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:

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

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

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

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:

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