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 (propellant) 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 (which reduces mass) or changes in gravitational acceleration, for example in orbital or interplanetary contexts.

Calculation

{| class="wikitable" style="float:right; margin-left:15px;"

|+ Thrust-to-weight from mass (assuming standard gravity)

| || N

| || kg

| TWR || ~

The thrust-to-weight ratio of an engine or vehicle is calculated by dividing its thrust by its weight (not to be confused with mass). The formula is:

<math>\mathrm{TWR} = \frac{T}{W} = \frac{T}{m \cdot g}</math>

where:

<math>T</math> is the thrust, in newtons (N), kilograms-force (kgf), or pounds-force (lbf),
<math>W</math> is the weight, in newtons (N), which can also be expressed as the product of:
mass <math>m</math>, in kilograms (kg) or pounds (lb), and
gravitational acceleration <math>g</math>, e.g., the standard gravitational acceleration on Earth of 9.80665 m/s2.

For valid comparison of the initial thrust-to-weight ratio of two or more engines or vehicles, thrust must be measured under controlled conditions. Because an aircraft's weight can vary considerably, depending on factors such as munition load, fuel load, cargo weight, or even the weight of the pilot, the thrust-to-weight ratio is also variable and even changes during flight operations. There are several standards for determining the weight of an aircraft used to calculate the thrust-to-weight ratio range.

Empty weight – The weight of the aircraft minus fuel, munitions, cargo, and crew.
Combat weight – Primarily for determining the performance capabilities of fighter aircraft, it is the weight of the aircraft with full munitions and missiles, half fuel, and no drop tanks or bombs.
Max takeoff weight – The weight of the aircraft when fully loaded with the maximum fuel and cargo that it can safely takeoff with.

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.

:<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:

:<math>\frac{T}{W} = \frac{550\eta_\mathrm{p{V} \frac{\text{hp{W},</math>

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

The metric formula is:

:<math>\frac{T}{W}=\left(\frac{\eta_\mathrm{p{V}\right)\left(\frac{P}{W}\right).</math>

Rockets

thumb|upright=1.6|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.

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.