fog 3 g / mm2 deposited per year
Vibration 10 g rms at 1,000 Hz: MIL STD 810, 648, 1670A
Shock Drop height 0.5 m, half sine wave 100 g / 10 ms: MIL STD 810, 1670A
Acoustic 160 dB
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Note: MIL-HDBK-310 and earlier MIL-STD-210B suggest 1% world-wide climatic extreme typical requirement.
* Lowest recorded temperature = -90° F. 20% probability temperature lower than -60° F during worst month of worst location.
** Highest recorded rain rate = 436 mm / h. 0.5% probability greater than 120 mm / h during worst month of worst location.*** Highest recorded steady wind = 342 km / h. 1% probability greater than 100 km / h during worst month of wors t location.
**** Highest recorded gust = 378 km / h. 1% probability greater than 150 km / h during worst month of worst location.
Summary of Measures of Merit and Launch
Platform Integration
Summary of Measures of Merit and Launch
Platform Integration Measures of Merit
Robustness
Warhead lethali ty Miss distance
Carriage and launch observables
Other survivability considerations
Reliability
Cost
Launch Platform Integration Firepower, weight, fitment
Store separation
Launch platform handling qualities, aeroelasticity Hang-fire
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g
Vibration
Standard launchers
Carriage and storage environment Discussion / Questions?
Classroom Exercise ( Appendix A )
Measures of Merit and Launch Platform
Integration Problems
Measures of Merit and Launch Platform
Integration Problems 1. IR signal attenuation is greater than 100 dB per km through a c____.
2. GPS / INS enhances seeker lock-on in adverse weather and ground c______.
3. A data link can enhance missile seeker lock-on against a m_____ target.
4. An example of a missile counter-counter measure to flares is an i______i_____ seeker.
5. Compared to a mid-wave IR seeker, a long wave IR seeker receives moreenergy from a c___ target.
6. High f ineness kinetic energy penetrators are required to defeat b_____targets.
7. For the same lethality with a blast fragmentation warhead, a small decrease inmiss distance allows a large decrease in the required weight of the w______.
F bl t / f h d h t t l ti f b t i i d t
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8. For a blast / frag warhead, a charge-to-metal ratio of about one is required toachieve a high total fragment k______ e_____.
9. A blast fragmentation warhead tradeoff is the number of fragments versus theindividual fragment w_____.
Measures of Merit and Launch Platform
Integration Problems ( cont )
Measures of Merit and Launch Platform
Integration Problems ( cont ) 10. Kinetic energy penetration is a function of the penetrator diameter, length,
density, and v_______.
11. In proport ional homing guidance, the objective is to make the line-of-sightangle rate equal to z___.
12. Aeromechanics contributors to missile time constant are flight controleffectiveness, flight control system dynamics, and dome e____ s____.
13. Miss distance due to heading error is a function of missile navigation ratio,velocity, time to correct the heading error, and the missile t___ c_______.
14. A missile must have about t_____ times the maneuverability of the target.
15. Minimizing the miss distance due to radar glint requires a high resolution
seeker, an optimum missile time constant and an optimum n_________ r____.
16 Weapons on low observable launch platforms use i carriage
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16. Weapons on low observable launch platforms use i_______ carriage.
17. Weapons on low observable launch platforms use m______ smoke propellant.
18. For an insensit ive munition, burning is preferable to detonation because itreleases less p____.
Measures of Merit and Launch Platform
Integration Problems ( cont )
Measures of Merit and Launch Platform
Integration Problems ( cont )
19. Missile system reliability is enhanced by subsystem reliability and low p____count.
20. High cost subsystems of missiles are sensors, electronics, and p_________.
21. Missile SDD cost is driven by the program duration and r___.
22. Missile unit production cost is driven by the number of units produced,learning curve, and w_____.
23. First level maintenance is conducted at a d____.
24. A standard launch system for U.S. Navy ships is the V_______ L_____ S_____.
25. Most light weight missiles use rail launchers while most heavy weight missiles
use e_______ launchers.26. Higher firepower is provided by c_________ carriage.
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27. The typical environmental requirement from MIL-HDBK-310 is the _% world-wide climatic extreme.
Outline Outline Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
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References and Communication
Appendices ( Homework Problems / Classroom Exercises,
Example of Request for Proposal, Nomenclature, Acronyms,Conversion Factors, Syllabus )
Sizing Examples Sizing Examples Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
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Velocity control
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
Ai -to-Air Engagement Analysis Process and
Assumptions
Ai -to-Air Engagement Analysis Process and
Assumptions
F-pole range provides kil l of head-on threat outside of
threat weapon launch range Aircraft contrast for typical engagement
C = 0.18
Typical visual detection range by target ( Required F-polerange ) RD = 3.3 nm
Typical alti tude and speed of launch aircraft, target aircraft,
and missile h = 20k ft altitude
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VL = Mach 0.8 = 820 ft / s
VT = Mach 0.8 = 820 ft / s
VM = 2 VT = 1,640 ft / s
Assumed Ai -to-Air Engagement Scenario for
Head-on Intercept
Assumed Ai -to-Air Engagement Scenario for
Head-on Intercept
t = 0 s (Launch Missi le)
RL= Launch Range = 10.0 nm
Red Aircraft
( 820 ft / s )
Blue Aircraft
t = tf = 24.4 s ( Missile Impacts Target )
Red Aircraft
Blue Aircraft( 820 ft / s )
Blue Missile( 1640 ft / s )
RL= VM t f + VT tf
RF-Pole = VM t f - VL tf
RF = Missile Flight Range = 6.7 nm
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( 820 ft / s )
R F-pole = 3.3 nm
Destroyed
0
2
4
6
8
R , V i s i b l e R a n g e f o r
5 0 f t 2 T a r g e t ,
n
Visual Detection Range,nm
Visual RecognitionRange, nm
Target Contrast and Size Drive Visual Detection
and Recognition Range
Target Contrast and Size Drive Visual Detection
and Recognition Range
Note:
RD
= Visual detection range for probability of detection PD = 0.5
C = Contrast
CT = Visual threshold contrast = 0.02
Atp= Target presented area = 50 ft2
RR = Visual recognition range
θF = Pilot v isual fovial angle = 0.8 deg
Clear weather
Pilot search glimpse time = 1 / 3 s
Example:
If C = 0.18
RD = 3.3 nm
RR = 1.0 nm
RD = 1.15 [ A tp( C – CT )]1/2, RD in nm, A tp
in ft2
RR = 0.29 RD
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0
0.01 0.1 1C, Contrast
Pilot search g limpse time = 1 / 3 s
C = 0.01 C = 0.02 C = 0.05 C = 0.1 C = 0.2 C = 0.5 C = 1.0
High Missile Velocity Improves Standoff Range High Missile Velocity Improves Standoff Range
0.2
0.4
0.6
0.8
1
F - P o l e R a n g e / L a u n c h R a n g
VL / VM = 0VL / VM = 0.2
VL / VM = 0.5
VL / VM = 1.0
Example:• VL = VT
• VM = 2 VT
RF-Pole / RL = 1 – ( VT + VL ) / ( VM + VT ) Note: Head-on intercept
RF-Pole = Standoff range at intercept
RL= Launch rangeVM = Missi le average velocity
VT = Target velocity
VL = Launch velocity
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0
0 0.2 0.4 0.6 0.8 1
Target Velocity / Missile Velocity
VM 2 VT
• Then VT / VM = VL / VM = 0.5• RF-Pole / RL = 0.33
• RF-Pole = RD = 3.3 nm• RL = 3.3 / 0.33 = 10.0 nm
Missile Flight Range Requirement Is Greatest for
a Tail Chase Intercept
Missile Flight Range Requirement Is Greatest for
a Tail Chase Intercept
0
0.5
1
1.5
2
2.5
3
R F / R L ,
M i s s i l e F l i g h t R a
n g e / L a u n c h R a
n g e
( RF / RL ) Head-on( RF / RL ) Tail Chase
Examples:
•Head-on Intercept
• VM = 1,640 ft / s, VT = 820 ft / s• VM / VT = 1640 / 820 = 2• RF / RL = 2 / ( 2 + 1 ) = 0.667• R = 10 0 nm
( RF / RL )Head-on = ( VM / VT ) / [(VM / VT ) + 1 ]
( RF / RL )TailChase = ( VM / VT ) / [(VM / VT ) - 1 ]
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0
0 1 2 3 4 5
VM / VT, Missi le Veloc ity / Target Veloc ity
• RL = 10.0 nm• RF = 0.667 ( 10.0 ) = 6.67 nm
•Tail Intercept at same condi tions• R
F/ R
L= 2 / ( 2 – 1 ) = 2.0
• RF = 2.0 ( 10.0 ) = 20.0 nm
Drawing of Rocket Baseline Missile Configuration Drawing of Rocket Baseline Missile Configuration
STA 60.8
19.4
3.418.5
STA 125.4
LEmac at STA 67.0BL 10.2
Λ = 45°
40.2STA 0 19.2 46.1 62.6 84.5 138.6
Nose Forebody PayloadBay
Midbody Aftbody Tailcone
Rocket Motor
Λ = 57°
12.0
LEmac atSTA 131.6
BL 8.0
16.18.0 d
cgBO cgLaunch
143.9
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Note: Dimensions in inches
Source: Bithell, R.A. and Stoner, R.C., “ Rapid Approach for Missile Synthesis, Vol. 1, Rocket Synthesis
Handbook,” AFWAL-TR-81-3022, Vol. 1, March 1982.
Mass Properties of Rocket Baseline Missile Mass Properties of Rocket Baseline Missile
1 Nose ( Radome ) 4.1 12.0
3 Forebody structure 12.4 30.5Guidance 46.6 32.62 Payload Bay Structure 7.6 54.3
Warhead 77.7 54.34 Midbody Structure 10.2 73.5
Control Actuation System 61.0 75.55 Aftbody Structure 0.0 –
Rocket Motor Case 47.3 107.5Insulation ( EDPM – Silica ) 23.0 117.2
6 Tailcone Structure 6.5 141.2
Nozzle 5.8 141.2Fixed Surfaces 26.2 137.8Movable Surfaces 38.6 75.5
Component Weight, lb. C.G. STA, in.
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Burnout Total 367.0 76.2Propellant 133.0 107.8
Launch Total 500.0 84.6
Rocket Baseline Missile Definition Rocket Baseline Missile Definition Body
Dome Material Pyroceram Airf rame Material Aluminum 2219-T81
Length, in 143.9Diameter, in 8.0
Airf rame thickness, in 0.16Fineness ratio 17.99Volume, ft3 3.82Wetted area, ft2 24.06
Nozzle exit area, ft2 0.078Boattail fineness ratio 0.38Nose fineness ratio 2.40Nose bluntness 0.0Boattail angle, deg 7.5
Movable surfaces ( forward )
Material Aluminum 2219-T81Planform area, ft2 ( 2 panels exposed ) 2.55Wetted area, ft2 ( 4 panels ) 10.20Aspect ratio ( 2 panels exposed ) 2 82
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Aspect ratio ( 2 panels exposed ) 2.82Taper ratio 0.175Root chord, in 19.4
Tip chord, in 3.4Span, in ( 2 panels exposed ) 32.2Leading edge sweep, deg 45.0
Rocket Baseline Missile Definition ( cont ) Rocket Baseline Missile Definition ( cont )
Movable surfaces ( continued )Mean aerodynamic chord, in 13.3Thickness ratio 0.044Section type Modified double wedgeSection leading edge total angle, deg 10.01xmac, in 67.0ymac, in ( from root chord ) 6.2
Actuator rate l imit, deg / s 360.0Fixed surfaces ( aft )
Material Aluminum 2219-T81Modulus of elastici ty, 106 psi 10.5Planform area, ft2 ( 2 panels exposed ) 1.54Wetted area, ft2 ( 4 panels ) 6.17
Aspect ratio ( 2 panels exposed ) 2.59Taper ratio 0.0
Root chord, in 18.5Tip chord, in 0.0Span, in ( 2 panels exposed ) 24.0Leading edge sweep, deg 57.0
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g g p, gMean aerodynamic chord, in 12.3Thickness ratio 0.027
Section type Modified double wedgeSection leading edge total angle, deg 6.17xmac, in 131.6ymac, in ( from root chord ) 4.0
Rocket Baseline Missile Definition ( cont ) Rocket Baseline Missile Definition ( cont ) References values
Reference area, ft2 0.349Reference length, ft 0.667
Pitch / Yaw Moment of inertia at launch, slug-ft2 117.0Pitch / Yaw Moment of inert ia at burnout, slug-ft2 94.0
Rocket Motor Performance ( altitude = 20k ft, temp = 70° F )
Burning time, sec ( boost / sustain ) 3.69 / 10.86
Maximum pressure, psi 2042
Average pressure, psi ( boost / sustain ) 1769 / 301
Average thrust, lbf ( boost / sustain ) 5750 / 1018
Total impulse, lbf-s ( boost / sustain ) 21217 / 11055
Specific impulse, lbf-s / lbm ( boost / sustain ) 250 / 230.4
PropellantWeight, lbm ( boost / sustain ) 84.8 / 48.2
Flame temperature @ 1 000 psi F 5282 / 5228
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Flame temperature @ 1,000 psi, °F 5282 / 5228
Propellant density, lbm / in3 0.065
Characteristic velocity, ft / s 5200
Burn rate @ 1000 psi, in / s 0.5
Burn rate pressure exponent 0.3
Rocket Baseline Missile Definition ( cont ) Rocket Baseline Missile Definition ( cont ) Propellant ( continued )
Burn rate sensitivity with temperature, % / °F 0.10
Pressure sensitivity with temperature, % / °F 0.14Rocket Motor Case
Yield / ultimate strength, psi 170,000 / 190,000Material 4130 Steel
Modulus of elasticity, psi 29.5 x 106 psiLength, in 59.4Outside diameter, in 8.00Thickness, in (minimum) 0.074Burst pressure, psi 3140Volumetric efficiency 0.76
Grain configuration Three slots + web
Dome ellipse ratio 2.0Nozzle
Housing material 4130 Steel
Exit geometry Contoured ( equiv 15° )
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2/24/2008 ELF 298
Exit geometry Contoured ( equiv. 15 )Throat area, in2 1.81Expansion ratio 6.2Length, in 4.9Exit diameter, in 3.78
Rocket Baseline Missile Has Boost-Sustain
Thrust - Time History
Rocket Baseline Missile Has Boost-Sustain
Thrust - Time History
2
4
6
8
Thrust – 1,000 lb
Boost Total Impulse = ∫Tdt = 5750 ( 3.69 ) = 21217 lb-s
Sustain Total Impulse = ∫Tdt = 1018 ( 10.86 ) = 11055 lb-s
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2/24/2008 ELF 299
Time – seconds0 4 8 12 16
0
Note: Alti tude = 20k ft, Temperature = 70° FTotal impu lse drives velocity change
Rocket Baseline Missile Aerodynamic
Characteristics
Rocket Baseline Missile Aerodynamic
Characteristics
12
8m
a l F o r c e
~ C N
P i t c h i n g M o m e n t – C m
20
16
-16.0
-8.0
-12.0
0
-4.0
1.2
0.6
M
1.5
2.02.352.873.954.60
2.352.0
M = 1.2 and 1.5
4.600.6
3.95
SRef = 0.349 ft2, lRef = d = 0.667 ft, CG at STA 75.7, δ = 0 deg
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2/24/2008 ELF 300
4
00 4 8 12 16
α, Angle of Attack – Deg20
N o r m
24
Rocket Baseline Missile Aerodynamic
Characteristics ( cont )
Rocket Baseline Missile Aerodynamic
Characteristics ( cont )
0.4
1.2
0.8
C A a tα = 0 d e g
0.1
0
Power Off
Power On
0.2
0.3
C
Nδ a
tα
= 0 d e g
, P e r D e g
0.4
1.2
0.8
.002
0
.004
.006
K2
K1
C A = C Aα = 0 + K1 δ2 + K2 α δ
a tα
= 0
d e g ,
P e r D e g
K 1 ,
K 2 ~ P e r
D e g 2
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2/24/2008 ELF 301
00 1 2 3 4
M, Mach Number 5
0 C mδ
0 1 2 3 4M, Mach Number
5
High Altitude Launch Enhances Rocket Baseline
Range
High Altitude Launch Enhances Rocket Baseline
Range
10
20
30
40
A l t i t u d e ~ 1 0 3 f t
Burnout
Boost /
Sustain
TerminationMach = 1.5
Coast
Vmax = 2147 ft / s
V = 1916 ft / s
Vmax = 2524 ft / s
ML = 0.7
CD AVG= 0.65
Constant Altitude Flight
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2/24/2008 ELF 302
Range ~ nm0 5 10 15 20
025
Vmax 1916 ft / s
Low Altitude Launch and High Alpha Maneuvers
Enhance Rocket Baseline Turn Performance
Low Altitude Launch and High Alpha Maneuvers
Enhance Rocket Baseline Turn Performance
C r o s s R a n g e
1 , 0
0 0 f t .
