a scientific guide to hobby...
TRANSCRIPT
A Scientific Guide to Hobby Rocketry
A Guide to Everything You Need to Know Before Launching Your First High Power Rocket
Aerodynamics
• One of the three primary forces in hobby rocket flight • Can greatly affect performance (altitude, etc.) • Drag force can rip fins apart or cause structural buckling • D= 1/2 ρ v↑2 C↓D A↓ref • Open Rocket can give you the drag coefficient
– Other variables easy to calculate
Aerodynamic Flight Regimes
Low speed Compressible Transonic Supersonic Hypersonic
0.3 0.7 1.2 5 Mach
Drag in Compressible Flows
• In subsonic flow C↓D ≈C↓D,0 /√1− M↓∞↑2
• In supersonic flow C↓D ≈C↓D,0 /√M↓∞↑2 −1
• Drag actually still increases in supersonic flow because of the dependence on v∞2!
Nose Cone Aerodynamics
• Various geometries have different drag coefficients
• Minimum drag bodies like the von Karman ogive have best across-the-board performance
• Some shapes perform best in certain Mach regimes
• Model rocketry nose cones are generally ogives
Effect of Rocket Length
• Longer rockets lead to increases in skin friction drag • Increased length-to-diameter ratio (fineness ratio) leads to
a decrease in pressure drag per rocket volume • Longer rockets are subject to extreme bending moments
Fin Aerodynamics Rectangular cross sec:on • Simple to manufacture • Rela:vely high drag coefficient for airfoils with similar thickness-‐to-‐chord ra:os
Rounded cross sec:on • Not too difficult to manufacture • Decent aerodynamic performance, but not the best
Airfoil cross sec:on • Op:mal fin cross sec:on for subsonic rockets, but prone to high drag and shocks at supersonic speeds • Should have a symmetric cross sec:on
Wedge cross sec:on • Good aerodynamic performance at supersonic speeds • Decent aerodynamic performance at subsonic speeds
Stability
• Stability margin defined as: m= x↓CG − x↓CP /Max body diameter – Unstable: m<1 – Marginally stable: m=1 – Stable: 1<m ≤ 2 – Overstable: m>2
• Always mark the CP on your rocket – Will not change with added weight/internal features like CG will
Stable Rockets
Center of mass
Center of presssure
Net aerodynamic force
Net rotation of rocket
Unstable Rockets
Center of mass
Center of presssure
Net aerodynamic force
Net rotation of rocket
Why Stability Matters
• Unstable rockets – BAD – Can spiral out of control under slight
disturbances • Stable rockets – GOOD
– Trajectory not perturbed by wind • Over-stable rockets – OKAY
– Tend to weathercock, or fly into the wind – Not terrible, but can lead to horizontal
flight on windy days
Effect of Geometry on Stability
• Based on weighted average of normal force coefficient C↓N,α
• Control surfaces such as fins have high values of C↓N,α – Larger surfaces have greater effects
• To move CP aft, place large control surfaces further behind the old CP location – Note, larger surfaces also contribute more mass
• x↓CP = ∑↑▒C↓N,α ↓i x↓i /∑↑▒C↓N,α ↓i
Effect of Weight on Stability
• Center of gravity should be above center of pressure • CG shifts upwards when mass is added above the old CG,
and downwards when mass is added below the old CG • CG moves more quickly when mass is added further from
old CG (from the concept of a moment arm) • Common solution to add dead weight (or payload) to the
nosecone • x↓CG = ∑↑▒x↓CG,i m↓i /∑↑▒m↓i
Effect of Speed on Stability
• Like drag, normal force coefficient varies with Mach number • In subsonic flow C↓N,α ≈C↓N,α,0 /√1− M↓∞↑2
• In supersonic flow C↓N,α ≈C↓N,α,0 /√M↓∞↑2 −1
• In general, stability margin drops approaching Mach 1
Structures
• Cardboard tubes with plywood interior structure generally suitable for low-thrust, low-speed flight
• Thicker structural materials needed for heavier, higher-thrust flights
• Fiberglass and other composites become necessary for high-speed flight
• Ductile metals as structural materials only permitted when deemed absolutely critical for structural integrity
Weight
• Heavier rockets require more robust structures • Landing can cause poorly constructed components to be
