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 instantaneous thrust-to-weight ratio of a vehicle varies continually during operation due to progressive consumption of fuel or propellant and in some cases a gravity gradient. The thrust-to-weight ratio based on initial thrust and weight is often published and used as a figure of merit for quantitative comparison of the initial performance of vehicles.
The thrust-to-weight ratio can be calculated by dividing the thrust (in SI units – in newtons) by the weight (in newtons) of the engine or vehicle. It is a dimensionless quantity. Note that the thrust can also be measured in pound-force (lbf) provided the weight is measured in pounds (lb); the division of these two values still gives the numerically correct thrust-to-weight ratio. For valid comparison of the initial thrust-to-weight ratio of two or more engines or vehicles, thrust must be measured under controlled conditions.
The thrust-to-weight ratio and wing loading are the two most important parameters in determining the performance of an aircraft. For example, the thrust-to-weight ratio of a combat aircraft is a good indicator of the manoeuvrability of the aircraft.
The thrust-to-weight ratio varies continually during a flight. Thrust varies with throttle setting, airspeed, altitude and air temperature. Weight varies with fuel burn and changes of payload. For aircraft, the quoted thrust-to-weight ratio is often the maximum static thrust at sea-level divided by the maximum takeoff weight.
For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows:
- is engine power
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.
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 earth 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, g0.
The thrust-to-weight ratio for a rocket varies as the propellant is burned. If the thrust is constant, then 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 exceeds that of the whole 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 more 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 g0).
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 a thrust-to-weight ratio. The instantaneous value typically varies over the flight with the variations of thrust due to speed and altitude along with the weight due to the remaining propellant and payload mass. The main factors 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.
The Russian-made RD-180 rocket engine (which powers Lockheed Martin’s Atlas V) produces 3,820 kN of sea-level thrust and has a dry mass of 5,307 kg. Using the Earth surface gravitational field strength of 9.807 m/s², the sea-level thrust-to-weight ratio is computed as follows: (1 kN = 1000 N = 1000 kg⋅m/s²)
|B-2 Spirit||0.205||Max take-off weight|
|Concorde||0.373||Max take-off weight, full reheat|
|Lightning||0.63||Maximum takeoff weight, no reheat|
|Lightning||c. 1.2||on an empty weight basis, full reheat|
|F-22||> 1.09 (1.26 with loaded weight and 50% fuel)||Maximum takeoff weight, dry thrust|
|MiG-29||1.09||Full internal fuel, 4 AAMs|
|Typhoon||1.07||100% fuel, 2 IRIS-T, 4 MBDA Meteor|
|Rafale||0.988||Version M, 100% fuel, 2 EM A2A missile, 2 IR A2A missiles|
|Space Shuttle||3||Peak (throttled back for astronaut comfort)|
Jet and rocket engines
|Jet or Rocket engine||Mass
|RD-0410 nuclear rocket engine||2,000||4,400||35.2||7,900||1.8|
|J58 jet engine (SR-71 Blackbird)||2,722||6,001||150||34,000||5.2|
|Rolls-Royce/Snecma Olympus 593
turbojet with reheat (Concorde)
|Pratt & Whitney F119||1,800||3,900||91||20,500||7.95|
|RD-0750 rocket engine, three-propellant mode||4,621||10,188||1,413||318,000||31.2|
|RD-0146 rocket engine||260||570||98||22,000||38.4|
|SSME rocket engine (Space Shuttle)||3,177||7,004||2,278||512,000||73.1|
|RD-180 rocket engine||5,393||11,890||4,152||933,000||78.5|
|RD-170 rocket engine||9,750||21,500||7,887||1,773,000||82.5|
|F-1 (Saturn V first stage)||8,391||18,499||7,740.5||1,740,100||94.1|
|NK-33 rocket engine||1,222||2,694||1,638||368,000||136.7|