25
20
15
10
5Termination at M = 1.0
Marks at 2 s intervals
Alt.
10k f t
10k f t
40k f t
40k ft
α
15°
10°
15°
10°
1
2
3
4
1
2
3
4
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2/24/2008 ELF 303
0-10 -5 0 5 10
Down Range 1,000 ft.
40k f t 10°4
Note: Off boresight envelope that is shown does not include the rocket baseline seeker field-of-regard limit ( 30 deg ).
Paredo Shows Range of Rocket Baseline Driven
by I SP , Propellant Weight, Drag, and Static Margin
Paredo Shows Range of Rocket Baseline Driven
by I SP , Propellant Weight, Drag, and Static Margin
-0.5
0
0.5
1
1.5
Isp Prop.
Weight
CD0 Drag-
Due-to-Lift
Static
Margin
Thrust Inert
Weight
Nondimensional
Range
Sensitivity to
Parameter
Note: Rocket baseline:
hL = 20k ft, ML = 0.7, MEC = 1.5
R@ ML = 0.7, hL = 20k ft = 9.5 nm
Example: 10% increase in propellantweight ⇒ 8.8% increase in f light range
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2/24/2008 ELF 304
-1
Parameter
Boost - Sustain Trajectory Assumptions Boost - Sustain Trajectory Assumptions
Assumptions
1 degree of freedom Constant altitude
Simplif ied equation for axial acceleration based on thrust,drag, and weight nX = ( T – D ) / W
Missile weight varies with burn rate and time W = WL – WP t / tB
Drag is approximated by D = CDO
q S
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2/24/2008 ELF 305
0
5
10
15
0 5 10 15 20 25
n x ,
A x i a l A c c e l e r a t i o n ,
Example of Rocket Baseline Axial Acceleration Example of Rocket Baseline Axial Acceleration
Note:
tf = 24.4 sML = 0.8hL = 20,000 ftTB = 5750 lbtB = 3.69 sTS = 1018 lb
tS = 10.86 sD = 99 lb at Mach 0.8D = 1020 lb at Mach 2.1WL = 500 lbWP = 133 lb
nX = ( T - D ) / W
Boost
Sustain
Coast
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2/24/2008 ELF 306
-5
t, Time, s
0
1000
2000
3000
V ,
V e l o c i t y
, f t / s
Example of Rocket Baseline Missile Velocity vs
Time
Example of Rocket Baseline Missile Velocity vs
Time
Boost
Sustain
Coast
ΔV / ( gc ISP ) = - ( 1 - D AVG / T ) ln ( 1 - Wp / Wi ), During Boost-Sustain
V / VBO = 1 / { 1 + t / { 2 WBO / [ gc ρ AVG SRef ( CD0) AVG VBO ]}}, During Coast
Note:
ML = 0.8hL = 20k feet
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2/24/2008 ELF 307
0 5 10 15 20 25
t, Time, s
Range and Time-to-Target of Rocket Baseline
Missile Meet Requirements
Range and Time-to-Target of Rocket Baseline
Missile Meet Requirements
0
2
4
6
8
10
R ,
F l i g h t R a n
g e , n m
Boost
Sustain
Coast
(RF)Req = 6.7 nm @ t =24.4 s
R = Δ Rboost
+ Δ Rsustain
+ Δ Rcoast
Note:ML = 0.8
hL = 20k ft
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2/24/2008 ELF 308
0 5 10 15 20 25
t, Time, s
Sizing Examples Sizing Examples Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
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2/24/2008 ELF 309
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
Example of Wing Sizing to Satisfy Required
Maneuver Acceleration
Example of Wing Sizing to Satisfy Required
Maneuver Acceleration Size Wing for the Assumptions
( nZ )Required = 30 g to counter 9 g maneuvering target )( nZ ) = Δ ( nZ )Wing + Δ ( nZ )Body + Δ ( nZ )Tail
Rocket Baseline @Mach 220,000 ft altitude367 lb weight ( burnout )
From Prior Example, ComputeαWing = α’Max = ( α + δ )Max = 22 deg for rocket baseline
α = 0.75δ, αBody = αTail = 9.4 deg
Δ ( nZ )Body = q SRef ( CN )Body / W = 2725 ( 0.349 ) ( 1.28 ) / 367 = 3.3 g ( f rom body )
Δ ( nZ )Tail = q STail [( CN )Tail ( SRef / STail )] / W = 2725 ( 1.54 ) ( 0.425 ) / 367 = 4.9 g ( from tail )
Video of Intercept of Maneuvering Target
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2/24/2008 ELF 310
Δ ( nZ )Wing = ( nZ )Required - Δ ( nZ )Body - Δ ( nZ )Tail = 30 – 3.3 – 4.9 = 21.8 g
( SW )Required = Δ ( nZ )Wing W / { q [( CN )Wing (SRef / SWing )]} = 21.8 ( 367 ) / {( 2725 ) ( 1.08 )} = 2.72 ft2
Note: ( SW )RocketBaseline = 2.55 ft2
Wing Sizing to Satisfy Required Turn Rate Wing Sizing to Satisfy Required Turn Rate Assume
( γ.)Required > 18 deg / s to counter 18 deg / s maneuvering aircraft
Rocket Baseline @
Mach 2
20,000 ft altitude
367 lb weight ( burnout )
γi = 0 deg
Compute
γ.= gc n / V = [ q SRef CNα α + q SRef CNδ δ - W cos ( γ ) ] / [( W / gc ) V ]
α / δ = 0.75
α’ = α + δ = 22 deg ⇒ δ = 12.6 deg, α = 9.4 deg
γ.= [ 2725 ( 0.349 )( 0.60 )( 9.4 ) +2725 ( 0.349 )( 0.19 )( 12.6 ) – 367 ( 1 )] / ( 367 / 32.2 )( 2074 ) = 0.31
rad / s or 18 deg / s
Note: ( S ) 18 deg / s Turn Rate
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2/24/2008 ELF 311
Note: ( SW )RocketBaseline ⇒ 18 deg / s Turn Rate
Wing Sizing to Satisfy Required Turn Radius Wing Sizing to Satisfy Required Turn Radius Assume Maneuvering Aircraft Target with
γ.= 18 deg / s = 0.314 rad / s
V = 1000 ft / s
( RT )Target = V / γ.= 1000 / 0.314 = 3183 ft
Assume Rocket Baseline @
Mach 2
20,000 ft altitude 367 lb weight ( burnout )
Compute γ.
= 18 deg / s ( prior f igure )
( RT )RocketBaselinet = V / γ.= 2074 / 0.314 = 6602 ft
Note: ( RT )RocketBaselinet > ( RT )Target ⇒ Rocket Baseline Can Be Counter-measured by Target in a Tight Turn
Counter-Countermeasure Alternatives Larger Wing
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2/24/2008 ELF 312
g g
Higher Angle of Attack
Longer Burn Motor with TVC
Sizing Examples Sizing Examples Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
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2/24/2008 ELF 313
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
Combined Weight / Miss Distance Drivers: Nozzle
Expansion and Motor Volumetric Efficiency
Combined Weight / Miss Distance Drivers: Nozzle
Expansion and Motor Volumetric Efficiency
Fixed surface number of panels 4 3 +0.054 +0.100Movable surface number of panels 4 2 +0.071 +0.106Design static margin at launch 0.40 0.30 +0.095 +0.167Wing movable surface sweep ( deg ) 45.0 49.5 -0.205 +0.015Tail fixed surface sweep ( deg ) 57.0 60.0 +0.027 +0.039Wing movable surface thickness ratio 0.044 0.034 +0.041 +0.005
Nose fineness ratio 2.4 2.6 -0.016 -0.745Rocket chamber sustain pressure ( psi ) 301 330 -0.076 -0.045Boattail fineness ratio ( length / diameter ) 0.38 0.342 +0.096 +0.140Nozzle expansion ratio 6.2 6.82 -0.114 -0.181Motor volumetric efficiency 0.76 0.84 -0.136 -0.453Propellant density ( lb / in3 ) 0.065 0.084 -0.062 +0.012
Boost thrust ( lb ) 5,750 6,325 +0.014 -0.018Sustain thrust ( lb ) 1,018 1,119 +0.088 +0.246Characteristic velocity ( ft / s ) 5,200 5,720 -0.063 -0.077Wing location ( percent total length ) 47.5 42.75 +0.181 -0.036
Parameter Baseline W* σ*SensitivityVariation
Note: Strong impact with synergyB li W i ht 500 lb Mi di t 62 3 ft
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2/24/2008 ELF 314
Note: Strong impact with synergy
Strong impact
Moderate impact with synergy
Moderate impact
Baseline: Weight = 500 lb, Miss distance = 62.3 ft
W* = weight sensitivity for parameter variation = ΔW / Wσ* = miss distance sensitiv ity for parameter variation = Δ σ / σ
A Harmonized Missile Can Have Smaller Miss
Distance and Lighter Weight
A Harmonized Missile Can Have Smaller Miss
Distance and Lighter Weight
Judicious changes
Boost thrust ( lb ) 5,750 3,382 3,382 3,382Wing location ( percent missile length to 1/4 mac ) 47.5 47 44 46Wing taper ratio 0.18 0.2 0.2 0.2Nose fineness ratio 2.4 3.2 2.55 2.6Nose blunting ratio 0.0 0.05 0.05 0.05Nozzle expansion ratio 6.2 15 15 15Sustain chamber pressure ( psi ) 301 1,000 1,000 1,000Boattail fineness ratio 0.38 0.21 0.21 0.21
Tail leading edge sweep ( deg ) 57 50 50 50Technology limited changes
No. wing panels 4 2 2 2No. tail panels 4 3 3 3Wing thickness ratio 0.044 0.030 0.030 0.030Wing leading edge sweep ( deg ) 45 55 55 55Static margin at launch ( diam ) 0.4 0.0 0.0 0.0
Propellant density ( lb / in3
) 0.065 0.084 0.084 0.084Motor volumetric efficiency 0.76 0.84 0.84 0.84
Measures of MeritTotal weight ( lb ) 500 385.9 395.0 390.1Miss distance ( ft ) 62.3 63.1 16.2 16.6Time to target ( s ) 21.6 23.8 23.6 23.8
Parameter Baseline Value Weight Miss Distance Harmonized
Missile Configured for Minimum:
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2/24/2008 ELF 315
g ( )Length ( in ) 144 112.7 114.7 114.9Mach No. at burnout 2.20 2.08 2.09 2.07Weight of propellant ( lb ) 133 78.3 85.4 85.9Wing area ( in2 ) 368.6 175.5 150.7 173.8Tail area ( in2 ) 221.8 109.1 134.5 112.0
*Note: Value of driving parameter
Baseline Missile vs Harmonized Missile Baseline Missile vs Harmonized Missile
144”
57°45°
Propellant Density( lb / in3 );
0.0650.084
50°55°
NoseFineness;
2.42.6
Surfaces; {4 wings / 4 tails
2 wings / 3 tailsWeight ( lb ); 500
390
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2/24/2008 ELF 316
50°55°
115”
Sizing Examples Sizing Examples Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
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2/24/2008 ELF 317
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design, Build, and Fly
Lofted Glide Trajectory Provides Extended Range Lofted Glide Trajectory Provides Extended Range
Using Rocket Baseline, Compare
Lofted Launch-Coast-Glide Trajectory
Lofted Launch-Ballis tic Trajectory Constant Altitude Trajectory
Assume for Lofted Launch-Coast-Glide Trajectory:
γi = 45 deg
γ = 45 deg dur ing boost and sustain
γ = 45 deg coast
Switch to ( L / D )max glide at optimum altitude
( L / D )maxg glide trajectory after apogee
hi = hf = 0 ft