crushed from impact force or moments when tipping over • Heavy-weight rockets require much larger parachutes to
land at safe speeds – Also need high-thrust motors to leave the launch pad at safe
speeds
Fin Shapes
• Stress tends to accumulate in sharp (acute) corners • Avoid highly swept fins with sharp corners
– If sweep is necessary, use right or obtuse angles with reasonably large side lengths
• Tapered fins that are not swept aft of the rocket tend to work really well
• Same rules apply to forward sweep
Fin Dimensions
• Fins with a long span can break easily due to excessive bending moments from aerodynamics and ground impacts
• Thicker fins can carry much more load and bend less • Try to minimize aspect ratio (span/chord) to minimize
chance of breaking a fin – Too low of an aspect ratio leads to bad stability characteristics
Adhesives
• Super glue – Forms bond almost instantly – Weak, brittle bond – Suitable for placing a component – Not suitable as only bond
• Wood glue – Works well on porous materials – Forms moderate strength bond
(sufficient for some high power) – Great for fillets
• 5-minute epoxy – Short set time, but the bond is not
as high in strength – Good for quick repairs
• 1-hour epoxy – Ideal for most structural components – Can use additives to enhance
various properties • JB Weld
– High strength, but more brittle
Recovery
• Good recovery is key for ensuring rocket safety • Landing speed should be slow, but not too slow
– Too fast: things break – Too slow: things float forever and get lost
• Ideal landing speeds are 15-20 ft/s – Some rocketeers recommend 17-22 ft/s
• Typically achieved by one or two parachutes
Sizing a Parachute
• Goal of parachute is to decelerate rocket – Ideally, the rocket will reach terminal velocity (dv/dt =0) – Statics problem (F = ma = 0), or weight equals aero forces
• W= 1/2 ρ v↓term↑2 C↓D A • Area= 2W/ρ v↓term↑2 C↓D and Diameter=2√Area/π
Sizing a Parachute
• Diameter= 2/v↓term √2W/ρπ C↓D • What values to use?
– W: weight of your rocket (after propellant burns out) – vterm: usually 15-20 ft/s (use higher end for light rockets) – ρ: approximately 1.12-1.2 kg/m3 at our launch site – CD: parachute drag coefficient, about 0.7-0.9 for Level 1 TFR
• Always check your units! You will have to do conversions!
Shock Cord
• Ejection charges usually apply 8-15 psi in a rocket – Up to 106 lbf on a 3” rocket, 189 lbf on a 4” rocket – Leads to high separation velocity – Quick deceleration at full shock cord extension and parachute
inflation • Recall F≈m∆v/∆t , where Δt is usually pretty small • Shock cord must be able to load at full extension and also
entire rocket weight (much smaller) during descent
Shock Chord
• Rocket structure (materials and adhesives) must be capable of supporting loads, too
• To reduce F during full shock cord extension, reduce Δv – Use drag force of rocket body to your advantage – Drag takes away some separation velocity so Δv is smaller
• To maximize effect of aerodynamics, make shock cord infinitely long – Not very practical, so use a minimum of 20 ft
Recovery Materials
Parachutes • Plastic
– Melts easily – Does not support large loads, mainly
for low power applications • Ripstop nylon
– Traditional parachute material – Easy to manufacture, buy
• Mylar – Expensive
• Traditional fabrics – Heavy
Shock cord • Elastic
– Absorb ejection energy via stretching – Burn easily, so not suitable for HPR
• Tubular nylon (climbing webbing) – High strength, but moderately heavy – Low cost, easily available – Preferred sizes 9/16” or 1”
• Kevlar – Very high strength, flame resistance,
and cost – Low in weight (typically use ¼” or ½”)
Recovery Protection
• Most recovery devices can be burned and damaged by hot gases from ejection charge
• Fireproof cellulose insulation (aka “dog barf”) can be stuffed between ejection charge and recovery device – Wadding functions similarly for low power rockets
• Kevlar or Nomex sheets often used to wrap parachutes – Much more expensive, but reusable and high quality
