# Thrust-to-weight ratio

Last updated

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.

In dimensional analysis, a dimensionless quantity is a quantity to which no physical dimension is assigned, also known as a bare, pure, or scalar quantity or a quantity of dimension one, with a corresponding unit of measurement in the SI of one unit that is not explicitly shown. Dimensionless quantities are widely used in many fields, such as mathematics, physics, chemistry, engineering, and economics. Examples of quantities to which dimensions are regularly assigned are length, time, and speed, which are measured in dimensional units, such as metre, second and metre per second. This is considered to aid intuitive understanding. However, especially in mathematical physics, it is often more convenient to drop the assignment of explicit dimensions and express the quantities without dimensions, e.g., addressing the speed of light simply by the dimensionless number 1.

Thrust is a reaction force described quantitatively by Newton's third law. When a system expels or accelerates mass in one direction, the accelerated mass will cause a force of equal magnitude but opposite direction on that system. The force applied on a surface in a direction perpendicular or normal to the surface is also called thrust. Force, and thus thrust, is measured using the International System of Units (SI) in newtons, and represents the amount needed to accelerate 1 kilogram of mass at the rate of 1 meter per second per second. In mechanical engineering, force orthogonal to the main load is referred to as thrust.

In science and engineering, the weight of an object is related to the amount of force acting on the object, either due to gravity or to a reaction force that holds it in place.

## Contents

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 vehicles initial performance.

A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives.

## Calculation

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 and 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 newton is the International System of Units (SI) derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.

The pound of force or pound-force is a unit of force or weight used in some systems of measurement including English Engineering units and the Foot–pound–second system. Pound-force should not be confused with foot-pound, a unit of energy, or pound-foot, a unit of torque, that may be written as "lbf⋅ft"; nor should these be confused with pound-mass, often simply called pound, which is a unit of mass.

## Aircraft

The thrust-to-weight ratio and wing loading are the two most important parameters in determining the performance of an aircraft. [1] For example, the thrust-to-weight ratio of a combat aircraft is a good indicator of the maneuverability of the aircraft. [2]

In aerodynamics, wing loading is the total weight of an aircraft divided by the area of its wing. The stalling speed of an aircraft in straight, level flight is partly determined by its wing loading. An aircraft with a low wing loading has a larger wing area relative to its mass, as compared to an aircraft with a high wing loading.

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 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. [3]

Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are indicated airspeed ("IAS"), calibrated airspeed ("CAS"), equivalent airspeed ("EAS"), true airspeed ("TAS"), and density airspeed.

The maximum takeoff weight (MTOW) or maximum gross takeoff weight (MGTOW) or maximum takeoff mass (MTOM) of an aircraft is the maximum weight at which the pilot is allowed to attempt to take off, due to structural or other limits. The analogous term for rockets is gross lift-off mass, or GLOW. MTOW is usually specified in units of kilograms or pounds.

In cruising flight, the thrust-to-weight ratio of an aircraft is the inverse of the lift-to-drag ratio because thrust is the opposite of drag, and weight is the opposite of lift. [4] A plane can take off even if the thrust is less than its weight: if the lift to drag ratio is greater than 1, the thrust to weight ratio can be less than 1, i.e. less thrust is needed to lift the plane off the ground than the weight of the plane.

In aerodynamics, the lift-to-drag ratio, or L/D ratio, is the amount of lift generated by a wing or vehicle, divided by the aerodynamic drag it creates by moving through the air. A higher or more favorable L/D ratio is typically one of the major goals in aircraft design; since a particular aircraft's required lift is set by its weight, delivering that lift with lower drag leads directly to better fuel economy in aircraft, climb performance, and glide ratio.

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

### Propeller-driven aircraft

For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows: [5]

${\displaystyle {\frac {T}{W}}=\left({\frac {550\eta _{p}}{V}}\right)\left({\frac {hp}{W}}\right)}$

where ${\displaystyle \eta _{p}\;}$ is propulsive efficiency (typically 0.8), ${\displaystyle hp\;}$ is the engine's shaft horsepower, and ${\displaystyle V\;}$is true airspeed in feet per second.

## 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. [6]

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 [7] and is sometimes called Thrust-to-Earth-weight ratio. [8] 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. [6]

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. [6] 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.

