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 Combustion Chamber Throat Nozzle Fuel Oxidizer Propellants Liquid Rocket Engine

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 = ma m = F am a = F

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 Nozzle Area times pressure differential Propellant Mass Flow times Velocity W. g VeVe F = + A e ( P e - P a )

Exhaust Plumes and Nozzles P exhaust < P ambient Under Expanded P exhaust > P ambient Over Expanded P exhaust = P ambient Ideal Expansion

Expansion Ratio Ratio of the nozzle exit area divided by the area at the nozzle throat. AtAt AeAe  = 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 = mimfmimf 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. The higher the thrust-to-weight ratio the faster the vehicle will accelerate The initial acceleration of a vehicle in “g’s” equals  = Thrust Vehicle Weight = FWFW a 

Ideal Rocket Equation The ideal velocity change (  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 Ideal means you do not consider gravity changes, drag, or rotating Earth  V i = I sp x g x ln MR