|Merlin 1D rocket engine||440||970||690||160,000||159.9|
Rocket thrusts are vacuum thrusts unless otherwise noted
|Specifications / Fighters||F-15K||F-15C||MiG-29K||MiG-29B||JF-17||J-10||F-35A||F-35B||F-35C||F-22|
|Engine(s) thrust maximum (lbf)||58,320 (2)||46,900 (2)||39,682 (2)||36,600 (2)||18,300 (1)||27,557 (1)||39,900 (1)||39,900 (1)||39,900 (1)||70,000 (2)|
|Aircraft weight empty (lb)||37,500||31,700||28,050||24,030||14,520||20,394||29,300||32,000||34,800||43,340|
|Aircraft weight, full fuel (lb)||51,023||45,574||39,602||31,757||19,650||28,760||47,780||46,003||53,800||61,340|
|Aircraft weight, max take-off load (lb)||81,000||68,000||49,383||40,785||28,000||42,500||70,000||60,000||70,000||83,500|
|Total fuel weight (lb)||13,523||13,874||11,552||07,727||05,130||08,366||18,480||14,003||19,000||18,000|
|T/W ratio (full fuel)||1.14||1.03||1.00||1.15||0.93||0.96||0.84||0.87||0.74||1.14|
|In International System||F-15K||F-15C||MiG-29K||MiG-29B||JF-17||J-10||F-35A||F-35B||F-35C||F-22|
|Engine(s) thrust maximum (kgf)||26,456 (2)||21,274 (2)||18,000 (2)||16,600 (2)||08,300 (1)||12,500 (1)||18,098 (1)||18,098 (1)||18 098 (1)||31,764 (2)|
|Aircraft weight, empty (kg)||17,010||14,379||12,723||10,900||06,586||09,250||13,290||14,515||15,785||19,673|
|Aircraft weight, full fuel (kg)||23,143||20,671||17,963||14,405||08,886||13,044||21,672||20,867||24,403||27,836|
|Aircraft weight, max take-off load (kg)||36,741||30,845||22,400||18,500||12,700||19,277||31,752||27,216||31,752||37,869|
|Total fuel weight (kg)||06,133||06,292||05,240||03,505||02,300||03,794||08,382||06,352||08,618||08,163|
|T/W ratio (full fuel)||1.14||1.03||1.00||1.15||0.93||0.96||0.84||0.87||0.74||1.14|
- Fuel density used in calculations: 0.803 kg/l
- The number inside brackets is the number of engines.
- Engines powering F-15K are the Pratt & Whitney engines.
- MiG-29K's empty weight is an estimate.
- JF-17's engine rating is of RD-93.
- JF-17 if mated with its engine WS-13, and if that engine gets its promised 18,969 lb then the T/W ratio becomes 0.97
- J-10's empty weight and fuelled weight are estimates.
- J-10's engine rating is of AL-31FN.
- J-10 if mated with its engine WS-10A, and if that engine gets its promised 132 KN(29,674 lbf) then the T/W ratio becomes 1.03
- 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
- Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Section 5.1
- John P. Fielding, Introduction to Aircraft Design, Section 4.1.1 (p.37)
- John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21)
- Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.2
- Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.1
- 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 g0) if it could fly by itself in a gravity-free vacuum”
- George 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.”
- "Thrust-to-Earth-weight ratio". The Internet Encyclopedia of Science. Retrieved 2009-02-22.
- Northrop Grumman B-2 Spirit
- Section 9 "The English Electric (BAC) Lightning". Vectorsite. Archived from the original on 2004-02-04. Retrieved 2012-10-12.
- "F-15 Eagle Aircraft". About.com:Inventors. Retrieved 2009-03-03.
- Kampflugzeugvergleichstabelle Mader/Janes
- Thrust: 6.781 million lbf, Weight: 4.5 million lb"Space Shuttle". Wikipedia. Retrieved 2009-09-10.
- Wade, Mark. "RD-0410". Encyclopedia Astronautica. Retrieved 2009-09-25.
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- Aircraft: Lockheed SR-71A Blackbird
- "Factsheets : Pratt & Whitney J58 Turbojet". National Museum of the United States Air Force. Retrieved 2010-04-15.
- "Rolls-Royce SNECMA Olympus - Jane's Transport News". Retrieved 2009-09-25. "With afterburner, reverser and nozzle ... 3,175 kg ... Afterburner ... 169.2 kN"
- Military Jet Engine Acquisition, RAND, 2002.
- "«Konstruktorskoe Buro Khimavtomatiky» - Scientific-Research Complex / RD0750.". KBKhA - Chemical Automatics Design Bureau. Retrieved 2009-09-25.
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- Encyclopedia Astronautica: F-1
- Astronautix NK-33 entry
- "Lockheed Martin Website".