# Marat Kulakhmetov.  AS8 AS8.

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Marat Kulakhmetov

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

 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 = 0X = 2 X=3

Beer, Russell, Johnston, DeWolf Mechanics of Materials

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

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

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

X = 0 5 7 11 13 14 20  Moment = 1152.2  Mass = 103  CG = Moment / Mass  = 1152.2/103 = 11.19 cm

 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 =1 1 1 1 2 1 3 B1=2B2=1 B3=2 H=5

 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

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  Moment = -1*Lift * x  This rocket will keep pitching and fly out of control y x X

 Little DragLots of Drag

 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

 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

 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

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

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

 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  F pressure =(P e - P a ) A e  Fgas = ρ U e 2 A e

 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

 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

 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

 Pressurized Air ◦ Balloon  Solid Propellant  Liquid Propellant  Nuclear  Electric

 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: ◦ Simple ◦ Cheap ◦ Easy to store ◦ Can be launched quickly  Cons: ◦ 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: ◦ Isp 800-1000  Cons: ◦ 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