### Rocket Engines

• Liquid Propellant – Mono propellant • Catalysts – Bi-propellant • Solid Propellant – Grain Patterns • Hybrid • Nuclear • Electric

Performance Energy Safety Simplicity Expanding Gases Thrust Termination Restart

Rocket Propulsion

### Liquid Rocket Engine

Oxidizer Fuel Propellants Combustion Chamber Throat Nozzle

### Newton’s Laws

The force required to accelerate a body is proportional to the product of the mass of the body and the acceleration desired.

F a F

m

### Rocket Thrust

• Thrust is produced by the expanding propellants.

• There is thrust from the difference between the ambient pressure and that of the exhaust gases at the nozzle exit ( Pressure Thrust ) and from the momentum of the propellants ( Momentum Thrust ).

Total Thrust = Momentum Thrust + Pressure Thrust Propellant Mass Flow times Velocity Nozzle Area times pressure differential .

W F = + A g V e e ( P e - P a )

### Exhaust Plumes and Nozzles

P exhaust < P ambient Under Expanded P exhaust = P ambient Ideal Expansion P exhaust > P ambient Over Expanded

### Expansion Ratio

• Ratio of the nozzle exit area divided by the area at the nozzle throat.

x

= A e A t Throat Exit

### Specific Impulse

• A measure of the energy in the propellants and of the efficiency of the rocket engine design • Specific Impulse is the ratio of the Thrust (Force) produced divided by the weight rate flow of propellants

I sp = W F .

Mass Ratio of a Vehicle Mass Ratio is the ratio between the booster mass before the rocket engine burn divided by the booster mass after rocket engine burn.

MR = m i m f The Mass Ratio for a multistage rocket is the product of the Mass Ratios of all the stages, i.e.

MR Over All = MR 1 x MR 2 x MR 3 x …x MR n

### Thrust-to-Weight Ratio

• Measure of booster or stage design and manufacturing technology.

Y

= Thrust Vehicle Weight = F W

• The higher the thrust-to-weight ratio the faster the vehicle will accelerate • The initial acceleration of a vehicle in “g’s” equals

a

= ( Y - 1 )

### Ideal Rocket Equation

• The ideal velocity change ( D

V

) for each stage of a rocket is a function of the mass ratio (

MR

) of the stage and the specific impulse (

I sp

) of the rocket D

V i = I sp

x

g

x

ln MR

• Ideal means you do not consider gravity changes, drag, or rotating Earth