aerospace engineering Aerospace engineering is the primary field of engineering concerned with the development of aircraft and spacecraft. It has two major and overlapping branches: aeronautical engineering and astronautical engineering. Avionics engineering is s ...

, mass ratio is a measure of the efficiency of a

rocket A rocket (from , and so named for its shape) is a vehicle that uses jet propulsion to accelerate without using any surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely ...

. It describes how much more massive the vehicle is with

propellant A propellant (or propellent) is a mass that is expelled or expanded in such a way as to create a thrust or another motive force in accordance with Newton's third law of motion, and "propel" a vehicle, projectile, or fluid payload. In vehicle ...

than without; that 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 Delta-''v'' (also known as "change in velocity"), symbolized as and pronounced , as used in spacecraft flight dynamics, is a measure of the impulse per unit of spacecraft mass that is needed to perform a maneuver such as launching from or l ...

. The mass ratio is a useful quantity for back-of-the-envelope rocketry calculations: it is an easy number to derive from either

\Delta

or from rocket and propellant mass, and therefore serves as a handy bridge between the two. It is also a useful for getting 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. Typical

multistage rocket A multistage rocket or step rocket is a launch vehicle that uses two or more rocket ''stages'', each of which contains its own engines and propellant. A ''tandem'' or ''serial'' stage is mounted on top of another stage; a ''parallel'' stage is ...

s have mass ratios in the range from 8 to 20. The

Space Shuttle The Space Shuttle is a retired, partially reusable launch system, reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. ...

, for example, has a mass ratio around 16.

Derivation

The definition arises naturally from Tsiolkovsky's rocket equation:

\Delta v = v_e \ln \frac

where * Δ''v'' is the desired change in the rocket's velocity *''v_e'' is the effective exhaust velocity (see

specific impulse Specific impulse (usually abbreviated ) is a measure of how efficiently a reaction mass engine, such as a rocket engine, rocket using propellant or a jet engine using fuel, generates thrust. In general, this is a ratio of the ''Impulse (physics), ...

) *''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:

\frac   = e ^

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

e^n

. For instance, for a vehicle to achieve a

\Delta v

of 2.5 times its exhaust velocity would require a mass ratio of

e^

(approximately 12.2). One could say that a "velocity ratio" of

n

requires a mass ratio of

e^n

Alternative definition

Sutton defines the mass ratio inversely as:Rocket Propulsion Elements, 7th Edition by George P. Sutton, Oscar Biblarz

M_R = \frac

In this case, the values for mass fraction are always less than 1.

References

{{reflist Astrodynamics Mass Ratios

Derivation

Alternative definition

See also

References