Thrust-to-weight ratio is a dimensionless ratio of thrust to weight of a reaction engine or a vehicle with such an engine. Reaction engines include jet engines, rocket engines, pump-jets, Hall-effect thrusters, and ion thrusters, among others. These generate thrust by expelling mass (propellant) in the opposite direction of intended motion, in accordance with Newton's third law. A related but distinct metric is the power-to-weight ratio, which applies to engines or systems that deliver mechanical, electrical, or other forms of power 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 a figure 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 in gravitational acceleration, for example in orbital or interplanetary contexts.

Calculation + Thrust-to-weight from mass (assuming standard gravity) N kg TWR ~ 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:

where:

is the thrust, in newtons (N), kilograms-force (kgf), or pounds-force (lbf), is the weight, in newtons (N), which can also be expressed as the product of: mass , in kilograms (kg) or pounds (lb), and gravitational acceleration , e.g., the standard 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.NASA Technical Memorandum 86352 - Some Fighter Aircraft Trends

Aircraft The thrust-to-weight ratio and lift-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 the maximum takeoff weight.John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21) Aircraft with thrust-to-weight ratio greater than 1:1 can pitch straight up and maintain airspeed until performance decreases at higher altitude.

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.

Propeller-driven aircraft For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows in imperial units:Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equations 3.9 and 5.1

where is propulsive 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's shaft horsepower, and is true airspeed in feet per second, weight is in lbs.

The metric formula is:

Rockets

The thrust-to-weight ratio of a rocket, or rocket-propelled vehicle, is an indicator of its acceleration expressed in multiples of gravitational acceleration g.George P. Sutton & Oscar Biblarz, Rocket Propulsion Elements (p. 442, 7th edition) "thrust-to-weight ratio F/Wg is a dimensionless parameter that is identical to the acceleration of the rocket propulsion system (expressed in multiples of g) if it could fly by itself in a gravity-free vacuum"

Rockets and rocket-propelled vehicles operate in a wide range of gravitational environments, including the weightless environment. The thrust-to-weight ratio is usually calculated from initial gross weight at sea level on earthGeorge P. Sutton & Oscar Biblarz, Rocket Propulsion Elements (p. 442, 7th edition) "The loaded weight Wg is the sea-level initial gross weight of propellant and rocket propulsion system hardware." and is sometimes called thrust-to-Earth-weight ratio. 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, g.

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 that any vehicle using that engine could theoretically achieve with minimum propellant and structure attached.

For a takeoff from the surface of the earth using thrust and no aerodynamic lift, the thrust-to-weight ratio for the whole vehicle must be greater than one. In general, the thrust-to-weight ratio is numerically equal to the g-force that the vehicle can generate. Take-off can occur when the vehicle's g-force exceeds local gravity (expressed as a multiple of g).

The thrust-to-weight ratio of rockets typically greatly exceeds that of airbreathing 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 air temperature, pressure, density, and composition. Depending on the engine or vehicle under consideration, the actual performance will often be affected by buoyancy and local gravitational field strength.