## Examples

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.[ citation needed ] 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)

${\displaystyle {\frac {T}{W}}={\frac {3,820\ \mathrm {kN} }{(5,307\ \mathrm {kg} )(9.807\ \mathrm {m/s^{2}} )}}=0.07340\ {\frac {\mathrm {kN} }{\mathrm {N} }}=73.40\ {\frac {\mathrm {N} }{\mathrm {N} }}=73.40}$

### Aircraft

VehicleT/WScenario
Northrop Grumman B-2 Spirit 0.205 [9] Max take-off weight, full power
Airbus A380 0.227Max take-off weight, full power
Boeing 737 MAX 8 0.310Max take-off weight, full power
Airbus A320neo 0.311Max take-off weight, full power
Tupolev Tu-160 0.363Max take-off weight, full afterburners
Concorde 0.372Max take-off weight, full afterburners
Rockwell International B-1 Lancer 0.38Max take-off weight, full afterburners
BAE Hawk 0.65 [10]
Lockheed Martin F-35 0.87 with full fuel (1.07 with 50% fuel)
Dassault Rafale 0.988 [11] Version M, 100% fuel, 2 EM A2A missile, 2 IR A2A missiles
Sukhoi Su-30MKM 1.00 [12] Loaded weight with 56% internal fuel
McDonnell Douglas F-15 1.04 [13] Nominally loaded
Mikoyan MiG-29 1.09 [14] Full internal fuel, 4 AAMs
Lockheed Martin F-22 > 1.09 (1.26 with loaded weight and 50% fuel) [15] Combat load?
General Dynamics F-16 1.096[ citation needed ]
Hawker Siddeley Harrier 1.1[ citation needed ] VTOL
Eurofighter Typhoon 1.15 [16] Interceptor configuration
Space Shuttle 1.5Take-off
Space Shuttle 3Peak (throttled back for astronaut comfort)

### Jet and rocket engines

Jet or rocket engine MassThrust (vacuum) Thrust-to-weight ratio
(kg)(lb)(kN)(lbf)
RD-0410 nuclear rocket engine [17] [18] 2,0004,40035.27,9001.8
J58 jet engine (SR-71 Blackbird) [19] [20] 2,7226,00115034,0005.2
Rolls-Royce/Snecma Olympus 593
turbojet with reheat (Concorde) [21]
3,1757,000169.238,0005.4
Pratt & Whitney F119 [22] 1,8003,9009120,5007.95
RD-0750 rocket engine, three-propellant mode [23] 4,62110,1881,413318,00031.2
RD-0146 rocket engine [24] 2605709822,00038.4
Rocketdyne RS-25 Space Shuttle Main Engine [25] 3,1777,0042,278512,00073.1
RD-180 rocket engine [26] 5,39311,8904,152933,00078.5
RD-170 rocket engine9,75021,5007,8871,773,00082.5
F-1 (Saturn V first stage) [27] 8,39118,4997,740.51,740,10094.1
NK-33 rocket engine [28] 1,2222,6941,638368,000136.7
Merlin 1D rocket engine, full-thrust version [29] 4671,030825185,000180.1

### Fighter aircraft

Table b: Thrust-to-weight ratios, fuel weights, and weights of different fighter planes (in metric units)
In International System F-15K F-15CMiG-29KMiG-29B JF-17 J-10 F-35AF-35BF-35CF-22 LCA Mk-1
Engine(s) thrust maximum (N)259,420 (2)208,622 (2)176,514 (2)162,805 (2)81,402 (1)122,580 (1)177,484 (1)177,484 (1)177,484 (1)311,376 (2)89,800 (1)
Aircraft mass, empty (kg)17,01014,37912,72310,90006,58609,25013,29014,51515,78519,6736,560
Aircraft mass, full fuel (kg)23,14320,67117,96314,40508,88613,04421,67220,86724,40327,8369,500
Aircraft mass, max take-off load (kg)36,74130,84522,40018,50012,70019,27731,75227,21631,75237,86913,300
Total fuel mass (kg)06,13306,29205,24003,50502,30003,79408,38206,35208,61808,16302,458
T/W ratio (full fuel)1.141.031.001.150.930.960.840.870.741.140.96
Table a: Thrust-to-weight ratios, fuel weights, and weights of different fighter planes
Specifications / FightersF-15KF-15CMiG-29KMiG-29BJF-17J-10F-35AF-35BF-35CF-22LCA Mk-1
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)20,200 (1)
Aircraft weight empty (lb)37,50031,70028,05024,03014,52020,39429,30032,00034,800 [30] 43,34014,300
Aircraft weight, full fuel (lb)51,02345,57439,60231,75719,65028,76047,78046,00353,80061,34020,944
Aircraft weight, max take-off load (lb)81,00068,00049,38340,78528,00042,50070,00060,00070,00083,50029,100
Total fuel weight (lb)13,52313,87411,55207,72705,13008,36618,48014,00319,000 [30] 18,00005,419
T/W ratio (full fuel)1.141.031.001.150.930.960.840.870.741.140.96
• Fuel density used in calculations: 0.803 kg/l
• The number inside brackets is the number of engines.
• 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.
• 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 1.10
• 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 1.08

## Related Research Articles

A jet engine is a type of reaction engine discharging a fast-moving jet that generates thrust by jet propulsion. This broad definition includes airbreathing jet engines. In general, jet engines are combustion engines.