Velocity, Horizontal Range, and Altitude During Initial Boost @ γ = 45 degΔV = - gc ISP [ 1 – ( D AVG / T ) - ( W AVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 250 ) [ 1 - ( 419 /
5750 ) – 458 ( 0.707 ) / 5750 ] ln ( 1 - 84.8 / 500 ) = 1,303 ft / s
ΔR = ( Vi + ΔV / 2 ) tB = ( 0 + 1303 / 2 ) 3.69 = 2,404 ft
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2/24/2008 ELF 318
ΔRx = ΔR cos γi = 2404 ( 0.707 ) = 1,700 ft
ΔRy = ΔR sin γi = 2404 ( 0.707 ) = 1,700 ft
h = h i + ΔRy = 0 + 1700 = 1,700 ft
Lofted Glide Trajectory Provides Extended
Range ( cont )
Lofted Glide Trajectory Provides Extended
Range ( cont ) Velocity, Horizontal Range, and Alti tude During Sustain @ γ = 45 deg
ΔV = - gc ISP [ 1 – ( D AVG / T ) – ( W AVG sin γ ) / T ] ln ( 1 - Wp / Wi ) = -32.2 ( 230.4 ) [ 1 – ( 650 /1018 ) – 391 ( 0.707 ) / 1018 ] ln ( 1 - 48.2 / 415.2 ) = 81 ft / sec
VBO = 1303 + 81 = 1,384 ft / s
ΔR = ( Vi + ΔV / 2 ) tB = ( 1303 + 81 / 2 ) 10.86 = 14,590 ft
ΔRx = ΔR cos γi = 14590 ( 0.707 ) = 10,315 ft
ΔRy = ΔR sin γi = 14,590 ( 0.707 ) = 10,315 ft
h = h i + ΔRy = 1700 + 10315 = 12,015 ft Velocity, Horizontal Range, and Alti tude During Coast @ γ = 45 deg to h@( L / D )max
Vcoast = Vi { 1 – [( gc sin γ ) / Vi ] t } / { 1 + {[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t } = 1384 { 1 –
[( 32.2 ( 0.707 )) / 1384 ] 21 } / { 1 + {[ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))}21 } = 674 ft / s
Rcoast = { 2 W / [ gc ρ AVG SRef ( CD0) AVG )]} ln { 1 – [ gc
2 ρ AVG SRef ( CD0) AVG / ( 2 W )] [ s in γ ] t2 +
{[ gc ρ AVG SRef ( CD0) AVG Vi ] / ( 2 W )} t } = { 2 ( 367 ) / [ 32.2 ( 0.001338 ) ( 0.349 ) ( 0.7 )] ln
{ 1 – [ (32.2)2 ( 0.001338 ) ( 0.349 ) ( 0.7 ) / (( 2 ( 367 ))] [ 0.707 ] ( 21 )2 + {[ 32.2 ( 0.001338 )( 0.349 ) ( 0.7 ) ( 1384 )] / ( 2 ( 367 ))} 21 } = 17148 ft
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2/24/2008 ELF 319
( Rx )coast = ( Ry )coast = Rcoast sinγ = 17148 ( 0.707 ) = 12124 ft
Lofted Glide Trajectory Provides Extended Range
( cont )
Lofted Glide Trajectory Provides Extended Range
( cont )
Flight Conditions At End-of-Coast Are:
t = 35 s
V = 674 ft / s
h = 24,189 ft
q = 251 psf
M = 0.66
( L / D )max = 5.22 α( L / D )max
= 5.5 deg
Initiate α = α( L / D )max= 5.5 deg at h = 24,189 ft
Incremental Horizontal Range During ( L / D )max Glide Is
ΔRx
= ( L / D ) Δh = 5.22 ( 24189 ) = 126,267 ft
Total Horizontal Range for Elevated Launch-Coast-Glide Trajectory Is
Rx = ΣΔRx = ΔRx,Boost + ΔRx,Sustain + ΔRx,Coast + ΔRx,Glide = 1700 + 10315 + 12124 + 126267 =150406 ft = 24.8 nm
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2/24/2008 ELF 320
Lofted Glide Trajectory Provides Extended
Range ( cont )
Lofted Glide Trajectory Provides Extended
Range ( cont )
0
10
20
30
0 10 20 30
R Range nm
h ,
A l t i t u d e ,
k f t
S u s t a i n
B a l l i s
t i c
®z
²
B a l l i s
t i c
G l i d e @ ( L / D ) m a x
z ÄCo-altitude
Note: Rocket Baseline
z End of boost
End of sustain
ÈLof ted ball istic apogee, t = 35 s, V = 667 ft / s, h = 21,590 ft
ÊLof ted coast apogee, t = 35 s, V = 674 ft / s, h = 24,189 ft
®Lofted ballistic impact, t = 68 s, γ = - 71 deg, V = 1368 ft / s
²Lofted glide impact, t = 298 s, γ = - 10.8 deg, V = 459 ft / s
Ä Co-alti tude fl ight impact, t = 115 s, V = 500 ft / s
ÈØ
C o a s t @
γ =
4 5
d e g
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2/24/2008 ELF 321
R, Range, nm
Sizing Examples Sizing Examples Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
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2/24/2008 ELF 322
p p g g
Soda Straw Rocket Design, Build, and Fly
Ramjet Baseline Is a Chin Inlet Integral Rocket
Ramjet ( IRR )
Ramjet Baseline Is a Chin Inlet Integral Rocket
Ramjet ( IRR )
Sta 0.
Guidance WarheadRamjet Fuel Boost Propellant
Booster, andRamjet Engine
Boost Nozzle
Tail Cone Af t-bodyMid-bodyPayload BayForebody
23.5 43.5 76.5 126.0
159.0 171.0
Sta 150.311.6
11.5
16.5
37°
Note: Dimensions are in inches
ChinInlet Transport A ir Duct
20.375 dia
Nose
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2/24/2008 ELF 323
Source: Bithell, R.A. and Stoner, R.C. “Rapid Approach for Missile Synthesis” , Vol. II, Air -breathingSynthesis Handbook, AFWAL TR 81-3022, Vol. II, March 1982.
Component Weight, lb CG Sta, in
Nose 15.9 15.7
Forebody Structure 42.4 33.5Guidance 129.0 33.5
Payload Bay Structure 64.5 60.0Warhead 510.0 60.0
Midbody Structure 95.2 101.2Inlet 103.0 80.0Electrical 30.0 112.0Hydraulic System for Control Actuation 20.0 121.0
Fuel Distribution 5.0 121.0 Af tbody Structure 44.5 142.5
Engine 33.5 142.5
Tailcone Structure 31.6 165.0Ramjet Nozzle 31.0 165.0Flight Control Actuators 37.0 164.0
Fins ( 4 ) 70.0 157.2End of Cruise 1,262.6 81.8
Ramjet Fuel ( 11900 in3 ) 476.0 87.0
Start of Cruise 1,738.6 83.2Boost Nozzle ( Ejected ) 31.0 164.0
Mass Properties of Ramjet Baseline Missile Mass Properties of Ramjet Baseline Missile
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2/24/2008 ELF 324
Frangible Port 11.5 126.0
End of Boost 1,781.1 84.9
Boost Propellant 449.0 142.5
Booster Ignition 2,230.1 96.5
Ramjet Baseline Missile Definition Ramjet Baseline Missile Definition
InletType Mixed compression
Material TitaniumConical forebody half angle, deg 17.7Ramp wedge angle, deg 8.36Cowl angle, deg 8.24Internal contraction ratio 12.2 PercentCapture area, ft2 0.79
Throat area, ft
2
0.29BodyDome Material Silicon nitride
Airframe Material TitaniumCombustor Material Insulated InconelLength, in 171.0
Diameter, in 20.375Fineness ratio 8.39Volume, ft3 28.33Wetted area, ft2 68.81Base area, ft2 ( cruise ) 0.58Boattail fineness ratio N/A
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Nose half angle, deg 17.7Nose length, in 23.5
Ramjet Baseline Missile Definition ( cont ) Ramjet Baseline Missile Definition ( cont )
Tail ( Exposed )Material Titanium
Planform area ( 2 panels ), ft2
2.24Wetted area ( 4 panels ), ft2 8.96
Aspect ratio ( 2 panels exposed ) 1.64
Taper ratio 0.70
Root chord, in 16.5
Span, in. ( 2 panels exposed ) 23.0Leading edge sweep, deg 37.0
Mean aerodynamic chord, in 14.2
Thickness ratio 0.04
Section type Modified double wedge
Section leading edge total angle, deg 9.1xmac, in 150.3
ymac, in ( from root chord ) 5.4
Reference valuesReference area ft2 2 264
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Reference area, ft2 2.264
Reference length, ft 1.698
0 1 2 3 4 5 6Subscripts0 Free stream f low into inlet ( Example, Ramjet Basel ine at Mach 4, α = 0 deg ⇒ A0 = 104 in2. Note: AC = 114 in2 )1 Inlet throat ( Ramjet Baseline A1 = AIT = 41.9 in2 )2 Diffuser exit ( Ramjet Baseline A2 = 77.3 in2 )3 Flame holder plane ( Ramjet Baseline A3 = 287.1 in2 )4 Combustor exit ( Ramjet Baseline A = 287 1 in2 )
Ac = Inlet capture area
SRef = Reference area
Engine Nomenclature and Flowpath Geometry for
Ramjet Baseline
Engine Nomenclature and Flowpath Geometry for
Ramjet Baseline
Ramjet Engine Station Identification
( CD0)Nose Corrected = ( CD0
)Nose Uncorrected x ( 1 - Ac / SREF )
120°
Ac = 114 in2
20.375 in
SRef
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4 Combustor exit ( Ramjet Baseline A4 = 287.1 in2 )
5 Nozzle throat ( Ramjet Baseline A5 = 103.1 in2 )6 Nozzle exit ( Ramjet Baseline A6 = 233.6 in2 )Ref Reference Area ( Ramjet Baseline Body Cross-sectional Area, SRef = 326 in2 )
N o r m
a l F o r c e C o e f f i c
i e n t , C N
α, Angle of Attack ~ deg
0 4 8 12 16
Mach1.21.52.0
3.04.0
.40
.30
.20
.10
0
A x i a l F o r c e C o e f f i c i e n t , C A
0 4 8 12 16
Mach1.2
1.5
2.0
3.0
4.0
SRef = 2.264 ft2
lRef = dRef = 1.698 ftXcg @ Sta 82.5 in
δ = 0 deg
4.0
3.0
2.0
1.0
0
α, Angle of Attack ~ deg
Aerodynamic Characteristics of Ramjet Baseline Aerodynamic Characteristics of Ramjet Baseline
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Source: Reference 27, based on year 1974 computer program from Reference 32.
+ .4
0
-.4
-.8
-1.2
-1.6
Aerodynamic Characteristics of Ramjet Baseline
( cont )
Aerodynamic Characteristics of Ramjet Baseline
( cont )
P i t c h i n g M o m e n t C o e f f i c i e n t , C m
α, Angle of Attack ~ deg0 4 8 12 16
Mach4.0
3.0
2.0
1.5
1.2
SRef = 2.264 ft2
lRef
= dRef
= 1.698 ftXcg @ Sta 82.5 inδ = 0 deg
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, g g
Source: Reference 27, based on year 1974 computer program from Reference 32.
Aerodynamic Characteristics of Ramjet Baseline
( cont )
Aerodynamic Characteristics of Ramjet Baseline
( cont )
.4
.3
.2
.1
0
C D 0
M, Mach Number
0 1 2 3 4
C N
δ ~ p e r d
e g
C m
δ ~ p e r d e g
.10
.05
SRef = 2.264 ft2
lRef = dRef = 1.698 ftXcg @ Sta 82.5 inδ= 0 deg
α = 0 deg.-.4
0
-.2
Source: Reference 27 based on year 1974 computer program from
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0 1 2 3 40M, Mach Number
Source: Reference 27, based on year 1974 computer program from
Reference 32.
100
1000
10000
100000
0 1 2 3 4
T m a x ,
M a x
T h r u s t , l b
h = Sea Level
h = 20k ft
h = 40k fth = 60k ft
h = 80k ft
Thrust Modeling of Ramjet Baseline Thrust Modeling of Ramjet Baseline
Note:
Standard atmosphere
T = Tmax ϕ
φ = 1 if stochiometric ( f / a = 0.0667 )
α = 0 deg
Example: M = 3.5, h = 60k ft, ϕ= 1 ⇒ Max Thrust = 1,750 lb
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M, Mach Number
Figure based on Reference 27 predict ion
Specific Impulse Modeling of Ramjet Baseline Specific Impulse Modeling of Ramjet Baseline
•
•
•
•
•
•
•
••
•
I S P ,
S p e c i f i c I m
p u l s e , s
1,500
1,000
500
00 1 2 3 4
Note:
Standard atmosphere
ϕ ≤ 1
ISP based on Reference 27 computer prediction.
