20-1 design of uav systems air vehicle geometryc 2002 lm corporation lesson objective - to discuss...

20-1

Design of UAV Systems

Air vehicle geometryc 2002 LM Corporation

Lesson objective - to discuss

Air vehicle geometryincluding …

• Fundamentals

• Design drivers

• Geometry models

Expectations - You will understand how to define an air vehicle without having to draw it

20-2



Editorial comment

Not drawing a configuration is generally a bad idea- Air vehicles are highly integrated machines and

good geometry is what makes them work- Drawings bring multi-discipline teams together

But drawing and analyzing airplanes takes time- Up front trade studies need to address a wide range

of concepts and time is always at a premiumAnd sometimes design teams (especially designers) fall in love with their concepts

- Alternate concepts don’t get much attention

Therefore we will develop simple analytical geometry models for initial trade studies and concept screening

- Physically capture the important design variables but minimize the time and effort required to assess them

- Use it to develop the “best” configuration concept- Then we will draw the airplane

20-2a



Notation and constraints

In this section, some notation could be confusing- For geometry, L and D represent length and diameter.- In previous sections, they represented lift and drag

- The differences should be obvious but be alertL/D (Length/Diameter) vs. Lift/Drag could also be confusing- Both are primary parametrics, one for geometry, the

other for aerodynamicsD(geom) typically is an equivalent, not a true diameter- It is calculated from cross sectional area (Ac) where

- D = Deq = 2sqrt(Ac/)Acceptable values of Lth/Deq vary with speed range and application- For low subsonic speeds, fuselage Lth/Deq 7, nacelles

and pods Lth/Deq 5- For higher speeds, higher values are required

20-3



Fundamentals

Air vehicle geometry is not just about aerodynamics, structures and signature - it is also about packaging• Efficient arrangement of pieces, parts and systems to

maximize performance and minimize penalties (cost, weight, drag, etc.)

Surface (wetted) area - the most powerful design driver• For any given volume nothing has less wetted area

(albeit at high drag) than a sphere where

V(sphere) = (4/3)**R^3 and Swet(sphere) = 4**R^2

Veff(max theoretical)* = V/Swet = R/3

• Cylinders are reasonably efficient but not at high fineness ratios. “Flattened” cylinders are inefficient

or

*Note - Volumetric efficiency(Veff) increases with size regardless of shape

20-4



Parametric cylinder comparison

For purposes of comparison we assume cylinders with hemispherical end domes so that

Vol = (4/3)(D/2)^3 + [(D/2)^2](L-D) = (/12)(3L/D-1)D^3 = 100 cuft

Swet = 4(D/2)^2 + D(L-D) = (L/D)D^2

Sphere (Lth/D = 1) D = 5.76 ft; Swet = 104.2 sqftCylinder (Lth/D = 4) D = 3.26 ft; Swet = 133.7 sqftCylinder (Lth/D = 8) D = 2.55 ft; Swet = 163.6 sqftCylinder (Lth/D = 16) D = 2.01 ft; Swet = 203.2 sqft

or

SideView

L EndView

D

Study this carefully – it is a generalized cylindrical tank geometry model.

• The required inputs are Volume or D and Lth/Deq (or fineness ratio)Later we will develop similar models for fuselages, wings and tails

- Minimize Swet, keep forward and aft facing slopes < 5 -15 Provide optimum “moment arm” for control surfaces

• Length-to-span ratios range from 0.5 to 2.5- Slow vehicles have low Lth/b

20-5



Overall geometry drivers

• Speed and L/D drive what an air vehicle looks like- Very high speeds require high fineness ratio while low

speed vehicles can be significantly “blunter”- (L/D)max establishes the allowable span (b) and Swet

• Aerodynamic “rules” focus on wings and tails - E.g. maximize span (b) to minimize induced drag

• Fuselage rules are subjective with few parametricsLength to span ratio

0.0

0.5

1.0

1.5

2.0

2.5

0 300 600 900 1200

Vmax (Kts)

