Thrust-to-weight ratio
Encyclopedia
Thrust-to-weight ratio is a ratio of thrust
to weight
of a rocket
, jet engine
, propeller
engine, or a vehicle propelled by such an engine. It is a dimensionless quantity
and 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 due to 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.
For valid comparison of the initial thrust-to-weight ratio of two or more engines or vehicles, thrust must be measured under controlled conditions.
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.
In cruising flight, the thrust-to-weight ratio of an aircraft is the inverse of the lift-to-drag ratio
because thrust is equal to drag, and weight is equal to lift.
where
is propulsive efficiency
at true airspeed
is engine power
Rockets and rocket-propelled vehicles operate in a wide range of gravitational environments, including the weightless environment. It is customary to calculate the thrust-to-weight ratio using initial gross weight at sea-level on earth. This 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.
It is important to note that the thrust-to-weight ratio for a rocket varies as the propellant gets utilized. If the thrust is constant, then the maximum ratio (maximum acceleration of the vehicle) is achieved just before the propellant is fully consumed (propellant weight is practically zero at this point). So for each rocket there a characteristic thrust-to-weight curve or acceleration curve, not just a scalar quantity.
The thrust-to-weight ratio of an engine is larger for the bare engine than for the whole launch vehicle. The thrust-to-weight ratio of a bare engine is of use since 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 has to be more than one. In general, the thrust-to-weight ratio is numerically equal to the g-force
that the vehicle can generate. Provided the vehicle's g-force exceeds local gravity (expressed as a multiple of g0) then takeoff can occur.
The thrust to weight ratio of rockets is typically far higher than that of airbreathing jet engine
s. This is because of the much higher density of the material that is formed into the exhaust, compared to that of air; so far less engineering materials are needed for pressurising it.
Many factors affect a thrust-to-weight ratio, and the instantaneous value typically varies over the flight with the variations of thrust due to speed and altitude, and the weight due to the remaining propellant and payload mass. The main factors that affect thrust 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.
n-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)
Note that the above duct engined aircraft do not have a thrust-to-weight ratio greater than one at maximum take-off weight, whereas rockets do.
Table b: Thrust To Weight Ratios, Fuels Weights, and Weights of Different Fighter Planes (In International System)
Thrust
Thrust is a reaction force described quantitatively by Newton's second and third laws. 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....
to weight
Weight
In science and engineering, the weight of an object is the force on the object due to gravity. Its magnitude , often denoted by an italic letter W, is the product of the mass m of the object and the magnitude of the local gravitational acceleration g; thus:...
of a rocket
Rocket
A rocket is a missile, spacecraft, aircraft or other vehicle which obtains thrust from a rocket engine. In all rockets, the exhaust is formed entirely from propellants carried within the rocket before use. Rocket engines work by action and reaction...
, jet engine
Jet engine
A jet engine is a reaction engine that discharges a fast moving jet to generate thrust by jet propulsion and in accordance with Newton's laws of motion. This broad definition of jet engines includes turbojets, turbofans, rockets, ramjets, pulse jets...
, propeller
Propeller (aircraft)
Aircraft propellers or airscrews convert rotary motion from piston engines or turboprops to provide propulsive force. They may be fixed or variable pitch. Early aircraft propellers were carved by hand from solid or laminated wood with later propellers being constructed from metal...
engine, or a vehicle propelled by such an engine. It is a dimensionless quantity
Dimensionless quantity
In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...
and 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 due to a gravity gradient. The thrust-to-weight ratio based on initial thrust and weight is often published and used as a figure of merit
Figure of merit
A figure of merit is a quantity used to characterize the performance of a device, system or method, relative to its alternatives. In engineering, figures of merit are often defined for particular materials or devices in order to determine their relative utility for an application...
for quantitative comparison of the initial performance of vehicles.
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. It is a dimensionless quantity.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 wing loadingWing loading
In aerodynamics, wing loading is the loaded weight of the aircraft divided by the area of the wing. The faster an aircraft flies, the more lift is produced by each unit area of wing, so a smaller wing can carry the same weight in level flight, operating at a higher wing loading. Correspondingly,...
