Thrust-to-weight ratio

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 is an indicator of 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 a vehicle's initial performance.

Calculation

The thrust-to-weight ratio is calculated by dividing the thrust (in SI units – in newtons) by the weight (in newtons) of the engine or vehicle. The weight (N) is calculated by multiplying the mass in kilograms (kg) by the acceleration due to gravity (m/s^2). Note that the thrust can also be measured in pound-force (lbf), provided the weight is measured in pounds (lb). Division using these two values still gives the numerically correct (dimensionless) 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.

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.<ref>John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21)</ref> Aircraft with thrust-to-weight ratio greater than 1:1 can pitch straight up and maintain airspeed until performance decreases at higher altitude.<ref name="thedrive20160509">Nickell, Paul; Rogoway, Tyler (2016-05-09). "What it's Like to Fly the F-16N Viper, Topgun's Legendary Hotrod". The Drive. Archived from the original on 2019-10-31. Retrieved 2019-10-31.</ref>

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.

<math>\left(\frac{T}{W}\right)_\text{cruise} = \left(\frac{D}{L}\right)_\text{cruise} = \frac{1}{\left(\frac{L}{D}\right)_\text{cruise}}</math>

Propeller-driven aircraft

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

<math>\frac{T}{W} = \frac{550\eta_p}{V} \frac{\text{hp}}{\text{W}}</math>

where <math>\eta_p\;</math> is propulsive efficiency (typically 0.65 for wooden props, 0.75 metal fixed pitch and up to 0.85 for constant speed props), <math>hp\;</math> is the engine's shaft horsepower, and <math>V\;</math>is true airspeed in feet per second, weight is in lbs.

For metric formula look below:

<math>\frac{T}{W}=\left(\frac{\eta_p}{V}\right)\left(\frac{P}{W}\right)</math>

Rockets

Rocket vehicle Thrust-to-weight ratio vs specific impulse for different propellant technologies

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.<ref name="sutton">George P. Sutton & Oscar Biblarz, Rocket Propulsion Elements (p. 442, 7th edition) "thrust-to-weight ratio F/W_g 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"</ref>

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<ref>George P. Sutton & Oscar Biblarz, Rocket Propulsion Elements (p. 442, 7th edition) "The loaded weight W_g is the sea-level initial gross weight of propellant and rocket propulsion system hardware."</ref> and is sometimes called Thrust-to-Earth-weight ratio.<ref>"Thrust-to-Earth-weight ratio". The Internet Encyclopedia of Science. Archived from the original on 2008-03-20. Retrieved 2009-02-22.</ref> 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.<ref name="sutton"/>

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.<ref name="sutton"/> 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 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	0.205<ref>Northrop Grumman B-2 Spirit</ref>	Max take-off weight, full power
Airbus A340	0.2229	Max take-off weight, full power (A340-300 Enhanced)
Airbus A380	0.227	Max take-off weight, full power
Boeing 747-8	0.269	Max take-off weight, full power
Boeing 777	0.285	Max take-off weight, full power (777-200ER)
Boeing 737 MAX 8	0.310	Max take-off weight, full power
Airbus A320neo	0.311	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/Kuznecov NK-82)
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	0.65<ref>BAE Systems Hawk</ref>
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	0.988<ref>"AviationsMilitaires.net — Dassault Rafale C". www.aviationsmilitaires.net. Archived from the original on 25 February 2014. Retrieved 30 April 2018.</ref>	Version M, 100% fuel, 2 EM A2A missile, 2 IR A2A missiles
Sukhoi Su-30MKM	1.00<ref name="Wikipedia">Sukhoi Su-30MKM#Specifications .28Su-30MKM.29</ref>	Loaded weight with 56% internal fuel
McDonnell Douglas F-15	1.04<ref>"F-15 Eagle Aircraft". About.com:Inventors. Archived from the original on July 9, 2012. Retrieved 2009-03-03.</ref>	Nominally loaded
Mikoyan MiG-29	1.09<ref name=militaire>Pike, John. "MiG-29 FULCRUM". www.globalsecurity.org. Archived from the original on 19 August 2017. Retrieved 30 April 2018.</ref>	Full internal fuel, 4 AAMs
Lockheed Martin F-22	1.09
General Dynamics F-16	1.096
Hawker Siddeley Harrier	1.1	VTOL
Eurofighter Typhoon	1.15<ref>"Eurofighter Typhoon". eurofighter.airpower.at. Archived from the original on 9 November 2016. Retrieved 30 April 2018.</ref>	Interceptor configuration
Space Shuttle	1.5Template:Source needed	Take-off
Simorgh (rocket)	1.83
Space Shuttle	3	Peak