Raw data sources - Roskam and Janes All the World’s Aircraft

20-6



Fuselage and pods

For minimum drag, we want to minimize wetted area and select shapes that match the design speed regime

- Subsonic - ogive or elliptical forebodies with tapered aftbodies (See RayAD 8.2) or shapes based on symmetrical NACA-4 Digit series

- Transonic - Sears-Haack bodies of revolution (See RayAD Fig 8.3)

- Supersonic - Modified Sears-Haack bodies per RayAD Eq. 12.46

For minimum weight, minimize wetted area and use simple geometry and “load paths”

20-7



Payload volume

• Varies widely with application- People + baggage ≈ 5 lbm/ft^3 (ppcf)- Typical cargo ≈ 10 ppcf- Typical cargo area / fuselage cross section ≈ 0.67

• UAV payloads vary with type- Density typically 25 ppcf (as is almost everything else!)

Payload density

0

2

4

6

8

10

0 10 20 30 40 50

Weight (Klbm)

Vo

lum

e (

Kcu

ft) Prop - pass

Jet - pass Cargo only

2.5 ppcf 5 ppcf

10 ppcf

Fuselage cross sectional area

10

40

70

100

10 40 70 100

Nominal external area (sqft)

No

min

al in

tern

al a

rea

(sq

ft)

Raw data sources - Janes All the World’s Aircraft

20-8



Wings and tails

During pre-concept design, the most critical design issues are area and span- Sweep, thickness and taper are important but are less

critical- See RayAD 4.3 (Wing Geometry)

Wing design drivers- Wing area establishes wing loading (W0/Sref)

- Slow flight or high flight (subsonic) means low W0/Sref- The other parameters drive weight and drag

- Thin wings have lower profile drag, but higher weight- Induced drag is driven by span, not aspect ratio

Di = (Cl^2)*q*S/(*e*AR) = (Cl^2)*q/(*e*b^2) Horizontal and vertical tail geometry is another consideration - For pre-concept design, we only need to know tail type

(conventional, “V”or tailless) and area

Parametrics provide inputs for initial sizing

20-9



Wing parametrics

Wing loading parametric(jet aircraft except as noted)

10000

20000

30000

40000

50000

60000

70000

0 40 80 120 160 200

Wing loading (PSF)

Initial cruiseFinal cruiseGlobal HawkPredator

Thickness ratio parametric(jet aircraft except as noted)

0

5

10

15

20

25

1 3 5 7 9 11

Aspect ratio

Root

Tip

Root

Tip

Aspect ratio parametric(jet aircraft except as noted)

2

6

10

14

18

1 3 5 7 9 11

Aspect ratio

Speed parametric(jet aircraft except as noted)

2

6

10

14

18

200 600 1000 1400 1800

Maximum speed (Kts)

(a) (b)

(c) (d)

Reasonable tip t/c upper limit = 13% (RosAD.2,pp 156)

Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources

20-10



Wing and tail parametrics

Tail area parametric

0.100 0.150 0.200 0.250 0.300

Average

Fighter

Jet Transp

Biz Jet

SE-prop

Exposed area/Sref

Vertical

Horizontal

Speed parametric(jet aircraft except as noted)

0

10

20

30

40

50

60

70

200 600 1000 1400 1800Maximum speed (Kts)

t/c > 10%

5 < t/c < 10

t/c < 5%

Sht/Sref Svt/Sref

Single engine - prop 0.20 0.14

Multi engine -prop 0.26 0.14

Business Jet 0.24 0.16

Regional Turbprop 0.25 0.19

Jet Transport 0.29 0.17

Military Trainer 0.23 0.13Fighter 0.25 0.13Average 0.246 0.151 (b)

See RayAD Fig’s 4.20 for Le vs. Mmax and 4.24 for wing taper ratio () vs. .25c

(a)

L

e (

de

gre

es

)

Raw data sources - Roskam, Janes All the World’s Aircraft and unbublished sources

20-11



Geometry models – why?