Examples

Aircraft

Vehicle thrust-weight ratio Notes Northrop Grumman B-2 Spirit 0.205Northrop Grumman B-2 Spirit Max take-off weight, full power Airbus A340-300 Enhanced 0.2229 Max take-off weight, full power Airbus A380 0.227 Max take-off weight, full power Boeing 747-8 0.269 Max take-off weight, full power Boeing 777-200ER 0.285 Max take-off weight, full power Boeing 737 MAX 8 0.311 Max take-off weight, full power Airbus A320neo 0.310 Max take-off weight, full power Boeing 757-200 0.341 Max take-off weight, full power (w/Rolls-Royce RB211) Tupolev 154B 0.360 Max take-off weight, full power (w/Kuznetsov NK-8-2) Tupolev Tu-160 0.363 Max take-off weight, full afterburners Concorde 0.372 Max take-off weight, full afterburners Rockwell International B-1 Lancer 0.38 Max take-off weight, full afterburners HESA Kowsar 0.61 With full fuel, afterburners. BAE Hawk 0.65BAE Systems Hawk Lightning F.6 0.702 Max take-off weight, full afterburners Lockheed Martin F-35 A 0.87 With full fuel (1.07 with 50% fuel, 1.19 with 25% fuel) HAL Tejas Mk 1 1.07 With full fuel CAC/PAC JF-17 Thunder 1.07 With full fuel Dassault Rafale 1.028 (1.219 with loaded weight & 50% internal fuel) Version C, 100% fuel Sukhoi Su-30MKM 1.00Sukhoi Su-30MKM#Specifications .28Su-30MKM.29 Loaded weight with 56% internal fuel McDonnell Douglas F-15 1.04 Nominally loaded Mikoyan MiG-29 1.09 Full internal fuel, 4 AAMs Lockheed Martin F-22 General Dynamics F-16 1.096 (1.24 with loaded weight & 50% fuel) Hawker Siddeley Harrier 1.1 VTOL Eurofighter Typhoon 1.15 Interceptor configuration Space Shuttle 1.3 Take-off Simorgh (rocket) 1.83 Space Shuttle 3 Peak

Jet and rocket engines

Engine Mass Thrust, vacuum Thrust-to-weight ratio (kN) (lbf)MD-TJ42 powered sailplane jet engine3.85kg (8.48 lb)0.3578.79.09 RD-0410 nuclear rocket engine 35.2 Pratt & Whitney J58 jet engine(Lockheed SR-71 Blackbird) 150 Rolls-Royce/Snecma Olympus 593turbojet with reheat (Concorde) 169.2 Williams FJ33-5A Williams F107 Pratt & Whitney F119Military Jet Engine Acquisition, RAND, 2002. PBS TJ40-G1NS jet engine RD-0750 rocket engine three-propellant mode RD-0146 rocket engine Rocketdyne RS-25 rocket engine(Space Shuttle Main Engine)SSME RD-180 rocket engine RD-170 rocket engine F-1(Saturn V first stage)Encyclopedia Astronautica: F-1 NK-33 rocket engine SpaceX Raptor 3 rocket engine 2,746 183.6 Merlin 1D rocket engine, full-thrust version 914 205,500 199.5

Fighter aircraft

+ Thrust-to-weight ratios, fuel weights, and weights of different fighter planesSpecifications F-15K F-15C MiG-29K MiG-29B JF-17 J-10 F-35A F-35B F-35C F-22 LCA Mk-1 Engines thrust, maximum (N) 259,420 (2) 208,622 (2) 176,514 (2) 162,805 (2) 84,400 (1) 122,580 (1) 177,484 (1) 177,484 (1) 177,484 (1) 311,376 (2) 84,516 (1) Aircraft mass, empty (kg) 17,010 14,379 12,723 10,900 7,965 09,250 13,290 14,515 15,785 19,673 6,560 Aircraft mass, full fuel (kg) 23,143 20,671 17,963 14,405 11,365 13,044 21,672 20,867 24,403 27,836 9,500 Aircraft mass, max. take-off load (kg) 36,741 30,845 22,400 18,500 13,500 19,277 31,752 27,216 31,752 37,869 13,500 Total fuel mass (kg) 06,133 06,292 05,240 03,505 02,300 03,794 08,382 06,352 08,618 08,163 02,458 T/W ratio, full fuel 1.14 1.03 1.00 1.15 1.07 1.05 0.84 0.87 0.74 1.14 1.07 T/W ratio, max. take-off load 0.72 0.69 0.80 0.89 0.70 0.80 0.57 0.67 0.57 0.84 0.80

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, the T/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.

See also Power-to-weight ratio Factor of safety

Notes

References John P. Fielding. Introduction to Aircraft Design, Cambridge University Press, Daniel P. Raymer (1989). Aircraft Design: A Conceptual Approach, American Institute of Aeronautics and Astronautics, Inc., Washington, DC. George P. Sutton & Oscar Biblarz. Rocket Propulsion Elements, Wiley,

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