Thrust-to-weight ratio is adimensionless ratio ofthrust toweight of areaction engine or a vehicle with such an engine. Reaction engines includejet engines,rocket engines,pump-jets,Hall-effect thrusters, andion thrusters, among others. These generate thrust by expelling mass (propellant) in the opposite direction of intended motion, in accordance withNewton's third law. A related but distinct metric is thepower-to-weight ratio, which applies to engines or systems that deliver mechanical, electrical, or other forms ofpower rather than direct thrust.

In many applications, the thrust-to-weight ratio serves as an indicator of performance. The ratio in a vehicle’s initial state is often cited as afigure of merit, enabling quantitative comparison across different vehicles or engine designs. The instantaneous thrust-to-weight ratio of a vehicle can vary during operation due to factors such as fuel consumption (which reduces mass) or changes ingravitational acceleration, for example in orbital or interplanetary contexts.

The thrust-to-weight ratio of an engine or vehicle is calculated by dividing its thrust by its weight (not to be confused with mass). The formula is:

${\displaystyle \mathrm{T}\mathrm{W}\mathrm{R}=\frac{T}{W}=\frac{T}{m\cdot g}}$

where:

• ${\displaystyle T}$ is thethrust, innewtons (N),kilograms-force (kgf), orpounds-force (lbf),
• ${\displaystyle W}$ is theweight, in newtons (N), which can also be expressed as the product of:
  • mass${\displaystyle m}$, in kilograms (kg) or pounds (lb), and
  • gravitational acceleration${\displaystyle g}$, e.g., thestandard gravitational acceleration on Earth of 9.80665 m/s².

For valid comparison of the initial thrust-to-weight ratio of two or more engines or vehicles, thrust must be measured under controlled conditions. Because an aircraft's weight can vary considerably, depending on factors such as munition load, fuel load, cargo weight, or even the weight of the pilot, the thrust-to-weight ratio is also variable and even changes during flight operations. There are several standards for determining the weight of an aircraft used to calculate the thrust-to-weight ratio range.

• Empty weight – The weight of the aircraft minus fuel, munitions, cargo, and crew.
• Combat weight – Primarily for determining the performance capabilities of fighter aircraft, it is the weight of the aircraft with full munitions and missiles, half fuel, and no drop tanks or bombs.
• Max takeoff weight – The weight of the aircraft when fully loaded with the maximum fuel and cargo that it can safely takeoff with.^[1]

The thrust-to-weight ratio andlift-to-drag ratio are the two most important parameters in determining the performance of an aircraft.

The thrust-to-weight ratio varies continually during a flight. Thrust varies with throttle setting,airspeed,altitude, air temperature, etc. Weight varies with fuel burn and payload changes. For aircraft, the quoted thrust-to-weight ratio is often the maximum static thrust at sea level divided by themaximum takeoff weight.^[2] Aircraft with thrust-to-weight ratio greater than 1:1 can pitch straight up and maintain airspeed until performance decreases at higher altitude.^[3]

A plane can take off even if the thrust is less than its weight as, unlike a rocket, the lifting force is produced by lift from the wings, not directly by thrust from the engine. As long as the aircraft can produce enough thrust to travel at a horizontal speed above its stall speed, the wings will produce enough lift to counter the weight of the aircraft.

${\displaystyle {\left(\frac{T}{W}\right)}_{\text{cruise}}={\left(\frac{D}{L}\right)}_{\text{cruise}}=\frac{1}{{\left(\frac{L}{D}\right)}_{\text{cruise}}}.}$

For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows in imperial units:^[4]

${\displaystyle \frac{T}{W}=\frac{550{\eta }_{\mathrm{p}}}{V}\frac{\text{hp}}{W},}$

where${\displaystyle {\eta }_{\mathrm{p}}}$ ispropulsive efficiency (typically 0.65 for wooden propellers, 0.75 metal fixed pitch and up to 0.85 for constant-speed propellers), hp is the engine'sshaft horsepower, and${\displaystyle V}$istrue airspeed in feet per second, weight is in lbs.

The metric formula is:

${\displaystyle \frac{T}{W}=\left(\frac{{\eta }_{\mathrm{p}}}{V}\right)\left(\frac{P}{W}\right).}$

The thrust-to-weight ratio of a rocket, or rocket-propelled vehicle, is an indicator of its acceleration expressed in multiples of gravitational accelerationg.^[5]

Rockets and rocket-propelled vehicles operate in a wide range of gravitational environments, including theweightless environment. The thrust-to-weight ratio is usually calculated from initial gross weight at sea level on earth^[6] and is sometimes calledthrust-to-Earth-weight ratio.^[7] The thrust-to-Earth-weight ratio of a rocket or rocket-propelled vehicle is an indicator of its acceleration expressed in multiples of earth's gravitational acceleration,g₀.^[5]

The thrust-to-weight ratio of a rocket improves as the propellant is burned. With constant thrust, the maximum ratio (maximum acceleration of the vehicle) is achieved just before the propellant is fully consumed. Each rocket has a characteristic thrust-to-weight curve, or acceleration curve, not just a scalar quantity.

The thrust-to-weight ratio of an engine is greater than that of the complete launch vehicle, but is nonetheless useful because it determines the maximum acceleration thatany vehicle using that engine could theoretically achieve with minimum propellant and structure attached.

For a takeoff from the surface of theearth using thrust and noaerodynamic lift, the thrust-to-weight ratio for the whole vehicle must be greater thanone. In general, the thrust-to-weight ratio is numerically equal to theg-force that the vehicle can generate.^[5] Take-off can occur when the vehicle'sg-force exceeds local gravity (expressed as a multiple ofg₀).

The thrust-to-weight ratio of rockets typically greatly exceeds that ofairbreathing jet engines because the comparatively far greater density of rocket fuel eliminates the need for much engineering materials to pressurize it.

Many factors affect thrust-to-weight ratio. The instantaneous value typically varies over the duration of flight with the variations in thrust due to speed and altitude, together with changes in weight due to the amount of remaining propellant, and payload mass. Factors with the greatest effect include freestream airtemperature,pressure,density, and composition. Depending on the engine or vehicle under consideration, the actual performance will often be affected bybuoyancy and localgravitational field strength.

• Table for Jet and rocket engines: jet thrust is at sea level
• Fuel density used in calculations: 0.803 kg/l
• For the metric table, theT/W ratio is calculated by dividing the thrust by the product of the full fuel aircraft weight and the acceleration of gravity.
• J-10's engine rating is of AL-31FN.

• Power-to-weight ratio
• Factor of safety

• John P. Fielding.Introduction to Aircraft Design, Cambridge University Press,ISBN 978-0-521-65722-8
• Daniel P. Raymer (1989).Aircraft Design: A Conceptual Approach, American Institute of Aeronautics and Astronautics, Inc., Washington, DC.ISBN 0-930403-51-7
• George P. Sutton & Oscar Biblarz.Rocket Propulsion Elements, Wiley,ISBN 978-0-471-32642-7

• NASA webpage with overview and explanatory diagram of aircraft thrust to weight ratio

• Jet engines
• Rocket engines
• Engineering ratios

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