Drawing and analyzing airplanes takes time- Up front trade studies need to address a wide range

of concepts and time is always at a premiumAnd sometimes design teams (especially designers) fall in love with their concepts

- Alternate concepts don’t get much attention

Therefore we will develop simple analytical geometry models for initial trade studies and concept screening- Physically capture the important design variables but

minimize the time and effort required to assess them- Use them to develop the “best” configuration concept- Then draw the airplane and analyze it to confirm the

geometry model estimates

From Chart 20-2

20-12



Analytical geometry model

Objective - to capture key pre-concept design variables (See RayAD 7.8-7.10)1. Independent variables

- Wing reference area (Sref)- Wing span (b) or aspect ratio (AR)- Wing taper ratio ()- Wing thickness ratio (t/c)- Fuselage length (L,Lf or Lth) and diameter (D,Df or Deq)- Horizontal tail exposed area ratio (Kht)- Vertical tail exposed area ratio (Kvt)- Engine length (Leng) and diameter (Deng)

2. Dependent variables- Total and component and wetted areas (Swet-wing,

fuse, ht, vt)- Component volumes (V-wing,fuse)

We will do this without making a configuration drawing

20-13



Fuselage model

• Geometry model – Similar to cylindrical tank models except we use elliptical fore and aft bodies

LL1 L2

D

V-fuse = (π/4)*[(L/D)*D^3]*[1-(k1+k2)/3] (20.1)

Swet-fuse = [(π/2)*D^2]*{1+(L/D)*[k1*(fe1-2)+ k2*(fe2-2)+2]}

Where (20.2)

k1 = L1/L, fe1 = arcsin(1)/ 1, 1 = sqrt(1-(D/L)/(2*K1))^2)

k2 = L2/L, fe2 = arcsin(2)/ 2, 2 = sqrt(1-(D/L)/(2*K2))^2)Note - arcsin() is expressed in radians

20-14



Example - TBProp

Calculate Vfuse and Swet for example TBProp UAV- We assume payload goes in a constant area payload section and previously caluclated required volume = 26.55 cuft (720 lbm at 27.1 lbm/cuft). We assume a cargo section packing efficiency (Pf) of 70% (30% not useable) - Center section volume required, therefore, is 37.7 cuft- We assume a minimum center section Lth/Diam = 4

and calculate diameter (Dcyl) of the cylindrical section Vcyl = (/4)*(Lcyl/Dcyl)*Dcyl^3 or Dcyl = 2.29 ft

- We assume the fuselage forebody transitions to maximum diameter over a length of one diameter and that the aftbody transitions in 2 fuselage diameters or Lth = 16.1 ft

2.29 ft2.29 9.16 4.58

20-15



Example – cont’d

From the resulting dimensions, we calculate:k1 = 1/7 = 0.143, k2 = 2/7 = 0.286

1 = sqrt(1-(0.143/(2*0.143))^2) = 0.866fe1 = arcsin(0.866)/0.866 = 1.2092 = sqrt(1-(0.143/(2*0.286))^2) = 0.968fe2 = arcsin(0.968)/0.968 = 1.361

Swet = ((π/2)*2.29^2)*(1+(0.143)*(0.143*(1.209-2) + 0.286*(1.361-2)+2) = 106.3 ft^2

Vol = (π/4)*[(7)*D^3]*[1-(.143+.286)/3] = 56.5 cuftOf the total fuselage volume available of 39.7 cuft- 26. 6 cuft is allocated to payload, leaving 13.1 cuft

available for fuel and systems

2.36 ft2.36 9.43 4.72

20-16



Fuselage/nacelle model

Combined Swet fuselage Swet+Kswet nacelle Swet (20.4)

Multi-engine prop

FrontL

D

Dnac

Top

Lnac

Combined Swet fuselage Swet + nengKswetnacelle SwetNote - 0.0 < Kswet < 1.0

- Dnac 1.25Deng- neng = Number of engines

(20.3)

L

D

Dnac

Side

Front

Single engine prop Lnac

20-17



Example – nacelle (prop)

