# Propellant mass fraction

Last updated

In aerospace engineering, the propellant mass fraction is the portion of a vehicle's mass which does not reach the destination, usually used as a measure of the vehicle's performance. In other words, the propellant mass fraction is the ratio between the propellant mass and the initial mass of the vehicle. In a spacecraft, the destination is usually an orbit, while for aircraft it is their landing location. A higher mass fraction represents less weight in a design. Another related measure is the payload fraction, which is the fraction of initial weight that is payload. It can be applied to a vehicle, a stage of a vehicle or to a rocket propulsion system.

## Formulation

The propellant mass fraction is given by:

{\begin{aligned}\zeta &={\frac {m_{\text{p}}}{m_{0}}}\\[3pt]&={\frac {m_{0}-m_{\text{f}}}{m_{0}}}={\frac {m_{\text{p}}}{m_{\text{p}}+m_{\text{f}}}}\\&=1-{\frac {m_{\text{f}}}{m_{0}}}\end{aligned}} Where:

$\zeta$ is the propellant mass fraction
$m_{0}=m_{\text{f}}+m_{\text{p}}$ is the initial mass of the vehicle
$m_{\text{p}}$ is the propellant mass
$m_{\text{f}}$ is the final mass of the vehicle

## Significance

In rockets for a given target orbit, a rocket's mass fraction is the portion of the rocket's pre-launch mass (fully fueled) that does not reach orbit. The propellant mass fraction is the ratio of just the propellant to the entire mass of the vehicle at takeoff (propellant plus dry mass). In the cases of a single stage to orbit (SSTO) vehicle or suborbital vehicle, the mass fraction equals the propellant mass fraction; simply the fuel mass divided by the mass of the full spaceship. A rocket employing staging, which are the only designs to have reached orbit, has a mass fraction higher than the propellant mass fraction because parts of the rocket itself are dropped off en route. Propellant mass fractions are typically around 0.8 to 0.9.

In aircraft, mass fraction is related to range, an aircraft with a higher mass fraction can go farther. Aircraft mass fractions are typically around 0.5.

When applied to a rocket as a whole, a low mass fraction is desirable, since it indicates a greater capability for the rocket to deliver payload to orbit for a given amount of fuel. Conversely, when applied to a single stage, where the propellant mass fraction calculation doesn't include the payload, a higher propellant mass fraction corresponds to a more efficient design, since there is less non-propellant mass. Without the benefit of staging, SSTO designs are typically designed for mass fractions around 0.9. Staging increases the payload fraction, which is one of the reasons SSTOs appear difficult to build.

For example, the complete Space Shuttle system has: 

• fueled weight at liftoff: 1,708,500 kg
• dry weight at liftoff: 342,100 kg

Given these numbers, the propellant mass fraction is $1-(342,100{\text{ kg}}/1,708,500{\text{ kg}})=0.7998$ .

The mass fraction plays an important role in the rocket equation:

$\Delta v=-v_{\text{e}}\ln {\frac {m_{\text{f}}}{m_{0}}}$ Where $m_{\text{f}}/m_{0}$ is the ratio of final mass to initial mass (i.e., one minus the mass fraction), $\Delta v$ is the change in the vehicle's velocity as a result of the fuel burn and $v_{\text{e}}$ is the effective exhaust velocity (see below).

The term effective exhaust velocity is defined as:

$v_{\text{e}}=g_{\text{n}}I_{\text{sp}}$ where Isp is the fuel's specific impulse in seconds and gn is the standard acceleration of gravity (note that this is not the local acceleration of gravity).

To make a powered landing from orbit on a celestial body without an atmosphere requires the same mass reduction as reaching orbit from its surface, if the speed at which the surface is reached is zero.

## Related Research Articles A rocket is a missile, spacecraft, aircraft or other vehicle that obtains thrust from a rocket engine. Rocket engine exhaust is formed entirely from propellant carried within the rocket. Rocket engines work by action and reaction and push rockets forward simply by expelling their exhaust in the opposite direction at high speed, and can therefore work in the vacuum of space. Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. Space propulsion or in-space propulsion exclusively deals with propulsion systems used in the vacuum of space and should not be confused with launch vehicles. Several methods, both pragmatic and hypothetical, have been developed each having its own drawbacks and advantages. A single-stage-to-orbit vehicle reaches orbit from the surface of a body using only propellants and fluids and without expending tanks, engines, or other major hardware. The term usually, but not exclusively, refers to reusable vehicles. No Earth-launched SSTO launch vehicles have ever been constructed. To date, orbital launches from Earth have been performed by either fully or partially expendable multi-stage rockets. An antimatter rocket is a proposed class of rockets that use antimatter as their power source. There are several designs that attempt to accomplish this goal. The advantage to this class of rocket is that a large fraction of the rest mass of a matter/antimatter mixture may be converted to energy, allowing antimatter rockets to have a far higher energy density and specific impulse than any other proposed class of rocket.

Specific impulse is a measure of how effectively a rocket uses propellant or a jet engine uses fuel. Specific impulse can be calculated in a variety of different ways with different units. By definition, it is the total impulse delivered per unit of propellant consumed and is dimensionally equivalent to the generated thrust divided by the propellant mass flow rate or weight flow rate. If mass is used as the unit of propellant, then specific impulse has units of velocity. If weight is used instead, then specific impulse has units of time (seconds). Multiplying flow rate by the standard gravity (g0) converts specific impulse from the weight basis to the mass basis.

