User:Milton Beychok/Sandbox

Rocket thrust and specific impulse

Thrust is the force (F) which moves a rocket through the air. Thrust is generated by the rocket engine through the reaction of accelerating a mass of gas. The gas is accelerated to the the rear and the rocket is accelerated in the opposite direction. Force may be mathematically expressed as:

$F={\dot {m}}V_{e}+(p_{e}-P_{o})A_{e}$

and also this form, by defining a new term v_eq :

$F={\dot {m}}V_{eq}={\dot {m}}\left[V_{e}+{\frac {(p_{e}-P_{o})A_{e}}{\dot {m}}}\right]$

The total impulse of a rocket ( I ) is defined as the average thrust multiplied by the total time ( t ) of propellant burning:

$I=F\Delta t=\int {Fdt}=\int {{\dot {m}}V_{eq}\,dt}={\dot {m}}V_{eq}$

The specific impulse ( I_sp ) is the total impulse divided by the weight of the exhaust gas:

$I_{sp}=I/{\text{weight}}={\frac {I}{{\dot {m}}g_{o}}}={\frac {F}{{\dot {m}}g_{o}}}$

where:

F = force in newtons, N

ṁ  = mass flow rate of exhaust gas, kg/s

V_e = exhaust velocity at nozzle exit, m/s

p_e = absolute pressure of exhaust gas at nozzle exit, Pa

p_o = external ambient pressure, Pa

A_e = cross-sectional area of nozzle exhaust exit, m²