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Marat Kulakhmetov

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AS8 AS8

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Did some rockets tumble? Did some rockets wobble? Did some rockets flip over? Maybe some rockets were unstable

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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

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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.

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Location where the forces will balance CG = Moment / Total Weight Example: ◦ Moment = 10 * (0) + 20 * 3 = 60 N * m ◦ Total Weight = = 30 N ◦ CG = Moment / Total Weight = 60 / 30 = 2 m X = 0X = 2 X=3

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Beer, Russell, Johnston, DeWolf Mechanics of Materials

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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 =

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PartCentroid Formula Distance To Centroid MassMoment Nose Conh/3 =1.675/3 = Parachuteh/2 = = Recovery Wadding h/2= = Launch Lugh/2= = Engine Mount h/2 = =

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X = PartCentroid Formula Distance To Centroid MassMoment From Above Rocket Engine h/2 = = Rocket Bodyh/2= Total

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X = Moment = Mass = 103 CG = Moment / Mass = /103 = cm

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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 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 = B1=2B2=1 B3=2 H=5

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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 = 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

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X = Moment with fins = (2.5+14)*3 Mass = CG = Moment / Mass =11.34 cm

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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

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Little DragLots of Drag

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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

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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

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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 =

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Nozzles push on high gasses and accelerate them out the back In return, the gasses push on the nozzle and accelerates it forward

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Air wants to go from high pressure to low pressure Pressure Force ( P1 – P2) * A Remember that Pressure = Force / Area High Pressure Low Pressure

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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

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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 = ρ U e 2 A e

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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

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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

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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

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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

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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

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Pressurized Air ◦ Balloon Solid Propellant Liquid Propellant Nuclear Electric

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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

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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 ◦ Cannot turn off after ignition ◦ Cannot throttle during flight

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Fuel and Oxidizer are both stored separately in liquid form Pros: ◦ Better performance (ISP ) Cons: ◦ More complex ◦ Requires pumps or pressurized gas tanks ◦ Heavier

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Nuclear Reactor heats working gas that is accelerated through a nozzle Pros: ◦ Isp Cons: ◦ Requires shielding, can be heavy ◦ It’s a NUKE

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Two types: ◦ Arcjet: Electricity is used to superheat the gases ◦ Ion Thrusters: ionized (charged) atoms are accelerated through an electro-magnetic field Pros: ◦ ISP ,000 Cons: ◦ Thrust usually <1N VASMIR

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