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 before use. 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 have been performed by either fully or partially expendable multi-stage rockets.

An ion thruster or ion drive is a form of electric propulsion used for spacecraft propulsion. It creates thrust by accelerating cations by utilizing electricity. The term refers strictly to gridded electrostatic ion thrusters, and is often incorrectly loosely applied to all electric propulsion systems including electromagnetic plasma thrusters.

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.

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 launch from, or landing on a planet or moon, or 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 reaction mass for forming a high-speed propulsive jet of fluid, usually high-temperature gas. Rocket engines are reaction engines, producing thrust 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 propellant or propellent is a chemical substance used in the production of energy or pressurized gas that is subsequently used to create movement of a fluid or to generate propulsion of a vehicle, projectile, or other object. Common propellants are energetic materials and consist of a fuel like gasoline, jet fuel, rocket fuel, and an oxidizer. Propellants are burned or otherwise decomposed to produce the propellant gas. Other propellants are simply liquids that can readily be vaporized.

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.

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.

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 spaceflight, an orbital maneuver is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far from Earth an orbital maneuver is called a deep-space maneuver (DSM).

The maximal total range is the maximum distance an aircraft can fly between takeoff and landing, as limited by fuel capacity in powered aircraft, or cross-country speed and environmental conditions in unpowered aircraft. The range can be seen as the cross-country ground speed multiplied by the maximum time in the air. The fuel time limit for powered aircraft is fixed by the fuel load and rate of consumption. When all fuel is consumed, the engines stop and the aircraft will lose its propulsion.

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 aircraft and rocket design, overall propulsive efficiency is the efficiency with which the energy contained in a vehicle's propellant is converted into kinetic energy of the vehicle, to accelerate it, or to replace losses due to aerodynamic drag or gravity. It can also be described as the proportion of the mechanical energy actually used to propel the aircraft. It is always less than one, because conservation of momentum requires that the exhaust have some of the kinetic energy, and the propulsive mechanism is never perfectly efficient. Overall propulsive efficiency is greatly dependent on air density and airspeed.

A reaction engine is an engine or motor that produces thrust by expelling reaction mass, in accordance with Newton's third law of motion. This law of motion is most commonly paraphrased as: "For every action force there is an equal, but opposite, reaction force."

In astronautics, a powered flyby, or Oberth maneuver, is a maneuver in which a spacecraft falls into a gravitational well, and then accelerates when its fall reaches maximum 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.

## 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

### Notes

1. Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Section 5.1
2. John P. Fielding, Introduction to Aircraft Design, Section 4.1.1 (p.37)
3. John P. Fielding, Introduction to Aircraft Design, Section 3.1 (p.21)
4. Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equation 5.2
5. Daniel P. Raymer, Aircraft Design: A Conceptual Approach, Equations 3.9 and 5.1
6. 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"
7. 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."
8. "Thrust-to-Earth-weight ratio". The Internet Encyclopedia of Science. Archived from the original on 2008-03-20. Retrieved 2009-02-22.
9. "AviationsMilitaires.net — Dassault Rafale C". www.aviationsmilitaires.net. Archived from the original on 25 February 2014. Retrieved 30 April 2018.
10. "F-15 Eagle Aircraft". About.com:Inventors. Retrieved 2009-03-03.
11. Pike, John. "MiG-29 FULCRUM". www.globalsecurity.org. Archived from the original on 19 August 2017. Retrieved 30 April 2018.
12. "AviationsMilitaires.net — Lockheed-Martin F-22 Raptor". www.aviationsmilitaires.net. Archived from the original on 25 February 2014. Retrieved 30 April 2018.
13. "Eurofighter Typhoon". eurofighter.airpower.at. Archived from the original on 9 November 2016. Retrieved 30 April 2018.
14. Wade, Mark. "RD-0410". Encyclopedia Astronautica . Retrieved 2009-09-25.
15. "Aircraft: Lockheed SR-71A Blackbird". Archived from the original on 2012-07-29. Retrieved 2010-04-16.
16. "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.
17. "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
18. Military Jet Engine Acquisition, RAND, 2002.
19. "«Konstruktorskoe Buro Khimavtomatiky» - Scientific-Research Complex / RD0750". KBKhA - Chemical Automatics Design Bureau . Retrieved 2009-09-25.
20. Wade, Mark. "RD-0146". Encyclopedia Astronautica . Retrieved 2009-09-25.
21. "RD-180" . Retrieved 2009-09-25.
22. Mueller, Thomas (June 8, 2015). "Is SpaceX's Merlin 1D's thrust-to-weight ratio of 150+ believable?" . 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.
23. "Lockheed Martin Website". Archived from the original on 2008-04-04.