School of Aeronautics and Astronautics

Class 4: Fundamentals of Rocket Propulsion

Marat Kulakhmetov

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Did Buzz Aldrin punch a reporter?

• http://www.youtube.com/watch?v=KaUqaVj51w4&feature=related

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Gases

•Gas is made up of molecules that fly in random directions

•Molecules collide with other molecules and with the walls

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Temperature

• Temperature describes how fast the molecules move

• At higher temperature, molecules move faster

• At room temperature air molecules move at 500m/s ( 1118.46 mi/h)

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Pressure

•How much momentum gases transfer to the surface

•How often and how fast the molecules hit the surface

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Density•How much stuff is in

a volume

• Solids are high density

•Gases are low density

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Ideal Gas Law

• Temperature, Pressure, Density describe what molecules do so they have to be related.

P RTP = Pressureρ = DensityR = Gas constantT = Temperature

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Thrust• Most vehicles need to overcome weight and drag

by generating thrust

• There are many ways of generating thrust:– Internal Combustion Engines

• Usually found in cars• They are small but require an oxygen supply

– Jet Engines• Usually found on fast airplanes• They can generate a lot of thrust but they still need an

oxygen supply– Rocket Engines

• These generate enough thrust to escape Earth’s gravity and often carry their own oxidizer so they work in space

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4 Stroke Internal Combustion Engine• Use gas expansion to rotate the cam shaft• The cam shaft turns the wheel or propeller and makes

cars or airplanes go forward• There is no ground or air in space, rockets cant use this

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Jet Engine•Compressor

– Compresses air• Bypass Fan

– Accelerates Air•Combustor

– Burns air• Turbine

– Powers compressor and Bypass Fan

•Needs Air•Max Speed: 3000 mi/h

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Thrust• Typically, rocket engines produce two types of

thrust:– Pressure Thrust

• Generate higher pressure behind the rocket • = (Pe-Pa)*A

– Jet Thrust• Pushes the rocket forward by throwing gasses out of the back• = mdot Ve

– Total Thrust = Pressure Thrust + Jet Thrust– Thrust produced depends on fuel, rocket nozzle, rocket

altitude, etc.

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Pressure Forces

• 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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Momentum Forces

• Action-Reaction

• 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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Rocket Nozzles

•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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Control Volume

• 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 Ue2 Ae

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Isentropic Nozzles

•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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Converging Section

• 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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Diverging 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

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Over and Under Expanded Gasses

• Performance of the nozzle depends on outside pressure

• Outside Pressure changes with altitude

• Over and Under expanded gasses are not as efficient

Under expanded

Perfectly Expanded

Over Exanded

Separated

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Example

• Lets Calculate Rocket Thrust and acceleration

»A = F/m = 3050 / 0.5 = 6100 m/s^2

Ambient Conditions:Pa = 101,000 PaExit 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[(150,000 101,000) 1.2(100) ]0.05 3050Thrust N

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Water Bottle Rocket Debriefing•Why did rockets filled with water go higher

than those filled with just air?

2[( ) ]Thrust Pe Pa V Ae

Ambient PressureConstant

ExitPressureConstant

Exit Velocity

AssumedConstant

Changes

Air Density = 1.2 kg/m^3Water Density = 1000 kg/m^3

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ISP

• 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

( / )

FISPmg

F Thrustm massflow kg sg gravity

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Types of Rocket Engines

• Pressurized Air• Solid Propellant• Liquid Propellant•Nuclear• Electric

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Compressed Air•Compressed air leaves

out of the back of the rocket

• The air pushes the rocket forward

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Solid Propellant

• 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

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Liquid 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

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Nuclear• 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

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Electric• 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• VASIMR

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Video

• http://www.youtube.com/watch?v=YOSBzFSZUx4&feature=related