Jet and rocket engines

Engine	Mass	Thrust, vacuum		Thrust-to- weight ratio
		(kN)	(lbf)
RD-0410 nuclear rocket engine<ref name="astronautix1">Wade, Mark. "RD-0410". Encyclopedia Astronautica. Retrieved 2009-09-25.</ref><ref name="KBKhA-RD0410">РД0410. Ядерный ракетный двигатель. Перспективные космические аппараты [RD0410. Nuclear Rocket Engine. Advanced launch vehicles] (in русский). KBKhA - Chemical Automatics Design Bureau. Archived from the original on 30 November 2010.</ref>	2,000 kg (4,400 lb)	35.2	7,900	1.8
Pratt & Whitney J58 jet engine (Lockheed SR-71 Blackbird)<ref>"Aircraft: Lockheed SR-71A Blackbird". Archived from the original on 2012-07-29. Retrieved 2010-04-16.</ref><ref>"Factsheets : Pratt & Whitney J58 Turbojet". National Museum of the United States Air Force. Archived from the original on 2015-04-04. Retrieved 2010-04-15.</ref>	2,722 kg (6,001 lb)	150	34,000	5.6
Rolls-Royce/Snecma Olympus 593 turbojet with reheat (Concorde)<ref>"Rolls-Royce SNECMA Olympus - Jane's Transport News". Archived from the original on 2010-08-06. Retrieved 2009-09-25. With afterburner, reverser and nozzle ... 3,175 kg ... Afterburner ... 169.2 kN</ref>	3,175 kg (7,000 lb)	169.2	38,000	5.4
Pratt & Whitney F119<ref>Military Jet Engine Acquisition, RAND, 2002.</ref>	1,800 kg (4,000 lb)	91	20,500	7.95
RD-0750 rocket engine three-propellant mode<ref name="KBKhA-RD0750">"Конструкторское бюро химавтоматики" - Научно-исследовательский комплекс / РД0750. [«Konstruktorskoe Buro Khimavtomatiky» - Scientific-Research Complex / RD0750.]. KBKhA - Chemical Automatics Design Bureau. Archived from the original on 26 July 2011.</ref>	4,621 kg (10,188 lb)	1,413	318,000	31.2
RD-0146 rocket engine<ref name="astronautix2">Wade, Mark. "RD-0146". Encyclopedia Astronautica. Retrieved 2009-09-25.</ref>	260 kg (570 lb)	98	22,000	38.4
Rocketdyne RS-25 rocket engine (Space Shuttle Main Engine)<ref>SSME</ref>	3,177 kg (7,004 lb)	2,278	512,000	73.1
RD-180 rocket engine<ref>"RD-180". Retrieved 2009-09-25.</ref>	5,393 kg (11,890 lb)	4,152		78.7
RD-170 rocket engine	9,750 kg (21,500 lb)	7,887	1,773,000	82.5
F-1 (Saturn V first stage)<ref>Encyclopedia Astronautica: F-1</ref>	8,391 kg (18,499 lb)	7,740.5	1,740,100	94.1
NK-33 rocket engine<ref name="NK33">Wade, Mark. "NK-33". Encyclopedia Astronautica. Retrieved 2022-08-24.</ref>	1,222 kg (2,694 lb)	1,638	368,000	136.7
SpaceX Raptor 2 rocket engine<ref>Sesnic, Trevor (2022-07-14). "Raptor 1 vs Raptor 2: What did SpaceX change?". Everyday Astronaut. Retrieved 2022-11-07.</ref>	1,600 kg (3,500 lb)	2,256	507,000	143.8
Merlin 1D rocket engine, full-thrust version<ref name="Merlin 1D">Mueller, Thomas (June 8, 2015). "Is SpaceX's Merlin 1D's thrust-to-weight ratio of 150+ believable?". Quora. Retrieved July 9, 2015. The Merlin 1D weighs 1030 pounds, including the hydraulic steering (TVC) actuators. It makes 162,500 pounds of thrust in vacuum. that is nearly 158 thrust/weight. The new full thrust variant weighs the same and makes about 185,500 lbs force in vacuum.</ref><ref>"SpaceX". SpaceX. Retrieved 2022-11-07.</ref>	467 kg (1,030 lb)	914	205,500	199.5

Fighter aircraft

Thrust-to-weight ratios, fuel weights, and weights of different fighter planes

Specifications	F-15K<ref group="lower-alpha"> Pratt & Whitney engines</ref>	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

References

• 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

External links

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