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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 specific impulse of a rocket can be defined in terms of thrust per unit mass flow of propellant. This is an equally valid (and in some ways somewhat simpler) way of defining the effectiveness of a rocket propellant. For a rocket, the specific impulse defined in this way is simply the effective exhaust velocity relative to the rocket, v e ...
This is just the rocket equation applied to the sum of the two maneuvers. This is convenient since it means that delta-v can be calculated and simply added and the mass ratio calculated only for the overall vehicle for the entire mission. Thus delta-v is commonly quoted rather than mass ratios which would require multiplication.
v e is the effective exhaust velocity (see specific impulse) m 0 is the initial mass (rocket plus contents plus propellant) m 1 is the final mass (rocket plus contents) 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.
The Oberth effect is used in a powered flyby or Oberth maneuver where the application of an impulse, typically from the use of a rocket engine, close to a gravitational body (where the gravity potential is low, and the speed is high) can give much more change in kinetic energy and final speed (i.e. higher specific energy) than the same impulse ...
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.
In the case of rockets, the impulse imparted can be normalized by unit of propellant expended, to create a performance parameter, specific impulse. This fact can be used to derive the Tsiolkovsky rocket equation , which relates the vehicle's propulsive change in velocity to the engine's specific impulse (or nozzle exhaust velocity) and the ...
The specific impulse relates the delta-v capacity to the quantity of propellant consumed according to the Tsiolkovsky rocket equation: [5] = where: m 0 {\displaystyle m_{0}} is the initial total mass, including propellant, in kg (or lb)