Example: M = 3.5 ⇒ ISP = 1,120 s
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M, Mach Number
Rocket Booster Acceleration / Performance of
Ramjet Baseline
Rocket Booster Acceleration / Performance of
Ramjet Baseline 30
20
10
0
0 1.0 2.0 3.0 4.0
B o o s t T h r u s t ~ 1 0 0 0 l b
Time ~ s5.0 6.0
( ISP )Booster = 250 s
3.0
2.5
2 0B u r n o u t M a c h N u m b e r
2.0
1.0
0
Standard atmosphere
ML = 0.80Constant altitude flyout
B o o s t R a n g e
~ n m
0 20 40 60
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2.0 B
h, Altitude 1,000 ft
0 20 40 600 20 40 60 80h, Altitude 1,000 ft
Ramjet Baseline Has Best Performance at High
Altitude
Ramjet Baseline Has Best Performance at High
Altitude
500
400
300
200
100
00 1 2 3 4
R a n g e ~
n m
M, Mach Number
h = SL
20,000 ft
40,000 ft
60,000 ft
Note: ML = 0.8, Constant Al titude Fly-out
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,
Example, Mach 3 / 60k ft flyout ⇒ 445 nm. Breguet Range Predict ion is R = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )] = 2901 ( 1040 )( 3.15 ) ln ( 1739 / ( 1739 - 476 )) = 3,039,469 ft or 500 nm. Predicted range is 10% greater than baseline missi le data.
L , y
From Paredo Sensitivity, Ramjet Baseline Range
Driven by I SP , Fuel Weight, Thrust, and C D 0
From Paredo Sensitivity, Ramjet Baseline Range
Driven by I SP , Fuel Weight, Thrust, and C D 0
-1
-0.5
0
0.5
1
1.5
ISP Fuel
Weight
Thrust CD0, Zero-
Lift Drag
Coefficient
CLA, Lift-
Curve-
Slope
Coefficient
Inert
Weight
Parameter
N o
n d i m e n s i o n a l R
a n g e S e n s i t i v i t y
t o P a r
a m e t e r
Sea Level Flyout at Mach 2.3 20k ft Flyout at Mach 2.5
Example: At Mach 3.0 / 60k f t alti tude
cruise, 10% increase in fuel weight⇒ 9.6% increase in fl ight range
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40k ft Flyout at Mach 2.8 60k ft Flyout at Mach 3.0
Ramjet Baseline Flight Range Uncertainty Is +/- 7%, 1 σRamjet Baseline Flight Range Uncertainty Is +/- 7%, 1 σ
Parameter Baseline Value at Mach 3.0 / 60k ft Uncertainty in Parameter ΔR / R from Uncertain ty
1. Specific Impulse 1040 s +/- 5%, 1σ +/- 5%, 1σ
2. Ramjet Fuel Weight 476 lb +/- 1%, 1σ +/- 0.9%, 1σ
3. Cruise Thrust ( φ = 0.39 ) 458 lb +/- 5%, 1σ +/- 2%, 1σ
4. Zero-Lift Drag Coefficient 0.17 +/- 5%, 1σ +/- 4%, 1σ
5. Lift Curve Slope Coefficient 0.13 / deg +/- 3%, 1σ +/- 1%, 1σ
6. inert Weight 1205 lb +/- 2%, 1σ +/- 0.8%, 1σ
Level of Maturi ty Based on Flight Demo of Prototype, Subsystem Tests, and Integration
Wind tunnel tests
Direct connect, freejet, and booster firing propulsion tests
Structure test
Mock-up
Hardware-in-loop simulation
Flight Test
Total Flight Range Uncertainty at Mach 3.0 / 60k ft Flyout
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g g y y
ΔR / R = [ (ΔR / R )12 + (ΔR / R )2
2 + (ΔR / R )32 + (ΔR / R )4
2 + (ΔR / R )52 + (ΔR / R )6
2 ]1/2 = +/- 6.9%, 1σ
R = 445 nm +/- 31 nm, 1σ
Sizing Examples Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
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Soda Straw Rocket Design, Build, and Fly
Slurry Fuel and Efficient Packaging Provide
Extended Range Ramjet
Slurry Fuel and Efficient Packaging Provide
Extended Range Ramjet Propuls ion / Configuration Fuel Type / Volumetric
Performance (BTU / in3) /Density (lb / in3)
Fuel Volume (in3) /Fuel Weight (lb)
ISP (s) / CruiseRange at Mach 3.5,60k ft (nm)
Liquid Fuel Ramjet RJ-5 / 581 / 0.040 11900 / 476 1120 / 390
Ducted Rocket ( Low Smoke ) Solid Hydrocarbon / 1132 /0.075
7922 / 594 677 / 294
Ducted Rocket ( HighPerformance )
Boron / 2040 / 0.082 7922 / 649 769 / 366
Solid Fuel Ramjet Boron / 2040 / 0.082 7056 / 579 1170 / 496
Slurry Fuel Ramjet 40% JP-10, 60% boroncarbide / 1191 / 0.050
11900 / 595 1835 / 770
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Note: Flow Path Available Fuel Rcruise = V ISP ( L / D ) ln [ WBC / ( WBC - Wf )]
Sizing Examples Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missile
Range robustness
Propulsion and fuel alternatives
Velocity control
Computer Aided Conceptual Design Sizing Tools
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Soda Straw Rocket, Design, Build, and Fly
Example of Ramjet Velocity Control Through Fuel
Control
Example of Ramjet Velocity Control Through Fuel
Control
0.1
1
10
0 1 2 3 4
Mi, Impact Mach Number at Sea Level
Ramjet BaselineEquivalence Ratio
Ramjet Baseline Fuel
Flow Rate, lb / s
T
W
D
N t R j t b li ti l i t t l l t d t t l i t t i t T th t W i ht D d
Example for Ramjet Baseline:
Mi = 4, h = sea level, T0 = 519R
T + W - D = 0
W = WBO = 1263 lb
D = CD0q SRef = 3353 CD0
MI2 = 3353 ( 0.14 )
( 4 )2 = 7511 lb
Trequired = D - W = 7511 - 1263 = 6248 lb
wf
.= T / ISP = 6248 / 1000 = 6.25 lb / s
φ = Trequired / Tφ = 1 = 6248 / 25000 = 0.25
Note: Excess air provides cooling of combustor
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Note: Ramjet baseline, vertical impact at sea level, steady state veloci ty at impact, T = thrust, W = weight, D = drag,WBO = burnout weight, CD0
= zero-lift drag coefficient, Mi= impact Mach number, Trequired = required thrust for steadystate flight, w f
.= fuel flow rate, ISP = specific impulse, φ = equivalence ratio ( φ = 1 stochiometric )
Sizing Examples Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missi le
Range robustness
Propulsion and fuel alternatives
Surface impact velocity
Computer Aided Conceptual Design Sizing Tools
S d St R k t D i B ild d Fl
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Soda Straw Rocket Design, Build, and Fly
Computer Sizing Code Should Have Fast
Turnaround and Be Easy to Use
Computer Sizing Code Should Have Fast
Turnaround and Be Easy to Use Objective of Conceptual Design
Search Broad Solution Space
Iterate to Design Convergence
Characteristics of Good Conceptual Design Sizing Code Fast Turnaround Time
Easy to Use Directly Connect Predictions of Aeromechanics and Physical
Parameters to Trajectory Code
Simple, Physics Based Methods
Includes Most Important, Driving Parameters Provides Insight into Relationships of Design Parameters
Stable Computation
Imbedded Baseline Missile Data
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Human Designer Makes the Creative Decisions
Example of DO -Based Conceptual Sizing
Computer Code –ADAM
Example of DO -Based Conceptual Sizing
Computer Code –ADAM Conceptual Sizing Computer Program
Advanced Design of Aerodynamic Missiles ( ADAM )
PC compatible Written in DOS
Aerodynamic Module Based on NACA 1307 Calculates Static and dynamic stability derivatives
Control effectiveness and trim conditions 3, 4, 5, and 6-DOF Simulation Modules
Proportional guidance
Input provided automatically by aerodynamic module
Configurations Benchmarked with Wind Tunnel Data Greater than 50 Input Parameters Available
Defaults to benchmark configuration ( s )
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Example of Spreadsheet Based Conceptual
Sizing Computer Code - TMD Spreadsheet
Example of Spreadsheet Based Conceptual
Sizing Computer Code - TMD Spreadsheet
Conceptual Sizing Computer Code Tactical Missile Design ( TMD ) Spreadsheet
PC compatible
Windows Excel spreadsheet
Based on Tactical Missile Design Short Course and Textbook Aerodynamics
Propulsion
Weight
Flight trajectory Measures of merit
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Example of Spreadsheet Based Conceptual
Sizing Computer Code, TMD Spreadsheet
Example of Spreadsheet Based Conceptual
Sizing Computer Code, TMD Spreadsheet Define Mission Requirements [ Flight Performance ( RMax, RMin, V AVG ) , MOM, Const raints ]
Establish Baseline ( Rocket , Ramjet )
Aerodynamics Input ( d, l, lN, A, c, t, xcg ) Aerodynamics Output [ CD0
, CN, xac, Cmδ, L / D, ST ]
Propulsion Input ( pc, ε, c*, Ab, At, A0, Hf , ϕ, T4, Inlet Type )Propulsion Output [ Isp, Tcruise, p t2
/ p t0, w
., Tboost, Tsustain, ΔV
Boost]
Weight Input ( WL, WP, ρ, σmax )Weight Output [ WL, WP, h, dT / dt, T, t, σbuckling, MB, σ, Wsubsystems, xcg, Iy ]
Trajectory Input ( h i, Vi, Type ( cruise, boost , coast, ballistic, turn, glide )
Trajectory Output ( R, h, V, and γ versus time )
MeetPerformance?
Measures of Merit and Constraints
No [ pBlast, PK, nHit,
Vfragments PKEKE
No [ RMax, RMin, V AVG ]
Yes
Al t Mission
Al t Baseline
Resize / Alt Config /Subsystems / Tech
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Measures of Merit and Constraints V g , P ,KEWarhead, τTotal,σHE, σMAN, Rdetect,
CSDD, C1000th, Cunit x ]Yes
Example of TMD Spreadsheet Sizing Code
Verification: Air-to-Air Range Requirement
Example of TMD Spreadsheet Sizing Code
Verification: Air-to-Air Range Requirement Example Launch Conditions
hL = 20k f t
ML = 0.8 Example Requirement
RF = 6.7 nm with tf < 24.4 s
Solutions for Rocket Baseline
ADAM: RF = 6.7 nm at t f = 18 s TMD Spreadsheet: RF = 6.7 nm at t f = 19 s
3 DOF using wind tunnel aero data: RF = 6.7 nm at t f = 21 s
Differences in Flight Time to 6.7 nm Most ly Due to Zero-Lift Drag Coefficient.For Example: ADAM prediction at Mach 2.0: ( CD0
)coast = 0.53
TMD Spreadsheet prediction at Mach 2.0: ( CD0)coast = 0.57
Wind tunnel aero data at Mach 2.0: ( CD0)coast = 1.05
Wind Tunnel Data / Baseline Missile Data Correction Required to Reduce
Uncertainty in CD0
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Uncertainty in CD0
Sizing Examples Sizing Examples
Rocket Baseline Missile
Standoff range requirement
Wing sizing requirement
Multi-parameter harmonization
Lofted range comparison
Ramjet Baseline Missi le
Range robustness
Propulsion and fuel alternatives
Surface impact velocity
Computer Aided Conceptual Design Sizing Tools
Soda Straw Rocket Design Build and Fly
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Soda Straw Rocket Design, Build, and Fly
Example of Design, Build, and Fly Customer
Requirements
Example of Design, Build, and Fly Customer
Requirements Objective – Design, Build, and Fly Soda Straw Rocket with:
Flight Range Greater Than 90 ft
Weight Less Than 2 g
Furnished Property
Launch System
Distance Measuring Wheel
Weight Scale Micrometer Scale
Engineer’s Scale
Scissors
Furnished Material 1 “Giant” Soda Straw: 0.28 in Diameter by 7.75 in Length, Weight = 0.6 g
1 Strip Tabbing: ½ in by 6 in, Weight = 1.4 g
1 Ear Plug: 0.33 – 0.45 in Diameter by 0.90 in Length, Weight = 0.6 g
1 “Super Jumbo” Soda Straw: 0 25 in Diameter by 7 75 in Length
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1 Super Jumbo Soda Straw: 0.25 in Diameter by 7.75 in Length
Example of Design, Build, and Fly Customer
Requirements ( cont )
Example of Design, Build, and Fly Customer
Requirements ( cont )
Furnished Property Launch System with Specified Launch Conditions
Launch Tube Diameter: 0.25 in
Launch Tube Length ( e.g., 6 in )
Launch Pressure ( e.g., 30 psi )
Launch Elevation Angle ( e.g., 40 deg )
Predict Flight Trajectory Range and Compare with Test
