Thrust-to-weight ratio
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 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 or changes in gravitational acceleration, for example in orbital or interplanetary contexts.
Calculation
The thrust-to-weight ratio of an engine or vehicle is calculated by dividing its thrust by its weight. The formula is:where:
- is the thrust, in newtons, kilograms-force, or pounds-force,
- is the weight, in newtons, which can also be expressed as the product of:
- * mass, in kilograms or pounds, and
- * gravitational acceleration, e.g., the standard gravitational acceleration on Earth of 9.80665 m/s2.
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. 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:where is propulsive efficiency, 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.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, g.
The thrust-to-weight ratio of a rocket improves as the propellant is burned. With constant thrust, the maximum ratio 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.
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 | 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 |
| Tupolev 154B | 0.360 | Max take-off weight, full power |
| 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 | |
| Lightning F.6 | 0.702 | Max take-off weight, full afterburners |
| Lockheed Martin F-35 A | 0.87 | With full fuel |
| HAL Tejas Mk 1 | 1.07 | With full fuel |
| CAC/PAC JF-17 Thunder | 1.07 | With full fuel |
| Dassault Rafale | 1.028 | Version C, 100% fuel |
| Sukhoi Su-30MKM | 1.00 | 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 | |
| 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 |
Fighter aircraft
| Specifications | 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 | 259,420 | 208,622 | 176,514 | 162,805 | 84,400 | 122,580 | 177,484 | 177,484 | 177,484 | 311,376 | 84,516 |
| Aircraft mass, empty | 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 | 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 | 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 | 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.