#### Transcript Rocket Engines - Troy University

### 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 = ma m =

**F a F**

### a =

**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