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Soda Straw Rocket Launcher and Targeting Soda Straw Rocket Launcher and Targeting
9. Rocket on Launcher
8. Launch Tube
7. Incl inometer
6b. Manual ValveLauncher ( 0.1 saverage response )
6a. Solenoid ValveLauncher ( 0.025 saverage response )
5. Launch Switch
4. Pressure Gauge
3. Air Hose
2. Pressure Tank
1. Pump
11. Rockets wi th Various Length, Tail Geometry, Nose Geometry, and Other Surfaces
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g , y, y,
10. Laser Pointer Targeting Device
It Is Easy to Make a Soda Straw Rocket It Is Easy to Make a Soda Straw Rocket
1. Cut Large Diameter “ Giant” Soda Straw to DesiredLength
3. Slide Ear Plug Inside Soda Straw
5. Apply Adhesive Tabs to Soda Straw
4. Cut Adhesive Tabs to Desired Height and Width of Surfaces
7. Slide Giant Soda Straw Rocket Over Smaller
Diameter “Super Jumbo” Soda Straw Launch Tube
2. Twist and Squeeze Ear Plug to Fit Inside SodaStraw
6. Wrap Front of Ear Plug and Straw with Tape
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Soda Straw Rocket Baseline Configuration Soda Straw Rocket Baseline Configuration
llcc = 6.0 in= 6.0 in
l = 7.0 inl = 7.0 in
Ear Plug Soda Straw Strip Tabbing
0.28 in0.25 in
0.5 in
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Soda Straw Rocket Baseline Weight and Balance Soda Straw Rocket Baseline Weight and Balance
Component Weight, g cg Station, inNose ( Plug ) 0.6 0.5
Body ( Soda Straw ) 0.5 3.5
Fins ( Four ) 0.5 6.75
Total 1.6 3.39
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Soda Straw Rocket Baseline Definition Soda Straw Rocket Baseline Definition
Body
Material Type HDPE Plastic
Material density, lb / in3 0.043
Material strength, psi 4,600Thickness, in 0.004
Length, in 7.0
Diameter, in 0.28
Fineness ratio 25.0
Nose fineness ratio 0.5Fins
Material Plastic
Planform area, in2 ( 2 panels exposed ) 0.25
Wetted area, in2 ( 4 panels ) 1.00
Aspect ratio ( 2 panels exposed ) 1.00Taper ratio 1.0
Chord, in 0.5
Span ( exposed ), in 0.5
Span ( total including body ), in 0.78
Leading edge sweep, deg 0
xmac, in 6.625
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Soda Straw Rocket Baseline Definition ( cont ) Soda Straw Rocket Baseline Definition ( cont )
Nose
Material Type Foam
Material densi ty, lb / in3 0.012 Average diameter 0.39 in
Length 0.90 in
Reference Values
Reference area, in2 0.0616
Reference length, in 0.28
Thrust Performance
Inside cavity length, in 6.0
Typical Pressure, psi 30
Maximum thrust @ 30 psi pressure, lb 1.47
Time constant, s ( standard temperature ) 0.025
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For body-tail geometry, static margin given by
( x AC – xCG ) / d = - {( CN α )B {[ xCG – ( x AC )B ] / d } + ( CNα )T {[ xCG – ( x AC )T ] / d }( ST /SRef )} / [( CNα )B + ( CNα )T ST / SRef ]
For baseline soda straw configurationxCG = 3.39 in, d = 0.28 in, ( CNα )B = 2 per rad, ST = 0.25 in2, SRef = 0.0616 in2
( x AC )B = [( x AC )B / lN ] lN = 0.63 ( 0.14 ) = 0.09 in
( CNα )T = π AT / 2 = π ( 1 ) / 2 = 1.57( x AC )T = 6.5 + 0.25 ( cmac )T = 6.63
Substituting( x AC - xCG ) / d = - { 2 ( 3.39 – 0.09 ) / 0.28 + [ 1.57 ( 3.39 – 6.63 ) / 0.28 ] [ ( 0.25 ) /
0.0616 ]} / [ 2 + 1.57 ( 0.25 ) / 0.0616 ] = 6.00 ( statically stable )
x AC = 6.00 ( 0.28 ) + 3.39 = 5.07 in from nose
Soda Straw Rocket Baseline Static Margin Soda Straw Rocket Baseline Static Margin
(( xx AC )Tl
( x AC ) B
x x AC AC
x x CG CG
d
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Soda Straw Rocket Has High Acceleration Boost
Performance
Soda Straw Rocket Has High Acceleration Boost
Performance
0
20
40
60
80
100
0 2 4 6 8 10
s, Distance Traveled During Launch, Inches
V ,
V e l o
c i t y ,
f p s
pgauge = 15 psi pgauge = 30 psi
pgauge = 60 psi
T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) A
a ≈ 32.2 T / W, V = ∫ a dt, s = ∫ V dtThrust ( T ) from Pressur ized Tube of Area A
T = ( p – p0 ) A = pgauge ( 1 – e – t / τ ) A
A = ( π / 4 ) ( 0.25 )2 = 0.0491 in2, τ = Valve Rise Time
Example: Assume pgauge = 30 psi , lt = 6 in, τ = 0.025 s ( Averagefor Solenoid Valve ), s = lc = 6 in
Thrust Equation Is:
T = 30 ( 1 - e – t / 0.025 ) ( 0.0491 ) = 1.4726 ( 1 - e – 40.00 t )
Note: Ac tual Boost Thrust Lower ( Pressure Loss,
Boundary Layer, Launch Tube Leakage, LaunchTube Friction )
Equations for Acceleration ( a ), Velocity ( V ), andDistance ( s ) During Boost Are:
a ≈ 32.2 T / W = 32.2 ( 1.4726 ) ( 1 - e – 40.00 t ) / 0.00352= 13471.1 ( 1 - e – 40.00 t )
V = ∫ a dt = 13471.1 t + 336.78 e – 40.00 t – 336.78
s = ∫ V dt = 6735.57 t2 – 8.419 e – 40.00 t – 336.78 t +8.419
End of Boost Conditions Are:
s = lc = 6 in = 0.500 ft ⇒ t = 0.0188 s
a = 7123 ft / s2 = 221 g
V = 75.2 ft / sq = ½ ρ V2 = ½ ( 0.002378 ) ( 75.2 )2 = 6.72 psf
Note: Time TicsEvery 0.01 s
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M = V / c = 75.2 / 1116 = 0.0674
Most of the Soda Straw Rocket Drag Coefficient
Is from Body Skin Friction
Most of the Soda Straw Rocket Drag Coefficient
Is from Body Skin Friction
0
0.5
1
1.5
0 2 4 6 8 10
ST / SRef, Tail Planform Area / Reference Area
C D 0 ,
Z e r o - L i f t D r
a g C o e f f i c i e n t
V = 40 fps V = 80 fps
Example: V = 75.2 fps, ST = 0.00174 ft2, SRef =0.000428 ft2 ⇒ ST / SRef = 4.07
Compute:CD0
= 0.053 ( 25.0 ){ 0.0674 / [( 6.72 ) ( 0. 583 )]}0.2 +0.12 + 2 { 0.0133 { 0.0674 / [( 6.72 ) ( 0.0417 )]} 0.2 }[ 2
( 4.07 )] = 0.58 + 0.12 + 0.16 = 0.86Note:• Above Drag Coefficient Not Exact• Based on Assumption of Turbulent Boundary
Layer • Soda Straw Rocket Small Size and Low Velocity ⇒
Laminar Boundary Layer ⇒ Large Boundary Layer Thickness on Aft Body at Tails
Compute Drag Force:Dmax = CD qmax SRef = 0.86 ( 6.72 ) ( 0.000428 ) =
0.00247 lbCompare Drag Force to Weight:Dmax / W = 0.00247 / 0.00352 = 0.70
Note: Drag Force Smaller Than Weight
CD0= ( CD0
)Body,Friction + ( CD0)Base,Coast + ( CD0
)Tail,Friction
= 0.053 ( l / d ) [ M / ( q l )]0.2 + 0.12 + nT { 0.0133 [ M / ( q cmac )]0.2 } ( 2 ST / SRef )
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0
10
20
30
40
0 20 40 60 80 100
Rx, Horizontal Range, ft
h - h i , H e i g h t a b o v e I n i
t i a l L a u n c h
H e i g h t , f t
Gamma = 10 Deg Gamma = 30 Deg Gamma = 50 Deg
Soda Straw Rocket Baseline Has a Ballistic Flight
Range Greater Than 90 Feet
Soda Straw Rocket Baseline Has a Ballistic Flight
Range Greater Than 90 Feet Rx = { 2 W cos γi / [ gc ρ SRef CD0
]} ln { 1 + t / { 2W / [ gc ρ SRef CD0
Vi ]}}
h = { 2 W sin γi / [ gc ρ SRef CD0]} ln { 1 + t / { 2
W / [ gc ρ SRef CD0 Vi ]}} + h i - gc t2
/ 2
Note: Time Ticsevery 0.5 s
Example, Assume l t = 6 in, pgauge = 30 psi , γi= 30 deg, τ = 0.025 sec, Soda StrawBaseline, t = t impact = 1.8 s
Horizontal Range At Impact = Rx = { 2 (0.00352 ) cos γi / [ 32.2 ( 0.002378 ) (0.000428 ) ( 0.86 )]} ln { 1 + t / { 2 (0.00352 ) / [ 32.2 ( 0.002378 ) (0.000428 ) ( 0.86 ) ( 75.2 )]}}
= 249.8 cos γi ln ( 1 + 0.301 t )
= 249.8 ( 0.866 ) ln [ 1 + 0.301 ( 1.8 )] =93.7 ft
Height At Impact = h = { 2 ( 0.00352 )sin γi / [ 32.2 ( 0.002378 ) ( 0.000428 ) (0.86 )} ln { 1 + t / { 2 ( 0.00352 ) / [ 32.2( 0.002378 ) ( 0.000428 ) ( 0.86 ) ( 75.2)]}} + h i – 32.2 t2 / 2
= 249.8 sin γi ln ( 1 + 0.301 t ) + hi –32.2 t2 / 2 = 249.8 ( 0.5 ) ln [ 1 + 0.301 (
1.8 )] + h i – 32.2 ( 1.2 )2
/ 2= h + 1 9 ft
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= h i + 1.9 ft
Soda Straw Rocket Range Driven by Inside
Chamber Length and Launch Angle
Soda Straw Rocket Range Driven by Inside
Chamber Length and Launch Angle
-0.2
0
0.2
0.4
0.6
0.8
lc Gamma pgauge W tau CD0
NondimensionalRange
Sensitivity to
Parameter
Note: Decreased chamber length ⇒shorter duration thrust ( decreasedtotal impulse ) ⇒ decreased end-of-boost velocity
Soda Straw Rocket Baseline:
W = Weight = 0.00423 lb
lc = inside chamber length = 6 in
τ = Time constant to open solenoidvalve = 0.025 s
pgauge = gauge pressure = 30 psi
γi = Initial / launch angle angle = 30 deg
l t = 7 inV = Launch veloci ty = 75.2 fps
CD0= Zero-lift drag coefficient = 0.86
t impact = Time from launch to impact =1.8 s
Rx = Horizontal range = 94 ft
Example: 10% decrease in
inside chamber length ⇒7.7% decrease in range at t =1.8 s. Note: Result isnonlinear because insidechamber length = launcher length. Increase in lc alsoleads to decrease in range.
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Soda Straw Rocket Baseline Flight Range
Uncertainty Is +/- 2.4%, 1 σ
Soda Straw Rocket Baseline Flight Range
Uncertainty Is +/- 2.4%, 1 σ
Estimate of Level of Maturity / Uncertainty of Soda Straw Rocket Baseline Parameters Based on
Wind tunnel test
Thrust static test
Weight measurement
Prediction methods
Total Flight Range Uncertainty for 30 psi launch at 30 deg
ΔR / R = [ (ΔR / R )1
2 + (ΔR / R )2
2 + (ΔR / R )3
2 + (ΔR / R )4
2 + (ΔR / R )5
2 + (ΔR / R )6
2 ]1/2 = +/- 2.4%, 1σ
R = 94 ft +/- 2.3 ft, 1σ
+/- 0.2%, 1σ+/- 20%, 1σ0.866. Zero-Lift Drag Coefficient
+/- 0.2%, 1σ+/- 20%, 1σ0.025 s5. Solenoid Time Constant
+/- 0.4%, 1σ+/- 6%, 1σ1.6 g4. Weight
+/- 0.5%, 1σ+/- 3%, 1σ30 psi3. Gauge Pressure
+/- 1.7%, 1σ+/- 3%, 1σ30 deg2. Launch Angle
+/- 1.5%, 1σ+/- 2%, 1 σ6 in1. Inside Chamber Length
ΔR / R Due toUncertainty
Uncertainty inParameter
Baseline ValueParameter
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1 - Customer Requirements2 – Customer Importance Rating ( Total = 10 )
3 – Design Characteristics
4 – Design Characterist ics Impor tance Rating ( Total = 10 )
5 – Design Characteristics Sensitivity Matrix
6 – Design Characteristics Weighted Importance7 – Design Characteristics Relative Importance
House of Quality Translates Customer
Requirements into Engineering Emphasis
House of Quality Translates Customer
Requirements into Engineering Emphasis
Weight
Flight Range
3
7
Tail Planform AreaChamber Length
46
28
26 = ( 7x2 + 3x4 )74 = ( 7x8 + 3x6 )
21
0
Note on Design Characteristics SensitivityMatrix: ( Room 5 ):
++ Strong Synergy
+ Synergy
0 Near Neutral Synergy
- Anti-Synergy- - Strong Anti-Synergy
Note: Based on House of Quality, ins ide chamber length most important design parameter.
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DOE Explores the Broad Possible Design Space
with a Reasonably Small Set of Alternatives
DOE Explores the Broad Possible Design Space
with a Reasonably Small Set of Alternatives
0.1254Lower Value
0.256Upper Value
ST, Tail Planform Area,
in2
lc, Inside Chamber
Length, in
Engineering
Characteristics Range
“Petite”
“Stiletto”
“Shorty”“ Big Kahuna”
Concept Sketch
0.1254
0.1256
0.2540.256
ST, Tail Planform Area,in2
lc, Inside Chamber Length, in
Full Factorial DOE Based on Upper / Lower Values of k = 2 Parameters:Number of Combinations = 2k = 22 = 4
Design Space for Design of Experiments ( DOE )
Note: DOE concepts should emphasize customer driving requirements and the driving engineering characteristics.