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
Airspeed
Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: indicated airspeed , calibrated airspeed , true airspeed , equivalent airspeed and density 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.
In cruising flight, the thrust-to-weight ratio of an aircraft is the inverse of the lift-to-drag ratio
Lift-to-drag ratio
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 drag it creates by moving through the air...
because thrust is equal to drag, and weight is equal to lift.
Propeller-driven aircraft
For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows:where
is propulsive efficiencyPropulsive efficiency
In aircraft and rocket design, overall propulsive efficiency \eta is the efficiency, in percent, with which the energy contained in a vehicle's propellant is converted into useful energy, to replace losses due to air drag, gravity, and acceleration. It can also be stated as the proportion of the...
at true airspeed
True airspeed
True airspeed of an aircraft is the speed of the aircraft relative to the airmass in which it is flying. True airspeed is important information for accurate navigation of an aircraft.-Performance:...
is engine powerRockets
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. It is customary to calculate the thrust-to-weight ratio using initial gross weight at sea-level on earth. This 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.
It is important to note that the thrust-to-weight ratio for a rocket varies as the propellant gets utilized. If the thrust is constant, then the maximum ratio (maximum acceleration of the vehicle) is achieved just before the propellant is fully consumed (propellant weight is practically zero at this point). So for each rocket there a characteristic thrust-to-weight curve or acceleration curve, not just a scalar quantity.
The thrust-to-weight ratio of an engine is larger for the bare engine than for the whole launch vehicle. The thrust-to-weight ratio of a bare engine is of use since 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
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
using thrust and no aerodynamic lift, the thrust-to-weight ratio for the whole vehicle has to be more than one. In general, the thrust-to-weight ratio is numerically equal to the g-force
G-force
The g-force associated with an object is its acceleration relative to free-fall. This acceleration experienced by an object is due to the vector sum of non-gravitational forces acting on an object free to move. The accelerations that are not produced by gravity are termed proper accelerations, and...
that the vehicle can generate. Provided the vehicle's g-force exceeds local gravity (expressed as a multiple of g0) then takeoff can occur.
The thrust to weight ratio of rockets is typically far higher than that of airbreathing jet engine
Airbreathing jet engine
An airbreathing jet engine is a jet engine propelled by a jet of hot exhaust gases formed from air that is drawn into the engine via an inlet duct....
s. This is because of the much higher density of the material that is formed into the exhaust, compared to that of air; so far less engineering materials are needed for pressurising it.
Many factors affect a thrust-to-weight ratio, and the instantaneous value typically varies over the flight with the variations of thrust due to speed and altitude, and the weight due to the remaining propellant and payload mass. The main factors that affect thrust include freestream air temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
, pressure
Pressure
Pressure is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.- Definition :...
, density
Density
The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...
, and composition. Depending on the engine or vehicle under consideration, the actual performance will often be affected by buoyancy
Buoyancy
In physics, buoyancy is a force exerted by a fluid that opposes an object's weight. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus a column of fluid, or an object submerged in the fluid, experiences greater pressure at the bottom of the...
and local gravitational field strength.
Examples
The RussiaRussia
Russia or , officially known as both Russia and the Russian Federation , is a country in northern Eurasia. It is a federal semi-presidential republic, comprising 83 federal subjects...
n-made RD-180
RD-180 (rocket engine)
The RD-180 is a Russian dual-combustion chamber, dual-nozzle rocket engine, derived from the RD-170 used in Soviet Zenit rockets, and currently provides first-stage power for American Atlas launch vehicles.-Design and specifications:The combustion chambers of the RD-180 share a single turbopump...
rocket engine (which powers Lockheed Martin
Lockheed Martin
Lockheed Martin is an American global aerospace, defense, security, and advanced technology company with worldwide interests. It was formed by the merger of Lockheed Corporation with Martin Marietta in March 1995. It is headquartered in Bethesda, Maryland, in the Washington Metropolitan Area....
