Power-to-weight ratio
![]() | This article may contain excessive or inappropriate references to self-published sources. (May 2021) |
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 actual performance of any engine or power source. It is also used as a measurement of 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. Power-to-weight is often quoted by manufacturers at the peak value, but the actual value may vary in use and variations will affect performance.
The inverse of power-to-weight, weight-to-power ratio (power loading) is a calculation commonly applied to aircraft, cars, and vehicles in general, to enable the 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) formula for an engine (power plant) is the power generated by the engine divided by the mass. Weight in this context is a colloquial term for mass. To see this, note that what an engineer means by the "power to weight ratio" of an electric motor is not infinite in a zero gravity environment.
A typical turbocharged V8 diesel engine might have an engine power of 250 kW (340 hp) and a mass of 380 kg (840 lb),[1] 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 352 kilograms (775 lb)) and produces 72,000 hp (54 MW)[2] 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) 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 allows the powerplant to operate at peak output power. 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 are able to 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 how the propulsive power of a jet or rocket engine is transferred to its vehicle.
Heat Engine/Heat pump type | Peak power output | Power-to-weight ratio | showExample use | ||
---|---|---|---|---|---|
SI | English | SI | English |
- Full vehicle power-to-weight ratio shown below
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 type | Weight | Peak power output | Power-to-weight ratio | showExample use | |||
---|---|---|---|---|---|---|---|
SI | English | SI | English | kW/kg | hp/lb |
- Full vehicle power-to-weight ratio shown below
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 type | Dry weight | Peak power output | Power-to-weight ratio | showExample use | |||
---|---|---|---|---|---|---|---|
SI | English | SI | English | SI | English |
Thermoelectric generators and electrothermal actuators[]
A variety of effects can be harnessed to produce thermoelectricity, thermionic emission, pyroelectricity and piezoelectricity. Electrical resistance and ferromagnetism of materials can be harnessed to generate thermoacoustic energy from an electric current.
Electrochemical (galvanic) and electrostatic cell systems[]
(Closed cell) batteries[]
All electrochemical cell batteries deliver a changing voltage as their chemistry changes from "charged" to "discharged". A nominal output voltage and a cutoff voltage are typically specified for a battery by its manufacturer. The output voltage falls to the cutoff voltage when the battery becomes "discharged". The nominal output voltage is always less than the open-circuit voltage produced when the battery is "charged". The temperature of a battery can affect the power it can deliver, where lower temperatures reduce power. Total energy delivered from a single charge cycle is affected by both the battery temperature and the power it delivers. If the temperature lowers or the power demand increases, the total energy delivered at the point of "discharge" is also reduced.
Battery discharge profiles are often described in terms of a factor of battery capacity. For example, a battery with a nominal capacity quoted in ampere-hours (Ah) at a C/10 rated discharge current (derived in amperes) may safely provide a higher discharge current – and therefore higher power-to-weight ratio – but only with a lower energy capacity. Power-to-weight ratio for batteries is therefore less meaningful without reference to corresponding energy-to-weight ratio and cell temperature. This relationship is known as Peukert's law.[48]
Battery type | Volts | Temp. | Energy-to-weight ratio | showPower-to-weight ratio |
---|
Electrostatic, electrolytic and electrochemical capacitors[]
Capacitors store electric charge onto two electrodes separated by an electric field semi-insulating (dielectric) medium. Electrostatic capacitors feature planar electrodes onto which electric charge accumulates. Electrolytic capacitors use a liquid electrolyte as one of the electrodes and the electric double layer effect upon the surface of the dielectric-electrolyte boundary to increase the amount of charge stored per unit volume. Electric double-layer capacitors extend both electrodes with a nanopourous material such as activated carbon to significantly increase the surface area upon which electric charge can accumulate, reducing the dielectric medium to nanopores and a very thin high permittivity separator.
While capacitors tend not to be as temperature sensitive as batteries, they are significantly capacity constrained and without the strength of chemical bonds suffer from self-discharge. Power-to-weight ratio of capacitors is usually higher than batteries because charge transport units within the cell are smaller (electrons rather than ions), however energy-to-weight ratio is conversely usually lower.
