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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 Presentation
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Class 2: Advanced Rocket Concepts
Marat Kulakhmetov
http://www.youtube.com/watch?v=13qeX98tAS8
Intro Video
Did some rockets tumble? Did some rockets wobble? Did some rockets flip over?
Maybe some rockets were unstable
Water Bottle Rocket Debriefing
http://www.youtube.com/watch?v=B47XEFw5l6w
Fun Video
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
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
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
Calculating CG of complex 2D and 3D Shapes
Beer, Russell, Johnston, DeWolf Mechanics of Materials
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
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
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
Example Continued
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
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
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
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
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
Little Drag Lots of Drag
Fins
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
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
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
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
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
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
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
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
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
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
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
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
Pressurized Air◦ Balloon
Solid Propellant Liquid Propellant Nuclear Electric
Types of Rocket Engines
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
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
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
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
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