Power-to-weight ratio (PWR, also called specific power, or power-to-mass ratio) is a calculation commonly applied to engines and mobile power sources to enable the comparison of one unit or design to another. Power-to-weight ratio is a measurement of the actual performance of any engine or power source. It is also used as a measurement of the performance of a vehicle as a whole, with the engine's power output being divided by the weight (or mass) of the vehicle, to give a metric that is independent of the vehicle's size. Manufacturers often quote power-to-weight at its peak value, but the actual value may vary in use, and these variations can affect performance.
The inverse of power-to-weight, the weight-to-power ratio (power loading), is a calculation commonly applied to aircraft, cars, and other vehicles to enable comparison of one vehicle's performance to another. Power-to-weight ratio is equal to thrust per unit mass multiplied by the velocity of any vehicle.
Power-to-weight (specific power) The power-to-weight ratio (specific power) is defined as the power generated by the engine(s) divided by the mass. In this context, the term "weight" is a misnomer, as it colloquially refers to mass. In a zero-gravity (weightless) environment, the power-to-weight ratio would not be considered infinite.
A typical turbocharged V8 diesel engine might have an engine power of and a mass of , giving it a power-to-weight ratio of 0.65 kW/kg (0.40 hp/lb).
Examples of high power-to-weight ratios can often be found in turbines. This is because of their ability to operate at very high speeds. For example, the Space Shuttle's main engines used turbopumps (machines consisting of a pump driven by a turbine engine) to feed the propellants (liquid oxygen and liquid hydrogen) into the engine's combustion chamber. The original liquid hydrogen turbopump is similar in size to an automobile engine (weighing approximately ) and produces for a power-to-weight ratio of 153 kW/kg (93 hp/lb).
Physical interpretation In classical mechanics, instantaneous power is the limiting value of the average work done per unit time as the time interval Δt approaches zero (i.e., the derivative with respect to time of the work done).
The typically used metric unit of the power-to-weight ratio is which equals . This fact allows one to express the power-to-weight ratio purely by SI base units. A vehicle's power-to-weight ratio equals its acceleration times its velocity; so at twice the velocity, it experiences half the acceleration, all else being equal.
Propulsive power If the work to be done is rectilinear motion of a body with constant mass , whose center of mass is to be accelerated along a (possibly non-straight) line to a speed and angle with respect to the centre and radial of a gravitational field by an onboard powerplant, then the associated kinetic energy is
where: is mass of the body is speed of the center of mass of the body, changing with time.
The work–energy principle states that the work done to the object over a period of time is equal to the difference in its total energy over that period of time, so the rate at which work is done is equal to the rate of change of the kinetic energy (in the absence of potential energy changes).
The work done from time t to time t + Δt along the path C is defined as the line integral , so the fundamental theorem of calculus has that power is given by .
where: is acceleration of the center of mass of the body, changing with time. is linear force – or thrust – applied upon the center of mass of the body, changing with time. is velocity of the center of mass of the body, changing with time. is torque applied upon the center of mass of the body, changing with time. is angular velocity of the center of mass of the body, changing with time.
In propulsion, power is only delivered if the powerplant is in motion, and is transmitted to cause the body to be in motion. It is typically assumed here that mechanical transmission enables the power plant to operate at peak power output. This assumption allows engine tuning to trade power band width and engine mass for transmission complexity and mass. Electric motors do not suffer from this tradeoff, instead trading their high torque for traction at low speed. The power advantage or power-to-weight ratio is then
where: is linear speed of the center of mass of the body.
Engine power The useful power of an engine with shaft power output can be calculated using a dynamometer to measure torque and rotational speed, with maximum power reached when torque multiplied by rotational speed is a maximum. For jet engines, the useful power is equal to the flight speed of the aircraft multiplied by the force, known as net thrust, required to make it go at that speed. It is used when calculating propulsive efficiency.