Capacitor type | Capacitance | Voltage | Temp. | Energy-to-weight ratio | Power-to-weight ratio |
---|---|---|---|---|---|
ACT Premlis lithium-ion capacitor[76] | 2000 F | 4.0 V | 25 °C | 54 kJ/kg to 2.0 V | 44.4 W/kg @ 5 A |
31 kJ/kg to 2.0 V | 850 W/kg @ 10 A | ||||
Nesccap Electric double-layer capacitor[77] | 5000 F | 2.7 V | 25 °C | 19.58 kJ/kg to 1.35 V | 5.44 W/kg C/1 (1.875 A) |
5.2 kJ/kg to 1.35 V | 5,200 W/kg[78] @ 2,547 A | ||||
EEStor EESU barium titanate supercapacitor[79] | 30.693 F | 3500 V | 85 °C | 1471.98 kJ/kg | 80.35 W/kg C/5 |
1471.98 kJ/kg | 8,035 W/kg 20 C | ||||
General Atomics 3330CMX2205 High Voltage Capacitor[80] | 20.5 mF | 3300 V | (unknown) | 2.3 kJ/kg | (unknown)[clarification needed] |
Fuel cell stacks and flow cell batteries[]
Fuel cells and flow cells, although perhaps using similar chemistry to batteries, do not contain the energy storage medium or fuel. With a continuous flow of fuel and oxidant, available fuel cells and flow cells continue to convert the energy storage medium into electric energy and waste products. Fuel cells distinctly contain a fixed electrolyte whereas flow cells also require a continuous flow of electrolyte. Flow cells typically have the fuel dissolved in the electrolyte.
Fuel cell type | Dry weight | Power-to-weight ratio | showExample use |
---|
- Full vehicle power-to-weight ratio shown below
Photovoltaics[]
Photovoltaic Panel type | Power-to-weight ratio |
---|---|
Thyssen Solartec 128 W Nanocrystalline Si Triplejunction PV module[93] | 6 W/kg |
Suntech/UNSW HiPerforma PLUTO220-Udm 220 W Ga-F22 Polycrystalline Si PERC PV module[94] | 13.1 W/kg STP |
9.64 W/kg nominal | |
Global Solar PN16015A 62 W CIGS polycrystalline thin-film PV module[95] | 40 W/kg |
Able (AEC) PUMA 6 kW GaInP2/GaAs/Ge-on-Ge Triplejunction PV array[96] | 65 W/kg |
Current spacecraft grade | ~77 W/kg[97] |
Vehicles[]
Power-to-weight ratios for vehicles are usually calculated using curb weight (for cars) or wet weight (for motorcycles), that is, excluding weight of the driver and any cargo. This could be slightly misleading, especially with regard to motorcycles, where the driver might weigh 1/3 to 1/2 as much as the vehicle itself. In the sport of competitive cycling athlete's performance is increasingly being expressed in VAMs and thus as a power-to-weight ratio in W/kg. This can be measured through the use of a bicycle powermeter or calculated from measuring incline of a road climb and the rider's time to ascend it.[98]
Locomotives[]
A locomotive generally must be heavy in order to develop enough adhesion on the rails to start a train. As the coefficient of friction between steel wheels and rails seldom exceeds 0.25 in most cases, improving a locomotive's power-to-weight ratio is often counterproductive. However, the choice of power transmission system, such as variable-frequency drive versus direct current drive, may support a higher power-to-weight ratio by better managing propulsion power.
Vehicle | Year | Power | Vehicle weight | showPower-to-weight ratio |
---|
Utility and practical vehicles[]
Most vehicles are designed to meet passenger comfort and cargo carrying requirements. Vehicle designs trade off power-to-weight ratio to increase comfort, cargo space, fuel economy, emissions control, energy security and endurance. Reduced drag and lower rolling resistance in a vehicle design can facilitate increased cargo space without increase in the (zero cargo) power-to-weight ratio. This increases the role flexibility of the vehicle. Energy security considerations can trade off power (typically decreased) and weight (typically increased), and therefore power-to-weight ratio, for fuel flexibility or drive-train hybridisation. Some utility and practical vehicle variants such as hot hatches and sports-utility vehicles reconfigure power (typically increased) and weight to provide the perception of sports car like performance or for other psychological benefit.