’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)
Aircraft
| Vehicle | T/W | Scenario |
|---|---|---|
| Concorde Concorde Aérospatiale-BAC Concorde was a turbojet-powered supersonic passenger airliner, a supersonic transport . It was a product of an Anglo-French government treaty, combining the manufacturing efforts of Aérospatiale and the British Aircraft Corporation... |
.373 | Max Takeoff Weight, Full Reheat |
| English Electric Lightning English Electric Lightning The English Electric Lightning is a supersonic jet fighter aircraft of the Cold War era, noted for its great speed and unpainted natural metal exterior finish. It is the only all-British Mach 2 fighter aircraft. The aircraft was renowned for its capabilities as an interceptor; Royal Air Force ... |
0.63 | maximum takeoff weight, No Reheat |
| F-22 Raptor F-22 Raptor The Lockheed Martin/Boeing F-22 Raptor is a single-seat, twin-engine fifth-generation supermaneuverable fighter aircraft that uses stealth technology. It was designed primarily as an air superiority fighter, but has additional capabilities that include ground attack, electronic warfare, and signals... |
0.84 | maximum takeoff weight, Dry Thrust |
| Mikoyan MiG-29 Mikoyan MiG-29 The Mikoyan MiG-29 is a fourth-generation jet fighter aircraft designed in the Soviet Union for an air superiority role. Developed in the 1970s by the Mikoyan design bureau, it entered service with the Soviet Air Force in 1983, and remains in use by the Russian Air Force as well as in many other... |
1.1 | |
| F-15 Eagle F-15 Eagle The McDonnell Douglas F-15 Eagle is a twin-engine, all-weather tactical fighter designed by McDonnell Douglas to gain and maintain air superiority in aerial combat. It is considered among the most successful modern fighters with over 100 aerial combat victories with no losses in dogfights... |
1.04 | nominally loaded |
| F-16 Fighting Falcon F-16 Fighting Falcon The General Dynamics F-16 Fighting Falcon is a multirole jet fighter aircraft originally developed by General Dynamics for the United States Air Force . Designed as an air superiority day fighter, it evolved into a successful all-weather multirole aircraft. Over 4,400 aircraft have been built since... |
1.096 | |
| Hawker Siddeley Harrier | 1.1 | |
| Eurofighter Typhoon Eurofighter Typhoon The Eurofighter Typhoon is a twin-engine, canard-delta wing, multirole combat aircraft, designed and built by a consortium of three companies: EADS, Alenia Aeronautica and BAE Systems; working through a holding company, Eurofighter GmbH, which was formed in 1986... |
1.25 | |
| English Electric Lightning | ~1.2 | light weight, full reheat |
| Space Shuttle Space Shuttle The Space Shuttle was a manned orbital rocket and spacecraft system operated by NASA on 135 missions from 1981 to 2011. The system combined rocket launch, orbital spacecraft, and re-entry spaceplane with modular add-ons... |
1.5 | Take-off |
| F-15 Eagle | ~1.6 | light weight, full afterburner |
| F-22 Raptor | 1.61 | light weight, full afterburner |
| Dassault Rafale Dassault Rafale The Dassault Rafale is a French twin-engine delta-wing multi-role jet fighter aircraft designed and built by Dassault Aviation. Introduced in 2000, the Rafale is being produced both for land-based use with the French Air Force and for carrier-based operations with the French Navy... |
1.69 | light weight, full afterburner |
| Space Shuttle | 3 | Peak (throttled back for astronaut comfort) |
Note that the above duct engined aircraft do not have a thrust-to-weight ratio greater than one at maximum take-off weight, whereas rockets do.
Fighter Aircraft
Table a: Thrust To Weight Ratios, Fuels Weights, and Weights of Different Fighter Planes| 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 (Thrust / AC weight full fuel) | 1.14 | 1.03 | 1.00 | 1.15 | 0.93 | 0.96 | 0.84 | 0.87 | 0.74 | 1.14 |
Table b: Thrust To Weight Ratios, Fuels Weights, and Weights of Different Fighter Planes (In International System)
| 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 (Thrust / AC weight 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 Kilograms/Liter
- The Number inside ( ) brackets is the Number of Engine(s).
- Engines powering F-15K are the Pratt & Whitney Engines, not General Electric's.
- 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 & fuel weight is an estimate.
- 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