Examples
Engines
Heat engines and heat pumps Thermal energy is made up from molecular kinetic energy and latent phase energy. Heat engines can convert thermal energy in the form of a temperature gradient between a hot source and a cold sink into other desirable mechanical work. Heat pumps take mechanical work to regenerate thermal energy in a temperature gradient. Standard definitions should be used when interpreting the transfer of a jet or rocket engine's propulsive power to its vehicle. Heat engine/Heat pump typePeak power outputPower-to-weight ratioExample useSIEnglishSIEnglish Wärtsilä RTA96-C 14-cylinder two-stroke diesel engine 0.03 kW/kg 0.02 hp/lb Emma Mærsk container ship ROTAX 900 ACE 60 900 cc, 3-cylinder, 4-stroke, naturally-aspirated marine engine 45 kW 0.24 kW/kg 0.15 hp/lb Sea-Doo SPARK 2 UP 2021 Suzuki 538 cc V-2 four-stroke petrol outboard motor 19 kW 0.27 kW/kg 0.16 hp/lb Runabout boats DOE/NASA/0032-28 Mod 2 502 cc petrol Stirling engine 62.3 kW 0.30 kW/kg 0.18 hp/lb Chevrolet Celebrity 1985 ('one-off' prototype) Yamaha TR-1 3-cylinder, 4-stroke, marine engine, 1049 cc 74.5 kW 0.44 kW/kg 0.27 hp/lb Yamaha SuperJet 2021 Kawasaki 1498 cc supercharged, intercooled, 4-stroke, 4-cylinder, DOHC 231 kW 0.47 kW/kg 0.29 hp/lb Kawasaki ULTRA 310LX Jet Ski GM Duramax LMM V-8 6.6 L turbo-diesel 246 kW 0.65 kW/kg 0.40 hp/lb Chevrolet Kodiak, GMC Topkick Junkers Jumo 205A two-stroke, diesel, opposed-piston engineJane's 1989, p. 294. 647 kW 1.1 kW/kg 0.66 hp/lb Ju 86C-1 airliner, B&V Ha 139 floatplane GE LM2500+ marine turboshaft 30,200 kW 1.31 kW/kg 0.80 hp/lb GTS Millennium cruise ship, QM2 ocean liner Mazda 13B-MSP Renesis 1.3 L Wankel engine 184 kW 1.5 kW/kg 0.92 hp/lb Mazda RX-8 PW R-4360 71.5 L 28-cylinder Radial engine (supercharged) 3,210 kW 1.83 kW/kg 1.11 hp/lb B-50, B-36, C-97, C-119, H-4 Wright R-3350 54.57 L 18-Cylinder Turbo-compound radial engine 2,535 kW 2.09 kW/kg 1.27 hp/lb B-29, DC-7 O.S. Engines 49-PI Type II 4.97 cc Wankel engine 0.934 kW 2.8 kW/kg 1.7 hp/lb UAV, Model aircraft, RC Aircraft Aston Martin-Cosworth RA V-12 6.5 L N/A 746 kW 3.62 kW/kg 2.20 hp/lb Aston Martin Valkyrie, sports car JetCat SPT10-RX-H turboshaft engine 9 kW 3.67 kW/kg 2.24 hp/lb UAV Model aircraft, RC Aircraft GE LM6000 marine turboshaft engine 44,700 kW 5.67 kW/kg 3.38 hp/lb Peaking power plant BMW V-10 3 L P84/5 2005 petrol engine N/A 708 kW 7.96 kW/kg 4.84 hp/lb Williams FW27 car, Formula One auto racing BMW I-4 1.49 L M12 1986 turbo engine 1030 kW 8.93 kW/kg 5.43 hp/lb Arrows A9 car, Formula One auto racing Rolls-Royce T406/AE1107C turboshaft engine 4,586 kW 6,150 hp kW/kg hp/lb V-22 Top Fuel supercharged V-8 (nitromethane) engine8203 kW11,000 hp36.46 kW/kg22.2 hp/lbU.S. Army Top Fuel Dragster PWR RS-24 (SSME) Block I H2 turbopump 53,690 kW 153 kW/kg 93 hp/lb Space Shuttle
Electric motors and electromotive generators An electric motor uses electrical energy to provide mechanical work, usually through the interaction of a magnetic field and current-carrying conductors. By the interaction of mechanical work on an electrical conductor in a magnetic field, electrical energy can be generated. Electric motor typeWeightPeak power outputPower-to-weight ratioExample use SI English SI EnglishkW/kghp/lb Kawak 4 kW 28 VDC brushless DC motor 0.29 kW/kg 0.18 hp/lb Flight-rated motor for aircraft auxiliary systems (fuel pumps, etc.) Panasonic MSMA202S1G AC servo motor 0.31 kW/kg 0.19 hp/lb Conveyor belts, robotics Kawak 7.5 kW 208 VAC 400 Hz 3-phase synchronous motor 0.47 kW/kg 0.29 hp/lb