• Strategically placed baffles reduce exposure to hot gas
Launching a Rocket
• Rockets launched using a rod or rail • As rocket accelerates, the rod or rail points the rocket in
the correct direction – Rocket cannot achieve reasonable stability at low speeds
• Rule of thumb: velocity of any rocket off the rod or rail should be at least 50 ft/s – Much easier to accelerate light rocket than heavy rocket
Launch Lugs
• Generally only used for low power rockets • Interface with launch rod (circular metal rod) • Common sizes are 1/8”, 3/16”, 1/4”, 3/8”, and 1/2” • Not used much for high power since the rod tends to
“whip” • Single or multiple lug (cardboard tube) aligned axially with
rocket to keep motion near vertical • Rods vary in length depending on compatible motor sizes
Rail Buttons
• Used for high power rocketry • “Rail buttons” screw into rocket and slide
down the launch rail • Common sizes are 1010 (1”) and 1515
(1.5”) • Use two rail buttons aligned axially with the rocket • Bottom rail button should be ~2 inches from aft of rocket • Second rail button should be 12-18 inches forward
Rail Buttons
• If the front rail button is too far forward, the rocket can pivot about the aft rail button once the first button has cleared the rail but velocity is not sufficient
• Anchor rail buttons into rocket using expanding rubber well nut or a tee nut – Aft button usually requires well nut – Forward rail button can be placed (with planning) using tee nut
• Rail length usually 8-10 ft for 1010 and 12+ ft for 1515
Propulsion
• Commercial, off the shelf solution for hobby rockets • Uses an ammonium perchlorate (AP) composite propellant
for high power, black powder (BP) for low power – Space Shuttle SRB used an AP-based propellant
• Fine-grained AP in HTPB rubber binder with other chemicals for effects
• Solid propellant with annular grain geometry (generally)
Thrust & Impulse
• Thrust is a function of time • Impulse=∫↑▒Tdt
– Also approximately average thrust times burn time
• Average thrust should be at least five times the rocket weight
• Very high thrust motors can cause rocket to go supersonic
What’s in a Name?
Impulse class
Average thrust (N)
Propellant type
Ejection charge delay
How High Will It Go?
• Depends on a number of factors, but you can use some order of magnitude estimation:
• h= 1/2 t↓burn↑2 (T/m −10)(T/10m ) – h: apogee (m)
tburn: motor burn time (s) T: average thrust (N) m: initial rocket mass (kg)
• Does not account for all forces and effects
National Rocketry Clubs
• Must be a registered member of National Association of Rocketry (NAR) or Tripoli Rocket Association (Tripoli) to launch and attempt high power certifications
• We are a NAR club, so NAR memberships help us maintain NAR national benefits – NAR members get a nice bi-monthly magazine
• Tripoli Level 2 members may use experimental propellant – But not the Georgia Tech Fire Marshal…
High Power Rocketry
• Refers to any launch where any of the following are true: – Total impulse exceeds 160 Ns (H motor and above) – Average thrust > 80 N – Propellant mass > 125 g – Rocket weight > 1500 g – Airframe includes ductile metal – Rocket uses a hybrid motor
• You must be a registered member of NAR or Tripoli before you can attempt a high power launch
High Power Rocketry
Certifications
• Level 1 certification procedures nearly the same for both NAR and Tripoli
• Must construct and fly a rocket on a single Level 1 high power motor and safely recover the rocket – Must not lose any components in flight – Must not break any components (zippering is at the discretion
of the certifier) – Generally, given a new motor, you should be able to
immediately fly the rocket again without modification
Certifications
• Things that disqualify you – Landing in a tree or lake – Motor CATO – Landing without successfully deploying a parachute
• For NAR members – I can sign off on your certification and would be happy to do so
• For Tripoli members – Local Prefect must sign off on your certification paperwork
• Must have certification form ready at the launch