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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 ...
The velocity and altitude of the rocket after burnout can be easily modeled using the basic physics equations of motion. When comparing one rocket with another, it is impractical to directly compare the rocket's certain trait with the same trait of another because their individual attributes are often not independent of one another.
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).
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}} .
This effective exhaust velocity represents an average or mass equivalent velocity at which propellant is being ejected from the rocket vehicle." [ 10 ] The two definitions of specific impulse are proportional to one another, and related to each other by: v e = g 0 ⋅ I sp , {\displaystyle v_{\text{e}}=g_{0}\cdot I_{\text{sp}},} where
In the relativistic case, the equation is still valid if is the acceleration in the rocket's reference frame and is the rocket's proper time because at velocity 0 the relationship between force and acceleration is the same as in the classical case. Solving this equation for the ratio of initial mass to final mass gives
As the velocity of the rocket increases, progressively more of the available kinetic energy goes to the rocket and its payload, and less to the exhaust. This is shown as follows. The mechanical work done on the rocket ( W {\displaystyle W} ) is defined as the dot product of the force of the engine's thrust ( F → {\displaystyle {\vec {F ...