A Scientific Guide to Hobby Rocketry A Guide to Everything You Need - PowerPoint PPT Presentation

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 ¡ Mach 0.3 0.3 0.7 0.7 1.2 1.2 5 5

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 • 5-minute epoxy – Forms bond almost instantly – Short set time, but the bond is not as high in strength – Weak, brittle bond – Good for quick repairs – Suitable for placing a component • 1-hour epoxy – Not suitable as only bond – Ideal for most structural components • Wood glue – Can use additives to enhance – Works well on porous materials various properties – Forms moderate strength bond • JB Weld (sufficient for some high power) – Great for fillets – 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) – v term : usually 15-20 ft/s (use higher end for light rockets) – ρ : approximately 1.12-1.2 kg/m 3 at our launch site – C D : 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 Δ t 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 Δ v – Use drag force of rocket body to your advantage – Drag takes away some separation velocity so Δ v 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 Shock cord • Plastic • Elastic – Melts easily – Absorb ejection energy via stretching – Does not support large loads, mainly – Burn easily, so not suitable for HPR for low power applications • Tubular nylon (climbing webbing) • Ripstop nylon – High strength, but moderately heavy – Traditional parachute material – Low cost, easily available – Easy to manufacture, buy – Preferred sizes 9/16” or 1” • Mylar • Kevlar – Expensive – Very high strength, flame resistance, and cost • Traditional fabrics – Low in weight (typically use ¼ ” or ½ ”) – Heavy

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