Slide 1

Marat Kulakhmetov Slide 2 http://www.youtube.com/watch?v=13qeX98t AS8 http://www.youtube.com/watch?v=13qeX98t AS8 Slide 3 Did some rockets tumble? Did some rockets wobble? Did some rockets flip over? Maybe some rockets were unstable Slide 4 http://www.youtube.com/watch?v=B47XEFw5 l6w http://www.youtube.com/watch?v=B47XEFw5 l6w Slide 5 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 Slide 6 Moment describe the objects 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. Slide 7 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 = 0X = 2 X=3 Slide 8 Beer, Russell, Johnston, DeWolf Mechanics of Materials Slide 9 PartLength (cm) Weight (g) Nose Cone510 Parachute sys. 35 Recovery Wadding 11 Launch Lug 32 Engine Mount 515 Rocket Engine 530 Fins53 Rocket Body 1540 X = 0 5 7 11 13 14 20 Slide 10 PartCentroid Formula Distance To Centroid MassMoment Nose Conh/3 =1.675/3 = 1.671016.7 Parachuteh/2 =1.511+1.5 =12.5562.5 Recovery Wadding h/2=0.513+0.5=13.5113.5 Launch Lugh/2= 1.57+1.5=8.5217 Engine Mount h/2 = 2.514+2.5=16.515247.5 Slide 11 X = 0 5 7 11 13 14 20 PartCentroid Formula Distance To Centroid MassMoment From Above33357.2 Rocket Engine h/2 =2.514+2.5=16.530495 Rocket Bodyh/2=7.55+7.540300 Total1031152.2 Slide 12 X = 0 5 7 11 13 14 20 Moment = 1152.2 Mass = 103 CG = Moment / Mass = 1152.2/103 = 11.19 cm Slide 13 Break it up into a triangle, rectangle and triangle Area 1 = *b1 * h = 5 Area 2 = b2 * h =5 Area 3 = * b3 * h=5 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 1 1 1 2 1 3 B1=2B2=1 B3=2 H=5 Slide 14 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 1 1 1 2 1 3 b1b2 b3 h 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 Slide 15 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 Slide 16 If : Rocket has no fins Thrust is aligned Rocket pitched a little Moment = -1*Lift * x This rocket will keep pitching and fly out of control y x X Slide 17 Little DragLots of Drag Slide 18 If : Thrust is aligned Rocket turned a little Moment = -1* Lift *x + Fin * x1 If Fin * x1 > Lift * x, the rocket will right itself X Fin Force X1 Slide 19 Fin force = 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 Slide 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 X = 0 5 7 11 13 14 20 Slide 21 Nozzles push on high gasses and accelerate them out the back In return, the gasses push on the nozzle and accelerates it forward Slide 22 Air wants to go from high pressure to low pressure Pressure Force ( P1 P2) * A Remember that Pressure = Force / Area High Pressure Low Pressure Slide 23 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 Slide 24 It is usually easy to study gas flows using control volumes Forces on the rocket could be calculated by only looking at control surfaces F pressure =(P e - P a ) A e Fgas = U e 2 A e Slide 25 Why did rockets filled with water go higher than those filled with just air? Ambient Pressure Constant Exit Pressure Constant Exit Velocity Assumed Constant Changes Slide 26 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 Slide 27 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 Slide 28 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 Slide 29 Lets Calculate Rocket Thrust and acceleration A = F/m = 3050 / 0.5 = 6100 m/s^2 Ambient Conditions: Pa = 101,000 Pa Exit Conditions: Pe = 150,000 Pa Ve = 100 m/s Density = 1.2 kg/m3 Area = 0.05 m^2 Mass = 0.5 kg Slide 30 Pressurized Air Balloon Solid Propellant Liquid Propellant Nuclear Electric Slide 31 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 Slide 32 Propellant is initially in the solid state and it becomes a hot gas during combustion Pros: Simple Cheap Easy to store Can be launched quickly Cons: ISP only 150-350 Cannot turn off after ignition Cannot throttle during flight Slide 33 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 Slide 34 Nuclear Reactor heats working gas that is accelerated through a nozzle Pros: Isp 800-1000 Cons: Requires shielding, can be heavy Its a NUKE Slide 35 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