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A rocket's required mass ratio as a function of effective exhaust velocity ratio. The classical rocket equation, or ideal rocket equation is a mathematical equation that describes the motion of vehicles that follow the basic principle of a rocket: a device that can apply acceleration to itself using thrust by expelling part of its mass with high velocity and can thereby move due to the ...
This equation can be rewritten in the following equivalent form: = / The fraction on the left-hand side of this equation is the rocket's mass ratio by definition. This equation indicates that a Δv of n {\displaystyle n} times the exhaust velocity requires a mass ratio of e n {\displaystyle e^{n}} .
The Tsiolkovsky rocket equation shows that the delta-v of a rocket (stage) is proportional to the logarithm of the fuelled-to-empty mass ratio of the vehicle, and to the specific impulse of the rocket engine. A key goal in designing space-mission trajectories is to minimize the required delta-v to reduce the size and expense of the rocket that ...
This relationship is described by the rocket equation. Exhaust velocity is dependent on the propellant and engine used and closely related to specific impulse, the total energy delivered to the rocket vehicle per unit of propellant mass consumed. Mass ratio can also be affected by the choice of a given propellant.
Rocket mass ratios versus final velocity calculated from the rocket equation. The Tsiolkovsky rocket equation, or ideal rocket equation, can be useful for analysis of maneuvers by vehicles using rocket propulsion. [2] A rocket applies acceleration to itself (a thrust) by expelling part of its mass at high speed. The rocket itself moves due to ...
Rocket mass ratios versus final velocity calculated from the rocket equation Main article: Tsiolkovsky rocket equation The ideal rocket equation , or the Tsiolkovsky rocket equation, can be used to study the motion of vehicles that behave like a rocket (where a body accelerates itself by ejecting part of its mass, a propellant , with high speed).