Thrust-to-weight Ratio
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Thrust-to-weight ratio is a
dimensionless A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
ratio of
thrust 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 to be applied to that syst ...
to
weight In science and engineering, the weight of an object is the force acting on the object due to gravity. Some standard textbooks define weight as a Euclidean vector, vector quantity, the gravitational force acting on the object. Others define weigh ...
of a
rocket A rocket (from it, rocchetto, , bobbin/spool) is a vehicle that uses jet propulsion to accelerate without using the surrounding air. A rocket engine produces thrust by reaction to exhaust expelled at high speed. Rocket engines work entirely fr ...
,
jet engine A jet engine is a type of reaction engine discharging a fast-moving jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition can include rocket, Pump-jet, water jet, and hybrid propulsion, the term ...
,
propeller A propeller (colloquially often called a screw if on a ship or an airscrew if on an aircraft) is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral which, when rotated, exerts linear thrust upon ...
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 A propellant (or propellent) is a mass that is expelled or expanded in such a way as to create a thrust or other motive force in accordance with Newton's third law of motion, and "propel" a vehicle, projectile, or fluid payload. In vehicles, the e ...
and in some cases a
gravity gradient Gravity gradiometry is the study and measurement of variations ( anomalies) in the Earth's gravity field. The gravity gradient tensor is the spatial rate of change of gravitational acceleration; as acceleration is a vector quantity, with magnit ...
. The thrust-to-weight ratio based on initial thrust and weight is often published and used as a
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. Examples *Clock rate of a CPU * Calories per serving *Contrast ratio of an LCD *Frequency response of a speaker * ...
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. Note that the thrust can also be measured in
pound-force The pound of force or pound-force (symbol: lbf, sometimes lbf,) is a unit of force used in some systems of measurement, including English Engineering units and the foot–pound–second system. Pound-force should not be confused with pound-ma ...
(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.


Electric vehicles


Aircraft

The thrust-to-weight ratio and
wing loading In aerodynamics, wing loading is the total mass of an aircraft or flying animal 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 or animal with a ...
are the two most important parameters in determining the performance of an aircraft. For example, the thrust-to-weight ratio of a
combat aircraft A military aircraft is any fixed-wing or rotary-wing aircraft that is operated by a legal or insurrectionary armed service of any type. Military aircraft can be either combat or non-combat: * Combat aircraft are designed to destroy enemy equi ...
is a good indicator of the maneuverability of the aircraft. The thrust-to-weight ratio varies continually during a flight. Thrust varies with throttle setting,
airspeed In aviation, airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: * Indicated airspeed ("IAS"), what is read on an airspeed gauge connected to a Pitot-static system; * Calibrated ...
,
altitude Altitude or height (also sometimes known as depth) is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The exact definition and reference datum varies according to the context ...
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 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 ...
. Aircraft with thrust-to-weight ratio greater than 1:1 can pitch straight up and maintain airspeed until performance decreases at higher altitude. In cruising flight, the thrust-to-weight ratio of an aircraft is the inverse of the
lift-to-drag ratio In aerodynamics, the lift-to-drag ratio (or L/D ratio) is the lift generated by an aerodynamic body such as an aerofoil or aircraft, divided by the aerodynamic drag caused by moving through air. It describes the aerodynamic efficiency under gi ...
because thrust is the opposite of drag, and weight is the opposite of lift. 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. :\left(\frac\right)_\text = \left(\frac\right)_\text = \frac


Propeller-driven aircraft

For propeller-driven aircraft, the thrust-to-weight ratio can be calculated as follows: :\frac = \frac \frac where \eta_p\; is
propulsive efficiency In aerospace engineering, concerning aircraft, rocket and spacecraft design, overall propulsion system efficiency \eta is the efficiency with which the energy contained in a vehicle's fuel is converted into kinetic energy of the vehicle, to accelera ...
(typically 0.8), hp\; is the engine's
shaft horsepower Horsepower (hp) is a unit of measurement of power, or the rate at which work is done, usually in reference to the output of engines or motors. There are many different standards and types of horsepower. Two common definitions used today are the ...
, and V\;is
true airspeed The true airspeed (TAS; also KTAS, for ''knots true airspeed'') of an aircraft is the speed of the aircraft relative to the air mass through which it is flying. The true airspeed is important information for accurate navigation of an aircraft. Tr ...
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.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" 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, g0. 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 Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of Earth's surfa ...
using thrust and no
aerodynamic lift A fluid flowing around an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direc ...
, 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 The gravitational force equivalent, or, more commonly, g-force, is a measurement of the type of force per unit mass – typically acceleration – that causes a perception of weight, with a g-force of 1 g (not gram in mass measure ...
'' that the vehicle can generate. 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 engine An airbreathing jet engine (or ''ducted jet engine'') is a jet engine that ejects a propelling (reaction) jet of hot exhaust gases after first taking in atmospheric air, followed by compression, heating and expansion back to atmospheric pressure ...
s 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 flight with the variations in thrust due to speed and altitude, together with changed in weight due to the amount of remaining propellant, and payload mass. Factors with the greatest effect include freestream air
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measured with a thermometer. Thermometers are calibrated in various temperature scales that historically have relied o ...
,
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
,
density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
, and composition. Depending on the engine or vehicle under consideration, the actual performance will often be affected by
buoyancy Buoyancy (), or upthrust, is an upward force exerted by a fluid that opposes the weight of a partially or fully immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the p ...
and local
gravitational field strength The gravitational constant (also known as the universal gravitational constant, the Newtonian constant of gravitation, or the Cavendish gravitational constant), denoted by the capital letter , is an empirical physical constant involved in th ...
.


Examples


Aircraft


Jet and rocket engines


Fighter aircraft

* 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 In engineering, a factor of safety (FoS), also known as (and used interchangeably with) safety factor (SF), expresses how much stronger a system is than it needs to be for an intended load. Safety factors are often calculated using detailed analy ...


Notes


References

* John P. Fielding. ''Introduction to Aircraft Design'', Cambridge University Press, * Daniel P. Raymer (1989). ''Aircraft Design: A Conceptual Approach'', American Institute of Aeronautics and Astronautics, Inc., Washington, DC. * George P. Sutton & Oscar Biblarz. ''Rocket Propulsion Elements'', Wiley,


External links


NASA webpage with overview and explanatory diagram of aircraft thrust to weight ratio
{{DEFAULTSORT:Thrust-To-Weight Ratio Jet engines Rocket engines Engineering ratios