- Mass ratio
Astrodynamics Orbital mechanics
In aerospace engineering, mass ratio is a measure of the efficiency of a rocket. It describes how much more massive the vehicle is with propellant than without; that is, it is the ratio of the rocket's wet mass (vehicle plus contents plus propellant) to its dry mass (vehicle plus contents). A more efficient rocket design requires less propellant to achieve a given goal, and would therefore have a lower mass ratio, however for any given efficiency a higher mass ratio typically permits the vehicle to achieve higher delta-v.
The mass ratio is a useful quantity for back-of-the-envelope rocketry calculations: it is an easy number to derive from either Δv numbers or from rocket and propellant mass numbers, and therefore serves as a handy bridge between the two. It is also a useful number to give an impression of the size of a rocket: while two rockets with mass fractions of, say, 92% and 95% may appear similar, the corresponding mass ratios of 12.5 and 20 clearly indicate that the latter system requires much more propellant.
The definition arises naturally from the Tsiolkovsky's rocket equation:
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 times the exhaust velocity requires a mass ratio of en. For instance, for a vehicle to achieve a Δv of 2.5 times its exhaust velocity would require a mass ratio of e2.5 (approximately 12.2). One could say that a "velocity ratio" of n requires a mass ratio of en.
Sutton defines the mass ratio inversely as:
In this case, the values for mass fraction are always less than 1.
Zubrin, Robert (1999). Entering Space: Creating a Spacefaring Civilization. Tarcher/Putnam. ISBN 0-87477-975-8.
- ^ Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz
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