Payload is the carrying capacity of an aircraft or launch vehicle, usually measured in terms of weight. Depending on the nature of the flight or mission, the payload of a vehicle may include cargo, passengers, flight crew, munitions, scientific instruments or experiments, or other equipment. Extra fuel, when optionally carried, is also considered part of the payload. In a commercial context, payload may refer only to revenue-generating cargo or paying passengers.

A tripropellant rocket is a rocket that uses three propellants, as opposed to the more common bipropellant rocket or monopropellant rocket designs, which use two or one propellants, respectively. Tripropellant systems can be designed to have high specific impulse and have been investigated for single stage to orbit designs. While tripropellant engines have been tested by Rocketdyne and Energomash, no tripropellant rocket has been built or flown.

Delta-v, symbolised as v and pronounced delta-vee, 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 landing on a planet or moon, or an in-space orbital maneuver. It is a scalar that has the units of speed. As used in this context, it is not the same as the physical change in velocity of the vehicle. A scramjet is a variant of a ramjet airbreathing jet engine in which combustion takes place in supersonic airflow. As in ramjets, a scramjet relies on high vehicle speed to compress the incoming air forcefully before combustion, but whereas a ramjet decelerates the air to subsonic velocities before combustion, the airflow in a scramjet is supersonic throughout the entire engine. That allows the scramjet to operate efficiently at extremely high speeds. A rocket engine uses stored rocket propellants as the reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Rocket engines are reaction engines, producing thrust by ejecting mass rearward, in accordance with Newton's third law. Most rocket engines use the combustion of reactive chemicals to supply the necessary energy, but non-combusting forms such as cold gas thrusters and nuclear thermal rockets also exist. Vehicles propelled by rocket engines are commonly called rockets. Rocket vehicles carry their own oxidizer, unlike most combustion engines, so rocket engines can be used in a vacuum to propel spacecraft and ballistic missiles. 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 attached alongside another stage. The result is effectively two or more rockets stacked on top of or attached next to each other. Two-stage rockets are quite common, but rockets with as many as five separate stages have been successfully launched. A two-stage-to-orbit (TSTO) or two-stage rocket launch vehicle is a spacecraft in which two distinct stages provide propulsion consecutively in order to achieve orbital velocity. It is intermediate between a three-stage-to-orbit launcher and a hypothetical single-stage-to-orbit (SSTO) launcher. A space vehicle or spaceship is a rocket-powered vehicle used to transport robotic spacecraft or people between the Earth's surface and outer space. The earliest space vehicles were expendable launch systems, consisting of two parts: a single or multistage rocket launch vehicle, which carried a spacecraft payload which were relatively small portions of the total vehicle size and mass. An early exception to this, the United States Space Shuttle space vehicle, which flew from 1981 to 2011, consisted of a reusable orbiter spaceplane carrying crew and payload, supported by an expendable external propellant tank and two reusable solid-fuel booster rockets.

Thrust-to-weight ratio is a dimensionless ratio of thrust to weight of a rocket, jet engine, propeller engine, or a vehicle propelled by such an engine that indicates the performance of the engine or vehicle. The Tsiolkovsky rocket equation, 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 can thereby move due to the conservation of momentum. 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, the ratio of the rocket's wet mass to its dry mass. 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. A rocket engine nozzle is a propelling nozzle used in a rocket engine to expand and accelerate the combustion gases produced by burning propellants so that the exhaust gases exit the nozzle at hypersonic velocities. In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well and then accelerates as it's falling, thereby achieving additional speed. The resulting maneuver is a more efficient way to gain kinetic energy than applying the same impulse outside of a gravitational well. The gain in efficiency is explained by the Oberth effect, wherein the use of an engine at higher speeds generates greater mechanical energy than use at lower speeds. In practical terms, this means that the most energy-efficient method for a spacecraft to burn its engine is at the lowest possible orbital periapsis, when its orbital velocity is greatest. In some cases, it is even worth spending fuel on slowing the spacecraft into a gravity well to take advantage of the efficiencies of the Oberth effect. The maneuver and effect are named after Hermann Oberth, the Austro-Hungarian-born German physicist and a founder of modern rocketry, who first described them in 1927.

A cold gas thruster is a type of rocket engine which uses the expansion of a pressurized gas to generate thrust. As opposed to traditional rocket engines, a cold gas thruster does not house any combustion and therefore has lower thrust and efficiency compared to conventional monopropellant and bipropellant rocket engines. Cold gas thrusters have been referred to as the "simplest manifestation of a rocket engine" because their design consists only of a fuel tank, a regulating valve, a propelling nozzle, and the little required plumbing. They are the cheapest, simplest, and most reliable propulsion systems available for orbital maintenance, maneuvering and attitude control. A pulsed nuclear thermal rocket is a type of nuclear thermal rocket (NTR) concept developed at the Polytechnic University of Catalonia, Spain and presented at the 2016 AIAA/SAE/ASEE Propulsion Conference for thrust and specific impulse (Isp) amplification in a conventional nuclear thermal rocket.