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Engineering Experience Should Guide the DOE
Set of Alternatives and the Preferred Design
Engineering Experience Should Guide the DOE
Set of Alternatives and the Preferred Design As an Example, for the Soda Straw Rocket, from
Experience We Know That
Soda Straw Rocket Must Fit on Launcher Maximum Boost Veloci ty Occurs When Chamber Length = Launch
Tube Length
Three or Four Tails Best for Stability
Tails That Are Too Small May Result in an Unstable Flight
Tails That Are Too Large Add Weight and Cause TrajectoryDispersal
Canards Require Larger Tails for Stabil ity, Add Weight, and CauseTrajectory Dispersal
Wings Add Weight, Add Drag, and Cause Trajectory Dispersal
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Engineering Experience Should Guide the DOE
Set of Alternatives and Preferred Design ( cont )
Engineering Experience Should Guide the DOE
Set of Alternatives and Preferred Design ( cont )
As an Example, Soda Straw Rocket Geometry Should Be Comparable to an OperationalRocket with Near-Neutral Static Stabil ity ( e.g., Hydra70 )
2.66
1.89
1.89
2.79
2.79
b / d,
Total Tail Span /Diameter
217.9“Petite”
Hydra 70
“Stiletto”
“Shorty”
“ Big Kahuna”
Concept Sketch
115.1
225
217.9
225
c / d,
Tail Chord /Diameter
l / d,
Total Length /Diameter
Note: For a subsonic rocket with the center-of-gravity in the center of the rocket, slender body theory and slender
surface theory give total tail span and chord for neutral stability of b NeutralStability ≈ 2 d and cNeutralStability > ≈ drespectively.
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Optimum Design Should Have Balanced
Engineering Characteristics
Optimum Design Should Have Balanced
Engineering Characteristics
As an Example, for the Soda Straw Rocket Design We
Should Reflect Customer Emphasis of Requirements for
Range
Weight
Provide Balanced Emphasis of Most Important EngineeringCharacteristics
Chamber Length
Tail Size / Span
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Summary of Sizing Examples Summary of Sizing Examples
Rocket Powered Missile ( Sparrow Derived Baseline ) Standoff range requirement
Wing area sizing requirements for maneuverability, turn rate, andturn radius
Multi-parameter harmonization
Ballistic versus lofted glide flight range
Ramjet Powered Missile ( ASALM Derived Baseline ) Robustness in range uncertainty
Propulsion and fuel alternatives
Surface target impact velocity Computer Aided Sizing Tools for Conceptual Design
ADAM
Analytical prediction of aerodynamics
Numerical solution of equations of motion
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Summary of Sizing Examples ( cont ) Summary of Sizing Examples ( cont )
Computer Aided Sizing Tools for Conceptual Design ( cont ) TMD analytical sizing spreadsheet ( based on this text )
Analytical prediction of aero, propulsion, and weight
Closed form analytical solution of s implif ied equations of motion
Soda Straw Rocket Design, Build, and Fly
Static margin Drag
Performance
Sensitivity study
House of Quality Design of Experiment ( DOE )
Discussion / Questions?
Classroom Exercise ( Appendix A )
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2/24/2008
Sizing Examples Problems Sizing Examples Problems
1. Required flight range is shorter for a head-on intercept and it is longer for a t___ c____ intercept.
2. The rocket baseline center-of-gravity moves f______ with motor burn.
3. The rocket baseline is an a_______ airf rame.4. The rocket baseline thrust profi le is b____ s______.
5. The rocket baseline motor case and nozzle are made of s____.
6. The rocket baseline flight range is driven by ISP, propellant weightfraction, drag, and s_____ m_____.
7. Contributors to the maneuverabili ty of the rocket baseline are its body,tail , and w___.
8. Although the rocket baseline has sufficient g’s and turn rate tointercept a maneuvering aircraft, it needs a smaller turn r_____.
9. Compared to a co-altitude trajectory, the rocket baseline has extendedrange with a l_____ glide trajectory.
10. The ramjet baseline has a c___ inlet.
11. The Mach 4 ramjet baseline has a t_______ airframe.
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2/24/2008 ELF 370
Sizing Examples Problems ( cont ) Sizing Examples Problems ( cont )
12. Although the ramjet baseline combustor is a nickel-based super alloy, itrequires insulation, due high temperature. The super alloy is i______.
13. The flight range of the ramjet baseline is dr iven by ISP, weight, thrust,
zero-lift coefficient, and the weight fraction of f___.14. Extended range for the ramjet baseline would be provided by more
efficient packaging of subsystems and the use of s_____ fuels.
15. A conceptual design sizing code should be based on the simplicity,
speed, and robustness of p______ based methods.16. The House of Quality room for design characteristics weighted
importance indicates which engineering design characteristics are mostimportant in meeting the c_______ r___________.
17. Paredo sensitivity identifies the design parameters that are mosti________.
18. DOE concepts should emphasize the customer driving requirements andthe dr iving e__________ characteristics
19. If the total tail span ( including body diameter ) is twice the bodydiameter, the missile is approximately n________ s_____.
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2/24/2008 ELF 371
Outline Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration Sizing Examples
Development Process
Summary and Lessons Learned References and Communication
Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,Conversion Factors, Syllabus )
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2/24/2008 ELF 372
Relationship of Technology Assessment /
Roadmap to the Development Process
Relationship of Technology Assessment /
Roadmap to the Development Process Technology Roadmap Establishes Time-phased
Interrelationships for Technology development and validation tasks
Technology options
Technology goals
Technology transition ( ATD, ACTD, DemVal, PDRR, SDD )
Technology Roadmap Identifies Key, enabling, high payoff technologies
Technology drivers
Key decision points Critical paths
Facili ty requirements
Resource needs
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2/24/2008 ELF 373
Research Technology Acquisition
Relationship of Design Maturity to the US
Research, Technology, and Acquisition Process
Relationship of Design Maturity to the US
Research, Technology, and Acquisition Process
BasicResearch
ExploratoryDevelopment
AdvancedDevelopment
Demonstration& Validation
SystemDevelopment
andDemonstration
Production
~ $0.1B ~ $0.9B~ $0.3B ~ $0.5B ~ $1.0B ~ $6.1B ~ $1.2B
6.1 6.2 6.3 6.4 6.5
SystemUpgrades
Technology
Development~ 10 Years
Technology
Demonstration~ 8 Years
Prototype
Demonstration~ 4 Years
Full Scale
Development~ 5 Years
Limited~ 2 Years
1-3 Block
Upgrades~ 5-15 Years
First
Block~ 5Years
ProductionNote:Total US DoD Research and Technology for Tactical Missi les ≈ $1.8 Billi on per year
Total US DoD Acquisi tion ( SDD + Production + Upgrades ) for Tactical Miss iles ≈ $8.3 Billi on per year Tactical Missiles ≈ 11% of U.S. DoD RT&A budgetUS Indust ry IR&D typically s imi lar to US DoD 6.2 and 6.3A
Matur ity Level Conceptual Design Prel iminary Design Detai l Design Production Design
Drawings ( type ) < 10 ( subsystems ) < 100 ( components ) > 100 ( parts ) > 1000 ( parts )
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2/24/2008 ELF 374
Technology Readiness Level ( TRL ) Indicates
the Maturity of Technology
Technology Readiness Level ( TRL ) Indicates
the Maturity of Technology TRL 1- 3
Category 6.1
Basicresearch
TRL 4
Category 6.2A
Exploratorydevelopmentof acomponent,conceptualdesignstudies, andpredictionmethods
TRL 5
Category 6.2B
Exploratorydevelopmentof asubsystem
TRL 6
Category 6.3
Advanced techdemo of asubsystem
TRL 7
Category 6.4
Prototypedemonstration
Initial assessment ⇒ component test ⇒ subsystem test ⇒ integrated subsystems ⇒ integrated missile
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2/24/2008 ELF 375
Conceptual Design Has Broad Alternatives
While Detail Design Has High Definition
Conceptual Design Has Broad Alternatives
While Detail Design Has High Definition
1
10
100
1000
0 5 10 15
Time ( Years )
T y p i c a l N u m b e r
o f A l t e r n a t i v e C o
n c e p t s
o r N u m b e r o f D e s i g n D r a w i n
g s
Number of Concepts
Number of Drawings
Conceptual Prelim. Detail Product ionDesign Design Design Design
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3 5
2/24/2008 ELF 376
US Tactical Missile Follow-On Programs Occur
about Every 24 Years
US Tactical Missile Follow-On Programs Occur
about Every 24 Years
Year Entering SDD
AIM-9X ( maneuverabili ty ), 1996 - Hughes
AIM-120 ( autonomous, speed,
range, weight ), 1981 - Hughes
Long Range ATS, AGM-86, 1973 - Boeing AGM-129 ( RCS ), 1983 - General Dynamics
PAC-3 (accuracy), 1992 - Lockheed MartinLong Range STA, MIM-104, 1966 - Raytheon
1950 1965 1970 1975 1980 1985 1990 1995 > 2000
AGM-88 ( speed, range ), 1983 - TI
Man-portable STS, M-47, 1970 - McDonnell Douglas
Anti -radar ATS, AGM-45, 1961 - TI
Short Range ATA, AIM-9, 1949 - Raytheon
Javelin ( gunner survivability,lethality , weight ), 1989 - TI
Medium Range ATA, AIM-7,1951 - Raytheon
Medium Range ATS, AGM-130, 1983 - Rockwell JASSM ( cost, range,observables ), 1999 - LM
Hypersonic Missile, > 2007
Hypersonic Missile > 2007
Long Range STS, BGM-109, 1972 - General Dynamics Hypersonic Missile > 2007
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Missile Design Validation / Technology
Development Is an Integrated Process
Missile Design Validation / Technology
Development Is an Integrated Process •Rocket Static•Turbojet Static•Ramjet Tests-Direct Connect-Freejet
StructureTest
HardwareIn-Loop
Simulation
Ballistic Tests
Lab Tests
Seeker
Ac tuators / Init iators
Sensors
Propulsion Model
Aero Model
Model Digital Simulation
Wind TunnelTests
Propulsion
Ai rf rame
Guidanceand Control
Power Supply
Warhead
EnvironmentTests•Vibration•Temperature
Sled Tests
IM Tests
IM Tests
Flight Test Progression( Captive Carry,Jettison,Separation, Unpowered
Guided Flights, PoweredGuided Flights, LiveWarhead Flights )Lab Tests
Tower Tests
Autopi lo t / Electronics
Witness / Arena Tests
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Airframe Wind Tunnel Test ………………………………………………………
Propulsion Static Firing with TVC ……..
Propulsion Direct Connect Test …………………………………….
Propulsion Freejet Test …………
Examples of Missile Development Tests and
Facilities
Examples of Missile Development Tests and
Facilities
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Examples of Missile Development Tests and
Facilities ( cont )
Examples of Missile Development Tests and
Facilities ( cont ) Warhead Arena Test ……………………………………………………….
Warhead Sled Test ………………………
Insensitive Munition Test ……………………………………………..
Structure Test …………………………………………..
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Examples of Missile Development Tests and
Facilities ( cont )
Examples of Missile Development Tests and
Facilities ( cont ) Seeker Test ……………………………………………………….
Hardware-In-Loop ………
Environmental Test ……………………………………………..
Submunition Dispenser Sled Test ……………………
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RCS Test ……………………………………………………………….
Store / Avionics Test
Flight Test ……………………………………………………………………….
Video of Facil ities and Tests
Examples of Missile Development Tests and
Facilities ( cont )
Examples of Missile Development Tests and
Facilities ( cont )
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Missile Flight Test Should Cover Extremes of
Flight Envelope
Missile Flight Test Should Cover Extremes of
Flight Envelope
Flight 7
Flight 7
Flight 3
Flight 7
Flight 1
Flight 3
F l ig h t 7
Flight 3
Flight 7
H i g h D
y n a m
i c P r
e s s u
r e
High Aero Heating
High L / D Cruise
L o w D y
n a m i
c P r e s
s u r e
B o o s t e r
T r a n s i t i o n :
T h r u s t - D r a g
Note: Seven Flights from Oct 1979 to May 1980.Flight 1 failure of fuel control. As a result of the high thrust , the flight Mach number exceeded the design Mach number.