• We estimate TBProp nacelle diameter from engine size required using uninstalled parametric engine weight = 100.7 lbm (chart 19-27) and density = 22 pcf

- Engine volume = Wprop/density = 100.7/22 = 4.58 cuft and nominal Leng/Deng = 2.5. Therefore, - Deng = [4*Vol/(*Lth/Deng)]^1/3 ≈ 1.33- Dnac, therefore, ≈ 1.33*1.25 = 1.66 ft

• We assume a minimum Lth/Dia = 5 for the pod mounted nacelle (Lth = 8.29 ft), K1 = .2 and K2 = .4- L1 and L2 are estimated at 1.66 and 3.32 ft and …

Swet-nac = 38.6 sqft• We also assume that nacelle volume is allocated

entirely to the propulsion subsystem- No other systems or fuel will be accommodated within

20-18



Fuselage/nacelle model

Multi-engine jet

Single engine jet

L

D

Lnac

Dnac

Top

Front

Combined Swet fuselage Swet+nengKswetDnacLnacNote - 0.0 < Kswet < 1.0

- Dnac 1.25Deng- neng = Number of engines

(20.5)

Combined Swet fuselage Swet+nengKswetDnacLnac (20.6)

Kswet0.5D

Lnac

Dnac

Side

FrontL

20-19



Fuselage/nacelle - cont’d

Combined area fuselage area + 5*AengNote - Aeng = Engine area at front face (20.7)

Integrated jet

L

D Dnac

Top FrontDeng

Swet-fuse = [(π/2)*De^2]*{1+(L/De)*[k1*(fe1-2)+k2*(fe2-2)+2]} *sqrt[h/w+w/h]/sqrt(2) (20.8)De = sqrt(wh)

Non-circular cross section

h

Front

Topw

L

L1 L2

where

20-19a



Example – nacelle (jet)

• Jet engine nacelle diameters are also estimated from engine size required but use engine airflow (WdotA) to calculate diameter using Raymer’s engine size parametric (chart 18-18)

- Deng(ft) = WdotA/26 • Nacelle Lnac/Dnac is assumed to equal engine

Leng/Deng - Leng/Deng is determined parametrically from BPR

- See the lower right hand plot in chart 18-17 • Jet engine nacelle volume is also assumed to be

allocated entirely to the propulsion subsystem

20-20



Pods, stores and multi-fuselages

……with non-circular cross sections

h

Front

Topw

L

L1 L2

Model as multiple ellipse-cylinders per Eqs. 20.1 and 20.2

Apply Eq. 20.8 as correction factors

20-21



• Fuselage volume and area data not widely published- RosA&P Table 5.1 has Swet-fuse data for some general

aviation (GA) aircraft and jet transports- Data correlates reasonably well with Eq’n 20.2 (+/- 10%)

- Eq 20.1 predicts Raymer Fig 7.3 fuselage volume (+/- 10%)

Data correlation

Fuselage wetted area

0

1000

2000

3000

4000

5000

6000

0 1000 2000 3000 4000 5000 6000

Swet - Roskam (RosAP) Table 5.1

Total wetted area

0

2000

4000

6000

8000

10000

0 2000 4000 6000 8000 10000

Swet – Raymer Fig 7.3

Sw

et-f

use

fro

m E

q 2

0.2

Sw

et-f

use

fro

m E

q 2

0.2

20-22



WIngs and tails

During pre-concept design, the most critical design issues are area and span

- Sweep, thickness and taper are important but are less critical

- See RayAD 4.3 (Wing Geometry)Wing design drivers

- Wing area establishes wing loading (W0/Sref) - Slow flight or high flight (subsonic) means low W0/Sref

- Other parameters drive weight and drag- Thin wings have lower profile drag, higher weight

- Induced drag is driven by span, not aspect ratioDi = (Cl^2)*q*S/(*e*AR) = (Cl^2)*q/(*e*b^2)

