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