Mass ratio
Encyclopedia
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
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.
Typical multistage rocket
s have mass ratios in the range from 8 to 20. The Space Shuttle
, for example, has a mass ratio around 16.
where
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
times the exhaust velocity requires a mass ratio of 
. For instance, for a vehicle to achieve a 
of 2.5 times its exhaust velocity would require a mass ratio of 
(approximately 12.2). One could say that a "velocity ratio" of 
requires a mass ratio of 
.
Sutton defines the mass ratio inversely as:
In this case, the values for mass fraction are always less than 1.
Aerospace engineering
Aerospace engineering is the primary branch of engineering concerned with the design, construction and science of aircraft and spacecraft. It is divided into two major and overlapping branches: aeronautical engineering and astronautical engineering...
, mass ratio is a measure of the efficiency of a rocket
Rocket
A rocket is a missile, spacecraft, aircraft or other vehicle which obtains thrust from a rocket engine. In all rockets, the exhaust is formed entirely from propellants carried within the rocket before use. Rocket engines work by action and reaction...
. It describes how much more massive the vehicle is with propellant
Propellant
A propellant is a material that produces pressurized gas that:* can be directed through a nozzle, thereby producing thrust ;...
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
Specific impulse
Specific impulse is a way to describe the efficiency of rocket and jet engines. It represents the derivative of the impulse with respect to amount of propellant used, i.e., the thrust divided by the amount of propellant used per unit time. If the "amount" of propellant is given in terms of mass ,...
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
In astrodynamics a Δv or delta-v is a scalar which takes units of speed. It is a measure of the amount of "effort" that is needed to change from one trajectory to another by making an orbital maneuver....
.
The mass ratio is a useful quantity for back-of-the-envelope rocketry calculations: it is an easy number to derive from either
Delta-v
In astrodynamics a Δv or delta-v is a scalar which takes units of speed. It is a measure of the amount of "effort" that is needed to change from one trajectory to another by making an orbital maneuver....
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.
Typical multistage rocket
Multistage rocket
A multistage rocket is a rocket that usestwo or more 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 attached alongside another stage. The result is effectively two or more rockets stacked on top of or...
s have mass ratios in the range from 8 to 20. The Space Shuttle
Space Shuttle
The Space Shuttle was a manned orbital rocket and spacecraft system operated by NASA on 135 missions from 1981 to 2011. The system combined rocket launch, orbital spacecraft, and re-entry spaceplane with modular add-ons...
, for example, has a mass ratio around 16.
Derivation
The definition arises naturally from the Tsiolkovsky's rocket equation:where
- ΔvDelta-vIn astrodynamics a Δv or delta-v is a scalar which takes units of speed. It is a measure of the amount of "effort" that is needed to change from one trajectory to another by making an orbital maneuver....
is the desired change in the rocket's velocity - ve is the effective exhaust velocity (see specific impulseSpecific impulseSpecific impulse is a way to describe the efficiency of rocket and jet engines. It represents the derivative of the impulse with respect to amount of propellant used, i.e., the thrust divided by the amount of propellant used per unit time. If the "amount" of propellant is given in terms of mass ,...
) - m0 is the initial mass (rocket plus contents plus propellant)
- m1 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.
This equation indicates that a Δv of
times the exhaust velocity requires a mass ratio of . For instance, for a vehicle to achieve a of 2.5 times its exhaust velocity would require a mass ratio of (approximately 12.2). One could say that a "velocity ratio" of requires a mass ratio of .Sutton defines the mass ratio inversely as:
In this case, the values for mass fraction are always less than 1.