Example: Ramjet Baseline Propuls ion Test Validation ( PTV )
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Example of Aero Technology Development Example of Aero Technology Development
Conceptual Design ( 5 to 50 input parameters ) Prediction
Preliminary Design ( 50 to 200 input parameters ) Prediction
Missile DATCOM. Contact: AFRL. Attr ibutes include: Low cost MISL3. Contact: NEAR. Attr ibutes include: Modeling vortex shedding
SUPL. Contact: NEAR. Attr ibutes include: Paneling complex geometry
AP02. Contact: NSWC. Attributes include: Periodic updates
CFD. Contact: Georgia Tech. Attributes include: Model runs on ParallelProcessing PCs
Preliminary Design Optimization
Response Surface Model: Contact: Georgia Tech. Attributes include10x more rapid computation
Probabilistic Analysis: Contact: Georgia Tech. Attr ibutes include anevaluation of design robustness
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Example of Missile Technology State-o -the-Art
Advancement: Air-to-Air Missile Maneuverability
Example of Missile Technology State-o -the-Art
Advancement: Air-to-Air Missile Maneuverability
0
10
20
30
40
50
60
1950 1960 1970 1980 1990 2000 2010
Year IOC
O p e r a t i o n a l A
n g l e o f A t t a c k ,
D e
AIM-7A
AM-9B
R530
AA-8 AIM-54
R550
Skyflash
Python 3
AA-10 Aspide
Super 530D
AA-11
AIM-120
Python 4
AA-12
MICA
AIM-132
AIM-9X
Controls Augmentedwith PropulsionDevices ( TVC,Reaction Jet )
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Example of Missile Technology State-o -the-Art
Advancement: Ramjet Propulsion
Example of Missile Technology State-o -the-Art
Advancement: Ramjet Propulsion
0
1
2
3
45
6
7
1950 1960 1970 1980 1990 2000 2010
Year Flight Demonstration
M c r u i s e ,
C r u i s e M a c h
N u m b e r
Cobra X-7 Vandal/Talos St-450 SE 4400RARE Bloodhound BOMARC Typhon STATEXD-21 CROW SA-6 Sea Dart LASRM ALVRJ 3M80 ASAL M AS-17 / Kh-31 ASMP
ANS Kh-41 SLAT BrahMos Meteor HyFly SED
Scramjet
Ramjet
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Enabling Technologies for Tactical Missiles Enabling Technologies for Tactical Missiles DomeFaceted / WindowMulti-modeMulti-spectralMulti-lens
Seeker
Multi-modeMulti-spectralSARStrapdownUncooled ImagingHigh Gimbal
G & CGPS / INSIn-flight Optimizeα, β Feedback ATR
Propulsion
Hypersonic Turbine-BasedLiqu id / Solid Fuel RamjetVariable Flow Ducted RocketScramjetCombined Cycle PropulsionHigh Temperature Turbine
High Temperature Combustor High Density Fuel / PropellantHigh Throttle Fuel ControlEndothermic FuelComposite CasePintle / Pulsed / Gel Motor High Burn Rate Exponent PropellantLow Observable
WarheadHigh Energy DensityMulti-modeHigh Density Penetrator Boosted Penetrator Smart Dispenser
Powered Submunition
InsulationHypersonicHigh Density
Flight ControlEM andPiezoelectricTVC / Reaction JetDedicated RollPower
MEMS
AirframeLifting BodyNeutral Static MarginLattice FinsSplit CanardLow Δx AC Wing / Low Hinge Moment ControlFree-to-Roll TailsCompressed Carriage
Low Drag InletMixed Compression InletSingle Cast StructureVARTM, Pultrusion, Extrusion , Filament WindHigh Temperature Compos itesTitanium Alloy
MEMS Data CollectionLow Observable Shaping and Materials
Electronics
COTS
Central
Data LinkBDI / BDAIn-flight RetargetMoving TargetPhased Array
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Summary of Development Process Summary of Development Process
Development Process
Technology roadmap
Development activities
Time frame
Level of Design Maturi ty Related to Stage of Development
Missile Follow-on Programs
Subsystems Development Activi ties
Subsystems Integration and Missile System Development
Flight Test Activi ties
Missi le Development Tests and Facil ities
State-of-the-Art Advancement in Tactical Missiles New Technologies for Tactical Missiles
Discussion / Questions?
Classroom Exercise ( Appendix A )
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Development Process Problems Development Process Problems
1. A technology roadmap establishes the high payoff technologies g____.
2. The levels of design maturity from the most mature to least mature areproduction, detail, preliminary, and c_________ design.
3. Technology transitions occur from basic research to exploratorydevelopment, to advanced development, to d____________ and v_________.
4. Approximately 11% of the U.S. RT&A budget is allocated to t_______m_______.
5. In the U.S., a tactical missile has a follow-on program about every __ years.
6. Compared to the AIM-9L, the AIM-9X has enhanced m______________.
7. Compared to the AIM-7, the AIM-120 has autonomous guidance, lighter weight, higher speed, and longer r____.
8. Compared to the PAC-2, the PAC-3 has h__ t_ k___ accuracy.
9. Guidance & control is verified in the h_______ in l___ simulation.
10. Airbreathing propulsion ground tests include direct connect tests and
f______ tests.11. Aerodynamic force and moment data are acquired in w___ t_____ tests.
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Outline Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration Sizing Examples
Development Process
Summary and Lessons Learned References and Communication
Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,Conversion Factors, Syllabus )
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Evaluate Alternatives and Iterate the System-o -
Systems Design
Evaluate Alternatives and Iterate the System-o -
Systems Design • Mission / Scenario
Definition
• WeaponRequirements,Trade Studiesand Sensitivity
Analysis
• Launch PlatformIntegration
• Weapon ConceptDesign Synthesis
• Technology Assessment andDev Roadmap
InitialTech
InitialReqs
BaselineSelected
Al tConcepts
Initial Carriage /Launch
Iteration
RefineWeapons
Req
Initial Revised
Trades / Eval Effectiveness / Eval
TechTrades
InitialRoadmap
RevisedRoadmap
Update
Note: Typical design cycle for conceptual design is usually 3 to 9 months
Al ternate Concepts ⇒ Select Preferred Design ⇒Eval / Refine
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Exploit Diverse Skills for a Balanced Design Exploit Diverse Skills for a Balanced Design
Customer ( requirements pull )
⇒ mission / MIR weight ing
Operations analysts⇒ system-of-systems analysis
System integration engineers⇒ launch platform integration
Missile design engineers⇒ missile concept synthesis
Technical specialists ( technology push )⇒ technology assessment / roadmap
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Utilize Creative Skills Utilize Creative Skills
Use Creative Skil ls to Consider Broad Range of Alternatives
Ask Why? of Requirements / Constraints
Project into Future ( e.g., 5 – 15 years )
State-of-the-art ( SOTA )
Threat
Scenario / Tactics / Doctrine
Concepts
Technology Impact Forecast Recognize and Disti ll the Most Important, Key Drivers
Develop Missile Concept that is Synergistic within aSystem-of-Systems
Develop Synergistic / Balanced Combination of HighLeverage Subsystems / Technologies
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Identify and Quantify the High Payoff Measures of Merit
Identify and Quantify the High Payoff Measures of Merit
Max / MinRange
Time toTarget
Robustness
WeightSurvivability
Lethality Miss Distance
Observables
Reliability
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Start with a Good Baseline Start with a Good Baseline
I would haveused the wheelas a baseline.
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Conduct Balanced, Unbiased Tradeoffs Conduct Balanced, Unbiased Tradeoffs
Aerodynamics
Propulsion
Structures
Seeker
Guidance andControl
Warhead – Fuze
Production
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AA- 8 / R-60 Python 4 Magic 550 U-Darter
Python 5 Derby / R-Darter AIM-9L Aspide
AA-10 / R-27 Skyflash AIM-7 R-37
AA-12 / R-77 AIM-9x Super 530D AIM-132
AA-11 / R-73 AIM-54 AIM-120 Mica
IRIS-T Meteor A-Darter Taildog
Evaluate Many Alternatives Evaluate Many Alternatives
Note: Although all of the above are supersonic air-to-air missiles, they have different configuration geometry
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Search a Broad Design Solution Space ( Global
Optimization vs Local Optimization )
Search a Broad Design Solution Space ( Global
Optimization vs Local Optimization )
Local Optimum ( e.g., Lowest Cost
Only in Local Solut ion Space )
Local Optimum ( e.g., Lowest CostOnly in Local Solut ion Space )
Global Optimum ( e.g., Lowest Cost inGlobal Solution Space ) within Constraints
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Evaluate and Refine as Often as Possible Evaluate and Refine as Often as Possible
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Provide Balanced Emphasis of Analytical vs
Experimental
Provide Balanced Emphasis of Analytical vs
Experimental
Thomas Edison: " Genius is 1%
inspiration and 99% perspiration."
Albert Einstein: " The only real
valuable thing is in tuition."
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2/24/2008 ELF 401
Use Design, Build, and Fly Process, for
Feedback That Leads to Broader Knowledge
Use Design, Build, and Fly Process, for
Feedback That Leads to Broader Knowledge
Design
Build
Fly ( Test )
Prediction SatisfiesCustomer
Requirements?
Test Results SatisfyCustomer Requirements
and Consistent withPrediction?
Is it Producible?
No
Yes
C l i m
b L
a d d
e r o
f K
n o w
l e d g e
Data
Failure /
Success
Information
Understanding
Wisdom
No
No
Where is the wisdom we have lost inknowledge? Where is the knowledgewe have lost in information?--T. S.
Eliot ( The Rock ) Knowledge comes by taking thingsapart: analysis. But wisdom comes byputting things together.--John A.Morrison
We are drowning in information but
starved for knowledge.--John Naisbitt( Megatrends: Ten New Directions Transforming Our Lives )
We learn wisdom from failure muchmore than from success. We oftendiscover what will do, by finding outwhat will no t do; and probably he who
never made a mistake never made adiscovery.--Samuel Smiles ( Self Help )
Knowledge
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Evaluate Technology Risk Evaluate Technology Risk
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Keep Track of Assumptions and Develop Real-
Time Documentation
Keep Track of Assumptions and Develop Real-
Time Documentation
It’s finallyfinished ! . . .
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2/24/2008 ELF 405
Utilize Group Skills Utilize Group Skills
Source: Nicolai, L.M., “ Designing a Better Engineer,” AIAA Aerospace America, April 1992
Detail /ProductionDesign –
30%
Other ThanDesign –
60%
Preliminary Design – 8%Conceptual Design – 2%
(Test, Analysis,Configuration
Management, Software,Program Management,
Integration,Requirements,
etc.)
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Balance the Tradeoff of Importance vs Priority Balance the Tradeoff of Importance vs Priority
Advanced Programs /
Conceptual Design
SDD Programs /
Preliminary Design
Production Programs /
Detail Design
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Evaluate Alternatives and Iterate the
Configuration Design
Evaluate Alternatives and Iterate the
Configuration Design
Yes
Establish Baseline
Meet
Performance?
No
No
Yes
Resize / Alt Conf ig / Subsystems / Tech
Al t Mission
Al t Baseline
Define Mission Requirements
Aerodynamics
Propulsion
Weight
Trajectory
Measures of Merit and Constraints
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Configuration Sizing Conceptual Design
Guidelines: Aeromechanics
Configuration Sizing Conceptual Design
Guidelines: Aeromechanics
Configuration Sizing Parameter Aeromechanics Design Guideline Body fineness ratio 5 < l / d < 25
Nose fineness ratio lN / d ≈ 2 if M > 1 Boattail or flare angle < 10 deg
Efficient cruise dynamic pressure q < 1,000 psf
Missile homing velocity VM / VT > 1.5
Ramjet combustion temperature > 4,000° F Oblique shocks prior to inlet normal > 2 obl ique shocks / compressions i f M >
shock to satisfy MIL-E-5008B 3.0, > 3 shocks / compressions if M > 3.5
Inlet flow capture Shock on cowl lip at Mmax cruise
Ramjet Minimum cruise Mach number M > 1.2 x MInletStart , M > 1.2 MMaxThrust = Drag
Subsystems packaging Maximize available volume for fuel /propellant
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Configuration Sizing Conceptual Design
Guidelines: Guidance & Control
Configuration Sizing Conceptual Design
Guidelines: Guidance & Control
Configuration Sizing Parameter G&C Design Guideline Body bending frequency ωBB > 2 ω ACT
Trim control power α / δ > 1 Neutral stability tail-body If low aspect ratio, b / d ≈ 2, c / d > ≈ 1
Stability & control cross coupling < 30%
Airframe time constant τ < 0.2 s
Missile maneuverability nM / nT > 3
Proportional guidance ratio 3 < N’ < 5
Target span resolution by seeker < btarget
Missile heading rate γ.
M> γ.
T Missile turn radius RTM
< RTT
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Wrap Up ( Part 1 of 2 ) Wrap Up ( Part 1 of 2 )
Missile design is a creative and i terative process that includes System considerations
Missile concepts and sizing Flight trajectory evaluation
Cost / performance drivers may be “ locked in” duringconceptual design
Missile design is an opportunity for a diverse group to worktogether for a better product Military customer ⇒ mission / scenario definition
Operations analysts ⇒ system-of-systems modeling System integration engineers ⇒ launch platform integration
Missi le design engineers ⇒ missile concept synthesis
Technical specialists ⇒ technology assessment / technology roadmap
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Wrap Up ( Part 2 ) Wrap Up ( Part 2 )
The missile conceptual design philosophy requires Iteration, iteration, iteration
Evaluation of a broad range of alternatives Traceable flow-down allocation of requirements
Starting with a good baseline
Paredo sensitivity analysis to determine the most important, driving
parameters Synergistic compromise / balanced subsystems and technologies
that are high leverage
Awareness of technology SOTA / technology assessment
Technology impact forecast
Robust design
Creative design decisions made by the designer ( not the computer )
Fast, simple, robust, physics-based prediction methods
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Outline Outline
Introduction / Key Drivers in the Design Process
Aerodynamic Considerations in Tactical Missile Design
Propulsion Considerations in Tactical Missile Design
Weight Considerations in Tactical Missile Design
Flight Performance Considerations in Tactical Missile Design
Measures of Merit and Launch Platform Integration
Sizing Examples
Development Process
Summary and Lessons Learned
References and Communication
Appendices ( Homework Problems / Classroom Exercises,Example of Request for Proposal, Nomenclature, Acronyms,
Conversion Factors, Syllabus )
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References References
1. “Missile.index,” http://missile.index.ne.jp/en/
2. AIAA Aerospace Design Engineers Guide, American Institu te of Aeronautics and Astronautics , 1993
3. Bonney, E.A., et al, Aerodynamics, Propulsion, Structures, and Design Practice , “ Principles of Guided Missile Design” ,D. Van Nostrand Company, Inc., 1956
4. Jerger, J.J., Systems Preliminary Design Principles of Guided Missile Design , “ Principles of Guided Missile Design” , D.Van Nostrand Company, Inc., 1960
5. Chin, S.S., Missile Configuration Design , McGraw-Hill Book Company, 1961
6. Mason, L.A., Devan, L., and Moore, F.G., “Aerodynamic Design Manual for Tactical Weapons,” NSWCTR 81-156, 1981
7. Pitts, W.C., Nielsen, J.N., and Kaattari, G.E., “Lif t and Center of Pressure of Wing-Body-Tail Combinations at Subsonic,Transonic, and Supersonic Speeds,” NACA Report 1307, 1957
8. Jorgensen, L.H., “Prediction of Static Aerodynamic Characteristics for Space-Shutt le-Like, and Other Bodies at Anglesof Attack From 0° to 180°,” NASA TND 6996, January 1973
9. Hoak, D.E., et al., “ USAF Stabil ity and Control DATCOM,” AFWAL TR-83-3048, Global Engineering, 1978
10. “ Nielsen Engineering & Research (NEAR) Aerodynamic Software Products,” http://www.nearinc.com/near/software.htm
11. Ash ley, H., Engineering Analysis of Flight Vehicles,Dover Publications, Inc., 1974
12. Anderson, John D. Jr., “Modern Compressible Flow,” Second Edition, McGraw Hill , 1990
13. Kinro th, G.D. and Anderson, W.R., “ Ramjet Design Handbook,” CPIA Pub. 319 and AFWAL TR 80-2003, June 1980
14. “Technical Aerodynamics Manual,” North American Rockwell Corporation , DTIC AD 723823, June 1970
15. Oswatitsch, K.L., “Pressure Recovery for Missi les with Reaction Propuls ion at High Supersonic Speeds” , NACA TM -1140, 1947
16. Carslaw, H.S. and Jaeger, J. C., Conduction of Heat in Solids, Clarendon Press, 1988
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References ( cont ) References ( cont )
17. Allen, J. and Eggers, A.J., “ A Study of the Motion and Aerodynamic Heating of Balli stic Missiles Entering the Earth ’s Atmosphere at High Supersonic Speeds” , NACA Report 1381, Apri l 1953.