Horizontal and vertical tail geometry is another consideration

- For pre-concept design, we need to know tail type and area

Parametrics provide inputs for initial sizing

20-23



Wing model

Geometry model - Truncated pyramid for fuel volume - Wing exposed area for Swet

V-fuel = (4/3)*{[(Kc*Pf*(t/c)*Sref^2]/[b*(1-)*(1+ )^2]}*[(1-1*(1- ))^3 - ((1-2*(1- ))^3] (20.9)

Where Kc = Tank chord ratioPf = packing factor (≈ 0.8) 1 = 2*Y1/b = taper ratio (Ct/Cr) 2 = 2*Y2/b

SrefExp = Sref*(1-(D/b)*(2-(D/b)*(1- ))/(1+ )) (20.10)

Cr

Ct

Y1

D/2

Y2

b/2

Kc*Cr

Cr = 2*Sref/b*(1+ )

Vpyrmd = A(base)hgt/3

20-24



Example

1. Calculate SwetExp for the example TBProp UAV - We select a nominal taper ratio ( = 0.5) and use starting values of t/c = 0.13, AR = 20 and Sref = 82.1 sqft

- Fuselage diameter is 2.29 ft (chart 20-14)- We calculate wing basic wing geometry

- b = sqrt (Sref*AR) = 40.5 ft - Cr = 2*Sref/[b*(1+ )] = 2*(82.1)/[40.5*(1.5)] = 2.7 ft- Ct = *Cr = 1.35 ft

- From equation 20.10, we calculate SrefExp = 76 sqft2. Calculate wing fuel volume - Assume the tank extends from centerline to 80% span

(1 = Df/b = 0, 2 =0.8) and nominal packing factor (Pf = 0.8) and tank chord ratios (Kc = 0.5)

- From equation 20.10, Vwing-fuel = (2/3)*{[Kc*Pf*(t/c)*Sref^2]/[b*(1-)*(1+ )^2]}*

[(1-1*(1- ))^3 - ((1-2*(1- ))^3] = 4.5 cuft

20-25



• Tails - Horizontal and vertical tail areas can be expressed as nominal fractions of Sref

Sht = Kht*Sref (20.11)

Svt = Kvt*Sref (20.12)Where for an average air vehicle (chart 20-10)

Kht ≈ .25Kvt ≈ .15

• Tail wetted area ≈ 2*planform area• For V-tails - Use projected areas or

KV-tail = 2*sqrt(Kht/2^2+Kvt^2) (20.13)

Tails

20-26



Final example – areas & aero

Using typical air vehicle horizontal and vertical tail area ratios (Kht = 0.25 and Kvt = 0.15) we can estimate tail areas for the example UAV:

- Sht = 0.25(82.1) =20.5 sqft, Svt = 0.15(82.1) =12.3 sqftWe can also calculate total wetted area (fuselage and nacelle plus 2 times the exposed wing and tail areas)

Swet = 106.3+38.6+2*(75.8+20.5+15.6) = 362.6 sqftWith these areas and assuming nominal values of Cfe = 0.0035 (RayAD Table 12.3) and e = 0.8 (chart 16-6) we can make basic aero performance estimates:

- b^2/Swet = 4.53, Swet/Sref = 4.42 and …- (L/D)max = 28.5 (Eq 16.8)

We can also use calculated component areas and wing-body-tail unit weights to estimate airframe weight

20-27



Example – airframe weights

Unfortunately, we have no data on UAV unit weights:- All we have are RayAD Table 15.2 unit weights for

fighters, transports/bombers and general aviation where from chart 19-31, for an aircraft at our estimated wing loading (W0/Sref = 30), Waf/Sref should be 30% greater than typical general aviation aircraft

- From this we can extrapolate from RayAD Table 15.2 unit weights:- Wing: UWW 1.3*2.5 = 3.25 psf- Tails: Uwht = Uwvt 1.3*2.0 = 2.6 psf- Fuselage (+nacelle) 1.3*1.4 = 1.8 psf