Flight-rated motor for aircraft auxiliary systems (fuel pumps, etc.) Toshiba 660 MVA water cooled 23 kV AC turbo generator 0.49 kW/kg 0.30 hp/lb Bayswater, Eraring coal-fired power stations Canopy Tech. Cypress 32 MW 15 kV AC PM generator 0.95 kW/kg 0.58 hp/lb Electric power stations Turncircles AF24PM–S axial flux motor 1.34 kW/kg 0.52 hp/lb Electric aircraft Toyota brushless AC NdFeB PM motor 1.37 kW/kg 0.84 hp/lb Toyota Prius 2004 Himax HC6332-250 brushless DC motor 3.78 kW/kg 2.30 hp/lb Radio-controlled cars Hi-Pa Drive HPD40 brushless DC wheel hub motor 4.8 kW/kg 2.92 hp/lb Mini QED HEV, Ford F150 HEV ElectriFly GPMG4805 brushless DC 5.68 kW/kg 3.45 hp/lbRadio-controlled aircraft Rolls-Royce SP260D-A brushless DC 5.9 kW/kg 3.6 hp/lbElectric aircraftTesla Model 3 6.26 kW/kg 3.82 hp/lbElectric Vehicle YASA-400 brushless AC 6.875 kW/kg 4.18 hp/lbElectric vehicles, Drive eOPorsche Taycan 7.5 kW/kg 4.55 hp/lbElectric Vehicle ElectriFly GPMG5220 brushless DC motor 7.78 kW/kg 4.73 hp/lbRadio-controlled aircraft Remy HVH250-090-POC3 brushless DC motor 8.87 kW/kg 5.39 hp/lbElectric vehicles TP POWER TP100XL brushless DC motor 9.0 kW/kg 5.5 hp/lbElectric vehicles MAD V118 IPE V2.0 UAV Emrax 268 brushless AC motor 11.56 kW/kg 7.03 hp/lbElectric aircraftLucid Motors brushless DC motor 15.8 kW/kg 9.68 hp/lbElectric vehicleH3X HPDM-250, direct drive 19.23 kW/kg 11.70 hp/lbElectric aircrafteHelix SPM177-165, direct drive 25.29 kW/kg 15.38 hp/lbElectric vehicle
Fluid engines and fluid pumps Fluids (liquid and gas) can be used to transmit and/or store energy using pressure and other fluid properties. Hydraulic (liquid) and pneumatic (gas) engines convert fluid pressure into other desirable mechanical or electrical work. Fluid pumps convert mechanical or electrical work into movement or pressure changes of a fluid, or storage in a pressure vessel. Fluid powerplant typeDry weightPeak power outputPower-to-weight ratioExample use SI English SI English SI English PlatypusPower Q2/200 hydroelectric turbine 43 kg 95 lb 2 kW 2.7 hp 0.047 kW/kg 0.029 hp/lb PlatypusPower PP20/200 hydroelectric turbine 330 kg 728 lb 20 kW 27 hp 0.060 kW/kg 0.037 hp/lb Atlas Copco LZL 35 pneumatic motor 20 kg 44.1 lb 6.5 kW 8.7 hp 0.33 kW/kg 0.20 hp/lb Atlas Copco LZB 14 pneumatic motor 0.30 kg 0.66 lb 0.16 kW 0.22 hp 0.53 kW/kg 0.33 hp/lb Bosch 0 607 954 307 pneumatic motor 0.32 kg 0.71 lb 0.1 kW 0.13 hp 0.31 kW/kg 0.19 hp/lb Atlas Copco LZB 46 pneumatic motor 1.2 kg 2.65 lb 0.84 kW 1.13 hp 0.7 kW/kg 0.43 hp/lb Bosch 0 607 957 307 pneumatic motor 1.7 kg 3.7 lb 0.74 kW 0.99 hp 0.44 kW/kg 0.26 hp/lb SAI GM7 radial piston hydraulic motor 300 kg 661 lb 250 kW 335 hp 0.83 kW/kg 0.50 hp/lb SAI GM3 radial piston hydraulic motor 15 kg 33 lb 15 kW 20 hp 1 kW/kg 0.61 hp/lb Denison GOLD CUP P14 axial piston hydraulic motor 110 kg 250 lb 384 kW 509 hp 3.5 kW/kg 2.0 hp/lb Denison TB vane pump 7 kg 15 lb 40.2 kW 53.9 hp 5.7 kW/kg 3.6 hp/lbRexroth A2FM 16cc/rev, bent axis hydraulic motor (continuous output)5.4 kg11.9 lb81.8 kW109.7 hp15.1 kW/kg9.21 hp/lbConcrete mixers, combine harvesters Hydroleduc M18, bent axis hydraulic motor (continuous output)5.5 kg12.1 lb92 kW123 hp16.7 kW/kg10.2 hp/lbVehicle transmissions, forestry equipment
Thermoelectric generators and electrothermal actuators A variety of effects can be harnessed to produce thermoelectricity, thermionic emission, pyroelectricity and piezoelectricity. The Electrical resistance and ferromagnetism of materials can be harnessed to convert electrical current into thermoacoustic energy.