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:

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

where:

    F = force in newtons, N

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

V_eq = equivalent exhaust velocity at nozzle exit, m/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

t = time, s

I = total impulse, N

g_o = gravitational acceleration on Earth at sea level = 9.807 m/s²

I_sp = specific impulse, s

Different rocket engines have different values of specific impulse. The higher is the specific impulse, the more efficient is the engine because it produces more thrust for the same amount of propellant.