class 2: advanced rocket concepts
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Class 2: Advanced Rocket Concepts. Marat Kulakhmetov. Intro Video. http://www.youtube.com/watch?v=13qeX98tAS8. Water Bottle Rocket Debriefing. Did some rockets tumble? Did some rockets wobble? Did some rockets flip over? Maybe some rockets were unstable. Fun Video. - PowerPoint PPT PresentationTRANSCRIPT
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Class 2: Advanced Rocket Concepts
Marat Kulakhmetov
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http://www.youtube.com/watch?v=13qeX98tAS8
Intro Video
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Did some rockets tumble? Did some rockets wobble? Did some rockets flip over?
Maybe some rockets were unstable
Water Bottle Rocket Debriefing
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http://www.youtube.com/watch?v=B47XEFw5l6w
Fun Video
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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
Stability
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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.
Moments
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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 = 10 + 20 = 30 N ◦ CG = Moment / Total Weight = 60 / 30 = 2 m
Center of Gravity (CG)
X = 0 X = 2 X=3
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Calculating CG of complex 2D and 3D Shapes
Beer, Russell, Johnston, DeWolf Mechanics of Materials
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Example: Moments of a Rocket Part Length
(cm)Weight (g)
Nose Cone 5 10Parachute sys.
3 5
Recovery Wadding
1 1
Launch Lug
3 2
Engine Mount
5 15
Rocket Engine
5 30
Fins 5 3Rocket Body
15 40
X = 0 5 7 11 13 14 20
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Example Continued
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 16.7Parachute h/2 =1.5 11+1.5 =12.5 5 62.5Recovery 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 17Engine Mount
h/2 = 2.5 14+2.5=16.5 15 247.5
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Example Continued
X = 0 5 7 11 13 14 20
Part Centroid Formula
Distance To Centroid
Mass Moment
From Above 33 357.2Rocket Engine
h/2 =2.5 14+2.5=16.5 30 495
Rocket Body h/2=7.5 5+7.5 40 300Total 103 1152.2
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Example Continued
X = 0 5 7 11 13 14 20
Moment = 1152.2 Mass = 103 CG = Moment / Mass = 1152.2/103 = 11.19 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
How about complex Fins?
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
1112
13
B1=2 B2=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 =.66
How about complex Fins?
1112
13
b1 b2
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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Example Continued
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
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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
Moments on a Rocket without Fins
y
x
X
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Little Drag Lots of Drag
Fins
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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
Moments on a Rocket with Fins
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
Fins21
2 dF C V A
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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
Aerodynamic Center
X = 0 5 7 11 13 14 20
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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
Rocket Nozzles
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Air wants to go from high pressure to low pressure
Pressure Force ( P1 – P2) * A
Remember that Pressure = Force / Area
Pressure Forces
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
Momentum Forces
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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
Fpressure =(Pe - Pa ) Ae Fgas = ρ Ue
2 Ae
Control Volume
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Why did rockets filled with water go higher than those filled with just air?
Water Bottle Rocket Debriefing
2[( ) ]Thrust Pe Pa V Ae
Ambient PressureConstant
ExitPressureConstant
Exit Velocity
AssumedConstant
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
Isentropic Nozzles
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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
Converging Section
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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
Diverging Section
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Lets Calculate Rocket Thrust and acceleration
A = F/m = 3050 / 0.5 = 6100 m/s^2
Example Ambient Conditions:Pa = 101,000 Pa
Exit Conditions:Pe = 150,000 PaVe = 100 m/sDensity = 1.2 kg/m3
Area = 0.05 m^2Mass = 0.5 kg
2[( ) ]Thrust Pe Pa V A
2[(101,000 150,000) 1.2(100) ]0.05 3050Thrust N
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Pressurized Air◦ Balloon
Solid Propellant Liquid Propellant Nuclear Electric
Types of Rocket Engines
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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
ISP
( / )
FISPmg
F Thrustm massflow kg sg gravity
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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 150-350◦ Cannot turn off after ignition◦ Cannot throttle during flight
Solid Propellant
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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
Liquid Propellant
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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
Nuclear
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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 400-10,000
Cons:◦ Thrust usually <1N
VASMIR
Electric