18. Schneider, S.H., Encyclopedia of Climate and Weather, Oxford University Press, 1996
19. Klein, L.A., Millimeter-Wave and Infrared Multisensor Design and Signal Processing, Artech House, Boston, 1997
20. US Army Ordnance Pamphlet ORDP-20-290-Warheads, 1980
21. Carleone, J. (Editor), Tactical Missile Warheads, “ AIAA Vol . 155 Progress in Astronautics and Aeronaut ics,” AmericanInstitute of Aeronautics and Astronautics, 1993
22. Christman, D.R. and Gehring, J.W., “ Analysis of High-Veloci ty Projecti le Penetration Mechanics,” Journal of AppliedPhysics, Vol. 37, 1966
23. Heaston, R.J. and Smoots, C.W., “Precision Guided Munit ions,” GACIAC Report HB-83-01, May 1983
24. Donatelli, G.A. and Fleeman, E.L., “ Methodology for Predict ing Miss Distance for Air Launched Missiles,” AIAA-82-0364, January 1982
25. Bennett, R.R. and Mathews, W.E., “ Analyt ical Determination of Miss Distances for L inear Homing NavigationSystems,” Hughes Tech Memo 260, 31 March 1952
26. Nicholas, T. and Rossi, R., “US Missi le Data Book, 1996,” Data Search Associates, 1996
27. Bithell, R.A. and Stoner, R.C., “Rapid Approach for Missile Synthesis,” AFWAL TR 81-3022, March 1982
28. Fleeman, E.L. and Donatelli, G.A., “Conceptual Design Procedure Applied to a Typical Air-Launched Missile,” AIAA 81-1688, August 1981
29. Hindes, J.W., “ Advanced Design of Aerodynamic Missiles ( ADAM ),” October 1993
30. Frits, A.P., et al, “ A Conceptual Sizing Tool for Tactical Missiles, “ AIAA Missi le Sciences Conference, November 2002
31. Bruns, K.D., Moore, M.E., Stoy , S.L., Vukelich, S.R., and Blake, W.B., “ Missile DATCOM,” AFWAL-TR-91-3039, Apr il
1991
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References ( cont ) References ( cont )
32. Moore, F.G., et al, “ The 2002 Version of the Aeroprediction Code” , Naval Surface Warfare Warfare Center, March 2002
33. Nicolai, L.M., “Design ing a Better Engineer,” AIAA Aerospace America, April 1992
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Bibliography of Other Reports and Web Sites Bibliography of Other Reports and Web Sites
System Design
Fleeman, E.L., “Tactical Missile Design,” American Institute of Aeronautics and Astronautics, 2006
“ DoD Index of Specifications and Standards,” http://stinet.dtic.mil/str/dodiss.html
“Periscope,” http://www.periscope1.com/
Defense Technical Information Center, http://www.dtic.mil/ NATO Research & Technology Organisation, http://www.rta.nato.int/
“ Missile System Flight Mechanics,” AGARD CP270, May 1979
Hogan, J.C., et al., “ Missile Automated Design ( MAD ) Computer Program,” AFRPL TR 80-21, March 1980
Rapp, G.H., “Performance Improvements With Sidewinder Missi le Airf rame,” AIAA Paper 79-0091, January 1979
Nicolai, L.M., Fundamentals of Aircraft Design , METS, Inc., 1984
Lindsey, G.H. and Redman, D.R., “ Tactical Missile Design,” Naval Postgraduate School, 1986
Lee, R.G., et al, Guided Weapons, Third Edition , Brassey’s, 1998
Giragosian, P.A., “ Rapid Synthesis for Evaluating Missile Maneuverability Parameters,” 10th AIAA Appl ied Aerodynamics Conference, June 1992
Fleeman, E.L. “ Aeromechanics Technologies for Tactical and Strategic Guided Missi les,” AGARD Paper
presented at FMP Meeting in London, England, May 1979 Raymer, D.P., Aircraft Design, A Conceptual Approach, American Institute of Aeronaut ics and Ast ronautics, 1989
Ball , R.E., The Fundamentals of Aircraft Combat Survivabili ty Analysis and Design, American Institute of Aeronautics and Astronaut ics, 1985
“ National Defense Preparedness Association Conference Presentations,” http://www.dtic.mil/ndia
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Bibliography of Other Reports and Web Sites ( cont ) Bibliography of Other Reports and Web Sites ( cont )
System Design ( continued ) Eichblatt , E.J., Test and Evaluation of the Tactical Missile, American Institute of Aeronaut ics and Astronautics,
1989 “ Aircraft Stores Interface Manual (ASIM),” http://akss.dau.mil/software/1.jsp “ Advanced Sidewinder Missi le AIM-9X Cost Analysis Requirements Description (CARD),”
http://deskbook.dau.mil/jsp/default.jsp Wertz, J.R and Larson W.J., Space Mission Analysis and Design, Microprism Press and Kluwer Academic
Publishers, 1999
“ Directory of U.S. Military Rockets and Missiles” , http://www.designation-systems.net/
Fleeman, E.L., et al, “ Technologies for Future Precision Strike Miss ile Systems,” NATO RTO EN-018, July 2001
“ The Ordnance Shop” , http://www.ordnance.org/portal/
“ Conversion Factors by Sandelius Instruments” , http://www.sandelius.com/reference/conversions.htm “Defense Acquisition Guidebook”, http://akss.dau.mil/dag/
Aerodynamics “ A Digital Library for NACA,” http://naca.larc.nasa.gov/ Briggs, M.M., Systematic Tactical Missile Design, Tactical Missile Aerodynamics: General Topics , “AIAA Vol.
141 Progress in Astronautics and Aeronautics,” American Institute of Aeronautics, 1992 Briggs, M.M., et al., “ Aeromechanics Survey and Evaluation, Vol. 1-3,” NSWC/DL TR-3772, October 1977 “ Missile Aerodynamics,” NATO AGARD LS-98, February 1979 “ Missile Aerodynamics,” NATO AGARD CP-336, February 1983 “ Missile Aerodynamics,” NATO AGARD CP-493, April 1990 “ Missile Aerodynamics,” NATO RTO-MP-5, November 1998
Nielsen, J.N., Missile Aerodynamics , McGraw-Hill Book Company, 1960
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Bibliography of Other Reports and Web Sites ( cont ) Bibliography of Other Reports and Web Sites ( cont )
Aerodynamics ( cont inued ) Mendenhall, M.R. et al, “ Proceedings of NEAR Conference on Missile Aerodynamics,” NEAR, 1989 Nielsen, J.N., “Missile Aerodynamics – Past, Present, Future,” AIAA Paper 79-1818, 1979 Dillenius, M.F.E., et al, “Engineering-, Intermediate-, and High-Level Aerodynamic Predict ion Methods and
Appl ications,” Journal of Spacecraft and Rockets, Vo l. 36, No. 5, September-October, 1999
Nielsen, J.N., and Pitts, W.C., “ Wing-Body Interference at Supersonic Speeds wi th an Application toCombinations with Rectangular Wings,” NACA Tech. Note 2677, 1952
Spreiter, J.R., “ The Aerodynamic Forces on Slender Plane-and Cruciform-Wing and Body Combinations” , NACAReport 962, 1950
Simon, J.M., et al, “ Missile DATCOM: High Angle of Attack Capabili ties, AIAA-99-4258 Burns, K.A., et al, “ Viscous Effects on Complex Configurations,” WL-TR-95-3060, 1995
Lesieutre, D., et al, “ Recent Appl ications and Improvements to the Engineering-Level Aerodynamic Predict ionSoftware MISL3,’’ AIAA-2002-0274 Moore, F.G., Approximate Methods for Weapon Aerodynamics, American Institute of Aeronaut ics and
Astronaut ics, 2000 “1976 Standard Atmosphere Calculator”, http://www.digitaldutch.com/atmoscalc/ “ Compressible Aerodynamics Calculator” , http://www.aoe.vt.edu/~devenpor/aoe3114/calc.html Ashley, H. and Landahl, M., Aerodynamics of Wings and Bodies , Dover Publications, 1965 John, James E.A., Gas Dynamics , Second Edition, Prentice Hall, 1984 Zucker, Robert D., Fundamentals of Gas Dynamics , Matrix Publ ishers, 1977
Propulsion Chemical Information Propulsion Agency, http://www.cpia.jhu.edu/
St. Peter, J., The History of Aircraft Gas Turbine Engine Development in the United States: A Tradition of Excellence, ASME International Gas Turbine Inst itute, 1999
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Bibliography of Other Reports and Web Sites ( cont ) Bibliography of Other Reports and Web Sites ( cont )
Propulsion ( continued ) Mahoney, J.J., Inlets for Supersonic Missiles, American Ins ti tu te of Aeronaut ics and Ast ronautics, 1990 Sutton, G.P., Rocket Propulsion Elements , John Wiley & Sons, 1986 “ Tri-Service Rocket Motor Trade-off Study, Missile Designer’s Rocket Motor handbook,” CPIA 322, May 1980
Humble, R.W., Henry, G.N., and Larson, W.J., Space Propulsion Analysis and Design, McGraw-Hill , 1995 Jenson, G.E. and Netzer, D.W., Tactical Missile Propulsion, American Institu te of Aeronaut ics and Astronautics,
1996
Durham, F.P., Aircraft Jet Powerplants, Prentice-Hall, 1961
Bathie, W.W., Fundamentals of Gas Turbines , John Wiley and Sons, 1996
Hill , P.G. and Peterson, C.R., Mechanics and Thermodynamics of Propulsion , Addison-Weshley Publishing
Company, 1970 Mattingly, J.D., et al, Aircraft Engine Design , American Institute of Aeronautics and Astronautics, 1987
Materials and Heat Transfer
Budinski , K.G. and Budinski , M.K., Engineering Materials Properties and Selection, Prentice Hall, 1999 “ Matweb’s Material Properties Index Page,” http://www.matweb.com
“ NASA Ames Research Center Thermal Protection Systems Expert (TPSX) and Material Properties Database” ,http://tpsx.arc.nasa.gov/tpsxhome.shtml
Harris , D.C., Materials for Infrared Windows and Domes, SPIE Optical Engineering Press, 1999 Kalpakjian, S., Manufacturing Processes for Engineering Materials, Addison Wesley, 1997 MIL-HDBK-5J, “Metallic Materials and Elements for Aerospace Vehicle Structures” , Jan 2003 “ Metallic Material Properties Development and Standardization ( MMPDS )” , http://www.mmpds.org
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Bibliography of Other Reports and Web Sites ( cont ) Bibliography of Other Reports and Web Sites ( cont )
Materials and Heat Transfer ( continued ) Malli ck, P.K., Fiber-Reinforced Composites: Materials, Manufacturing, and Design , Second Edition, Maecel
Dekker, 1993 Chapman, A.J., Heat Transfer , Third Edition, Macmil lan Publishing Company, 1974 Incropera, F.P. and DeWitt, D.P., Fundamentals of Heat and Mass Transfer , Fourth Edition, John Wiley and
Sons, 1996
Guidance, Navigation, Control, and Sensors Zarchan, P., Tactical and Strategic Missile Guidance , “ AIAA Vol. 124 Progress in Ast ronautics and
Aeronautics,” American Insti tu te of Aeronautics and Astronaut ics, 1990 “ Proceedings of AGARD G&C Conference on Guidance & Contro l of Tactical Miss iles,” AGARD LS-52, May 1972
Garnell, P., Guided Weapon Control Systems, Pergamon Press, 1980 Locke, A. S., Guidance , “ Principles of Guided Missile Design” , D. Van Nostrand, 1955 Blakelock, J. H.,Automatic Control of Aircraft and Missiles, John Wiley & Sons, 1965 Lawrence, A.L., Modern Inertial Technology , Springer, 1998 Siouris, G.M., Aerospace Avionics Systems , Academic Press, 1993 Stimson, G.W., Introduction to Airborne Radar, SciTech Publish ing, 1998
Lecomme, P., Hardange, J.P., Marchais , J.C., and Normant, E.,Air and Spaceborne Radar Systems, SciTechPublishing and William Andrew Publishing, 2001 Wehner, D.R., High-Resolution Radar, Ar tech House, Norwood, MA, 1995 Donati, S., Photodetectors, Prentice-Hall , 2000 Jha, A.R., Infrared Technology , John Wiley and Sons, 2000 Schlessinger, M., Infrared Technology Fundamentals , Marcel Decker, 1995
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Follow-up Communication Follow-up Communication
I would appreciate receiving your comments and
corrections on this text, as well as any data,
examples, or references that you may offer.
Thank you,Gene FleemanTactical Missile Design
E-mail: [email protected] Site: http://genefleeman.home.mindspring.com
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