Notable low ratio[]
![]() | This section possibly contains original research. Citations given are mostly primary sources that verify the base statistics but don't assert that the power-to-weight ratio is notable compared to other vehicles. (August 2021) |
Vehicle | Year | Power | Vehicle weight | showPower-to-weight ratio |
---|
Common power[]
Vehicle | Date | Power | Vehicle weight | showPower-to-weight ratio |
---|
Performance luxury, roadsters and mild sports[]
Increased engine performance is a consideration, but also other features associated with luxury vehicles. Longitudinal engines are common. Bodies vary from hot hatches, sedans (saloons), coupés, convertibles and roadsters. Mid-range dual-sport and cruiser motorcycles tend to have similar power-to-weight ratios.
Vehicle | Year | Power | Vehicle weight | showPower-to-weight ratio |
---|
Sports vehicles[]
Power-to-weight ratio is an important vehicle characteristic that affects the acceleration of sports vehicles.
![]() | This article may contain excessive or inappropriate references to self-published sources. (May 2021) |
Vehicle | Year | Power | Vehicle weight | showPower-to-weight ratio |
---|
Early vehicles[]
Vehicle | Year | Power | Vehicle weight | showPower-to-weight ratio |
---|
Aircraft[]
Propeller aircraft depend on high power-to-weight ratio to generate sufficient thrust to achieve sustained flight, and then to fly fast.
Aircraft | Power | MTOW | showPower-to-weight ratio |
---|
Thrust-to-weight ratio[]
Jet aircraft produce thrust directly.
Aircraft | Thrust | MTOW | Thrust-to-weight ratio |
---|---|---|---|
Airbus A380 | 4 × 80,210 lbf (356.8 kN) | 575 t / 1,267,658 lb | 0.127 |
Northrop Grumman B-2 Spirit | 4 × 77 kN (17,000 lbf) | 170.6 t / 376,000 lb | 0.181 |
Boeing 747-300 | 4 × 247 kN (56,000 lbf) | 378 t / 833,000 lb | 0.269 |
Airbus A340-500 | 4 × 61,902 lbf (275.35 kN) | 380 t / 840,000 lb | 0.295 |
Boeing 777-300ER | 2 × 115,300 lbf (513 kN) | 351.5 t / 775,000 lb | 0.298 |
Concorde | 4 × 38,050 lbf (169.3 kN) | 185.07 t / 408,010 lb | 0.373 |
Lockheed Martin F-35 Lightning II | 1 × 43,000 lbf (190 kN) | 31.751 t / 70,000 lb | 0.614 |
Grumman F-14 Tomcat | 2 × 23,400 lbf (104 kN) | 33.725 t / 74,350 lb | 0.629 |
Boeing F/A-18E/F Super Hornet | 2 × 22,000 lbf (98 kN) | 29.937 t / 66,000 lb | 0.667 |
General Dynamics F-16 Fighting Falcon | 1 × 29,500 lbf (131 kN) | 19.187 t / 42,300 lb | 0.697 |
McDonnell Douglas F-15 Eagle | 2 × 23,770 lbf (105.7 kN) | 30.844 t / 68,000 lb | 0.699 |
Eurofighter Typhoon | 2 × 20,000 lbf (89 kN) | 23.5 t / 51,809 lb | 0.772 |
Lockheed Martin F-22 Raptor | 2 × 37,000 lbf (160 kN) | 38 t / 83,500 lb | 0.886 |
Human[]
Power to weight ratio is important in cycling, since it determines acceleration and the speed during hill climbs. Since a cyclist's power to weight output decreases with fatigue, it is normally discussed with relation to the length of time that he or she maintains that power. A professional cyclist can produce over 20 W/kg (0.012 hp/lb) as a 5-second maximum.[558]
See also[]
- Energy density
- Engine power
- Propulsive efficiency
- Specific output
- Thrust-to-weight ratio
- Vehicle metrics
- von Kármán–Gabrielli diagram
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External links[]
- Mechanics
- Power (physics)
- Engineering ratios