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Marat Kulakhmetov http://www.youtube.com/watch?v=13qeX98t AS8 Did some rockets tumble? Did some rockets wobble? Did some rockets flip over? Maybe some rockets were unstable http://www.youtube.com/watch?v=B47XEFw5 l6w Stability refers to how likely an object will return to its initial position or orientation if it is disturbed ◦ Stable – Object returns to initial position ◦ Neutrally Stable – Object does not move ◦ Unstable – Object continues moving away from its initial position Moment describe the object’s tendency to rotate ◦ Moment = Force * Perpendicular Distance In the example above, the moments generated by the two weights generate 20 N*m and -20 N*m. They are balanced Moments are usually calculated about their center of gravity (CG) Unbalanced moments on a rocket will cause the rocket to tumble. Location where the forces will balance CG = Moment / Total Weight Example: ◦ Moment = 10 * (0) + 20 * 3 = 60 N * m ◦ Total Weight = 10 + 20 = 30 N ◦ CG = Moment / Total Weight = 60 / 30 = 2 m X=0 X=2 X=3 Beer, Russell, Johnston, DeWolf Mechanics of Materials X=0 5 7 11 13 14 20 Part Length (cm) Weight (g) Nose Cone 5 10 Parachute sys. 3 5 Recovery Wadding 1 1 Launch Lug 3 2 Engine Mount 5 15 Rocket Engine 5 30 Fins 5 3 Rocket Body 15 40 X=0 5 7 11 13 14 20 Part Centroid Formula Distance To Centroid Mass Moment Nose Con h/3 =1.67 5/3 = 1.67 10 16.7 Parachute h/2 =1.5 11+1.5 =12.5 5 62.5 Recovery Wadding h/2=0.5 13+0.5=13.5 1 13.5 Launch Lug h/2= 1.5 7+1.5=8.5 2 17 Engine Mount h/2 = 2.5 14+2.5=16.5 15 247.5 X=0 Part 5 Centroid Formula 7 11 13 14 Distance To Centroid From Above 20 Mass Moment 33 357.2 Rocket Engine h/2 =2.5 14+2.5=16.5 30 495 Rocket Body h/2=7.5 5+7.5 40 300 103 1152.2 Total X=0 5 7 11 13 14 Moment = 1152.2 Mass = 103 CG = Moment / Mass = 1152.2/103 = 11.19 cm 20 B3=2 1 3 H=5 1 1 1 2 B1=2 Break it up into a triangle, rectangle and triangle Area 1 = ½ *b1 * h = 5 Area 2 = b2 * h =5 Area 3 = ½ * b3 * h=5 B2=1 Total Area = Area 1 + Area 2 + Area 3 = 15 Mass1 = Total Mass * Area 1 / Total Area = 1 Mass2 = Total Mass * Area 2 / Total Area =1 Mass3 = Total Mass * Area 3 / Total Area =1 b3 1 3 h 1 1 b1 1 2 b2 Part 1 is a triangle Centroid 1 = b1/3 =.66 Part 2 is a rectangle Centroid 2 = b2/2 = 0.5 Part 3 is a triangle Centroid 3 = b3/2 =.66 Moment Fin = Mass1 * (b1 – Centroid 1) + Mass2 * ( b1 + Centroid 2) + Mass3 * ( b1 + b2 + Centroid 3)= 7.5 CG Fin = Moment Fin / Total Fin Mass =2.5 X=0 5 7 11 13 14 20 Moment with fins = 1152.2 +(2.5+14)*3 Mass = 103+3 CG = Moment / Mass =11.34 cm If : ◦ Rocket has no fins ◦ Thrust is aligned ◦ Rocket pitched a little X Moment = -1*Lift * x y x This rocket will keep pitching and fly out of control Little Drag Lots of Drag If : ◦ Thrust is aligned ◦ Rocket turned a little X Moment = -1* Lift *x + Fin * x1 X1 Fin Force If Fin * x1 > Lift * x , the rocket will right itself Fin force = 1 2 F Cd V A 2 ◦ Larger Area = More force provided by fins ◦ Larger Velocity = More Force provided by fins Fin Moment = Fin Force * Distance ◦ Larger Force = Larger Moment ◦ Larger Distance = Larger Moments For stability, we want large fins as far away from CG as possible. If fins are too large they create more drag X=0 5 7 11 13 14 20 Calculating aerodynamic center will require Computational Fluid Dynamic (CFD) analysis. We will estimate that the aerodynamic center is at Fin centroid We calculated that this is at 16.5cm Nozzles push on high gasses and accelerate them out the back In return, the gasses push on the nozzle and accelerates it forward High Pressure Low Pressure Air wants to go from high pressure to low pressure Pressure Force ( P1 – P2) * A Remember that Pressure = Force / Area Action-Reacting If you throw something out one way it will push you the other way If the rocket nozzle throws gases down, the gasses push the rocket up It is usually easy to study gas flows using control volumes Forces on the rocket could be calculated by only looking at control surfaces Fpressure =(Pe - Pa ) Ae 2 A = ρ U Fgas e e Why did rockets filled with water go higher than those filled with just air? Changes Thrust [( Pe Pa) V ] Ae 2 Exit Pressure Constant Ambient Pressure Constant Exit Velocity Assumed Constant Rockets usually use converging-diverging nozzles. These could also be called isentropic nozzles The thrust through the C-D nozzle depends on chamber pressure, ambient pressure, and nozzle shape Upstream of the nozzle, in the combustion chamber, the gas velocity is small All fluids (water, air, etc.) accelerate through a converging section The fastest they could get in the converging section is Mach 1 If the gases reached Mach 1 in converging section then they will continue accelerating in the diverging section If the gasses did not reach Mach 1 in the converging section then they will decelerate in the diverging section This is why our water bottle rockets only had converging section Ambient Conditions: Pa = 101,000 Pa Area = 0.05 m^2 Mass = 0.5 kg Exit Conditions: Pe = 150,000 Pa Ve = 100 m/s Density = 1.2 kg/m3 Lets Calculate Rocket Thrust and acceleration 2 Thrust [( Pe Pa) V ] A Thrust [(101,000 150,000) 1.2(100) ]0.05 3050 N 2 A = F/m = 3050 / 0.5 = 6100 m/s^2 Pressurized Air ◦ Balloon Solid Propellant Liquid Propellant Nuclear Electric F ISP mg F Thrust m massflow(kg / s ) g gravity ISP is used to classify how well a rocket performs Low ISP = need a lot of fuel to achieve thrust High ISP =do not need as much fuel to achieve same thrust Propellant is initially in the solid state and it becomes a hot gas during combustion Pros: Cons: ◦ ◦ ◦ ◦ Simple Cheap Easy to store Can be launched quickly ◦ ISP only 150-350 ◦ Cannot turn off after ignition ◦ Cannot throttle during flight Fuel and Oxidizer are both stored separately in liquid form Pros: ◦ Better performance (ISP 300-460) Cons: ◦ More complex ◦ Requires pumps or pressurized gas tanks ◦ Heavier Nuclear Reactor heats working gas that is accelerated through a nozzle Pros: Cons: ◦ Isp 800-1000 ◦ Requires shielding, can be heavy ◦ It’s a NUKE Two types: ◦ Arcjet: Electricity is used to superheat the gases ◦ Ion Thrusters: ionized (charged) atoms are accelerated through an electro-magnetic field Pros: ◦ ISP 400-10,000 Cons: ◦ Thrust usually <1N VASMIR