Using these values we can estimate from geometry: - Waf = (106.3+38.6)*1.8+75.8*3.25+32.8*2.6 = 593 lbm

or Waf/Sref = 7.23 psfThis value is 80% of the previous estimate (chart 19-27) but it should be more accurate since it captures geometry features not previously included

20-28



New weights and volume

Using on the area based Waf/Sref, the bottoms up weight spreadsheet will converge to a new set of weights

Using typical densities for fuel (50 pcf) and payload and remaining systems (25 pcf), fuselage volume required for payload, fuel (less 4 cuft in the wing) and systems is:

Vr pfs = [26.55+(360/40)+350/25-4.5]/0.7 = 64.4 cuftWhich compares to total fuselage volume available of 56.5 cuft (chart 20-15)

Converged TBP weights (lbm)Waf 496 Wpay 720Weng (instl) 109 WF 360Wlg 103 Wmisc 22Wspa 247 W0 2056We 954 EWF = 0.46

20-29



Since the volume available exceeds volume required, we need to resize the fuselage (and the rest of the air vehicle) to eliminate the excess- Since fuselage volume scales with the cube root of

diameter (Eq 20.1), new fuselage geometry would beDf = 2.29*cube(64.4/56.5) = 2.4 ftAt Lf/Df = 7, Lf = 2.4*7 = 16.8

- Engine size would also changeBhp0 = 0.092*2056 lbm = 189.1 BhpWeng = 189.1/2.25 = 84.1 lbm, Vol eng = 84.1/22 = 3.8 cuft, Deng = [4*Vol/(*Lth/Deng)]^1/3 = 1.25 ft and Dnac = 1.25*1.25 = 1.56 ft

- Which then changes the geometry model, the calculated areas and weight and aero calculations …..

And the cycle continues until weight, aero, propulsion and geometry converge

New size and airframe weights

20-30



After a number of iterations, the weight, volume and size calculations will converge to a consistent set of values- Volume available = Volume required/0.7 = 67.4 cuft Df = 2.44 ft, Lf = 2.43*7 = 17 ft- Engine size = 201 Bhp, Weng(uninstalled) = 89.3 lbm Vol eng = 4.0s cuft, Dnac = 1.6 ft- Sref = 72.9 sqft, Swet = 348 sqft, b = 38.2 ft, Swet/Sref =

4.78, b^2/Swet = 4.19; LoDmax = 27.4, Waf/Sref = 7.88

Converged weight/volume/size

Converged TBP weights (lbm)Waf 572 Wpay 720Weng (instl) 116 WF 382Wlg 109 Wmisc 22Wspa 262 W0 2184We 1160 EWF = 0.49

20-31



Parametric comparison

Airframe Weight Comparisons - Manned Aircraft (data from Roskam)

0

10

20

30

40

0 50 100 150

GTOW/Sref (psf)

Biz JetSE Piston PropME Piston PropReg TurboJet TransJet fightersMil Train

UAV Fuel Fractions

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 8 16 24 32 40 48

Max Endurance (hrs)

Piston

Turboprop

Jet

Jet

Piston

Global Hawk

Comparison shows the airframe weights are consistent with the parametric data but that fuel fraction continues to be low for a TBProp

20-32



Reference

For more information on geometry model methodology see my paper

- Preliminary Sizing Methodology for Hypersonic Vehicles, AIAA Journal of Aircraft, March 1992

20-33



Homework

1. Work your way through the example problems in this lesson and check/document the area, volume available, volume required, LoDmax and weight calculations. Compare your results using ASE261.Geometry.xls and identify any differences (team grade)

2. Use spreadsheet ASE261.Geometry.xls to calculate first and second pass values for your proposed air vehicle using the example problem inputs for Cfe, e and component unit weights (individual grade)

3. Discuss ABET issues #3 and #4 and document your conclusions (one paragraph each – team grade)

2nd week

20-34



Intermission

20-1 design of uav systems air vehicle geometryc 2002 lm corporation lesson objective - to discuss...

Documents