Power-to-weight ratio

Power-to-weight ratio (or 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 (53.6 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.

P = \lim _{\Delta t\rightarrow 0} \tfrac{\Delta W(t)}{\Delta t} = \lim _{\Delta t\rightarrow 0} P_\mathrm{avg}\,

The typically used metrical unit of the power-to-weight ratio is \tfrac{W}{kg}\; which equals \tfrac{m^2}{s^3}\;. This fact allows one to express the power-to-weight ratio purely by SI base units.

Propulsive power

If the work to be done is rectilinear motion of a body with constant mass m\;, whose center of mass is to be accelerated along a straight line to a speed |\mathbf{v}(t)|\; and angle \phi\; with respect to the centre and radial of a gravitational field by an onboard powerplant, then the associated kinetic energy to be delivered to the body is equal to

E_K =\tfrac{1}{2} m|\mathbf{v}(t)|^2

where:

m\; is mass of the body
|\mathbf{v}(t)|\; is speed of the center of mass of the body, changing with time.

The instantaneous mechanical pushing/pulling power delivered to the body from the powerplant is then

P_K =\tfrac{1}{2} m 2|\mathbf{v}(t)| \lim _{\Delta t\rightarrow 0} \tfrac{\Delta |\mathbf{v}(t)|}{\Delta t} = m \mathbf{a}(t) \cdot \mathbf{v}(t) = \mathbf{F}(t) \cdot \mathbf{v}(t) = \mathbf{\tau}(t) \cdot \mathbf{\omega}(t)

where:

\mathbf{a}(t)\; is acceleration of the center of mass of the body, changing with time.
\mathbf{F}(t)\; is linear force - or thrust - applied upon the center of mass of the body, changing with time.
\mathbf{v}(t)\; is velocity of the center of mass of the body, changing with time.
\mathbf{\tau}(t)\; is torque applied upon the center of mass of the body, changing with time.
\mathbf{\omega}(t)\; 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

\mbox{P-to-W} = \frac{|\mathbf{a}(t)||\mathbf{v}(t)|}{|\mathbf{g}|}\;

where:

|\mathbf{v}(t)|\; is linear speed of the center of mass of the body.

Engine power

The actual useful power of any traction engine can be calculated using a dynamometer to measure torque and rotational speed, with peak power sustained when transmission and/or operator keeps the product of torque and rotational speed maximised. For jet engines there is often a cruise speed and power can be usefully calculated there, for rockets there is typically no cruise speed, so it is less meaningful.

Peak power of a traction engine occurs at a rotational speed higher than the speed when torque is maximised and at or below the maximum rated rotational speed - Max RPM. A rapidly falling torque curve would correspond with sharp torque and power curve peaks around their maxima at similar rotational speed, for example a small, lightweight engine with a large turbocharger. A slowly falling or near flat torque curve would correspond with a slowly rising power curve up to a maximum at a rotational speed close to Max RPM, for example a large, heavy multi-cylinder engine suitable for cargo/hauling. A falling torque curve could correspond with a near flat power curve across rotational speeds for smooth handling at different vehicle speeds.

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. Care should be made when interpreting propulsive power, especially for jet engines and rockets, deliverable from heat engines to a vehicle.

Heat Engine/Heat pump type Peak Power Output Power-to-weight ratio Example Use
SI English SI English
Wärtsilä RTA96-C 14-cylinder two-stroke Turbo Diesel engine[3] 80,080 kW 108,920 hp 0.03 kW/kg 0.02 hp/lb Emma Mærsk container ship
Suzuki 538 cc V2 4-stroke gas (petrol) outboard Otto engine[4] 19 kW 25 hp 0.27 kW/kg 0.16 hp/lb Runabout boats
DOE/NASA/0032-28 Mod 2 502 cc gas (petrol) Stirling engine[5] 62.3 kW 83.5 hp 0.30 kW/kg 0.18 hp/lb Chevrolet Celebrity[•] 1985
GM 6.6 L Duramax LMM (LYE option) V8 Turbo Diesel engine[1] 246 kW 330 hp 0.65 kW/kg 0.40 hp/lb Chevrolet Kodiak[•], GMC Topkick[•]
Junkers Jumo 205A opposed-piston two-stroke Diesel engine[6] 647 kW 867 hp 1.1 kW/kg 0.66 hp/lb Ju 86C-1 airliner, B&V Ha 139 floatplane
GE LM2500+ marine turboshaft Brayton gas turbine[7] 30,200 kW 40,500 hp 1.31 kW/kg 0.80 hp/lb GTS Millennium cruiseship, QM2 ocean liner
Mazda 13B-MSP Renesis 1.3 L Wankel engine[8] 184 kW 247 hp 1.5 kW/kg 0.92 hp/lb Mazda RX-8[•]
PW R-4360 71.5 L 28-cylinder supercharged Radial engine 3,210 kW 4,300 hp 1.83 kW/kg 1.11 hp/lb B-50 Superfortress, Convair B-36
C-97 Stratofreighter, C-119 Flying Boxcar
Hughes H-4 Hercules "Spruce Goose"
Wright R-3350 54.57 L 18-c s/c Turbo-compound Radial engine 2,535 kW 3,400 hp 2.09 kW/kg 1.27 hp/lb B-29 Superfortress, Douglas DC-7
C-97 S/f prototype, Kaiser-Frazer C-119F
O.S. Engines 49-PI Type II 4.97 cc UAV Wankel engine[9] 0.934 kW 1.252 hp 2.8 kW/kg 1.7 hp/lb Model aircraft, Radio-controlled aircraft
JetCat SPT10-RX-H UAV turboshaft[10] 9 kW 12 hp 3.67 kW/kg 2.24 hp/lb Model aircraft, Radio-controlled aircraft
GE LM6000 marine turboshaft Brayton gas turbine[11][12] 44,700 kW 59,900 hp 5.67 kW/kg 3.38 hp/lb Peaking power plant
GE CF6-80C2 Brayton high-bypass turbofan jet engine[12] Boeing 747[•], 767, Airbus A300
BMW V10 3L P84/5 2005 gas (petrol) Otto engine[13] 690 kW 925 hp 7.5 kW/kg 4.6 hp/lb Williams FW27 car[•], Formula One auto racing
GE90-115B Brayton turbofan jet engine[14][15] 83,164 kW 111,526 hp 10.0 kW/kg 6.10 hp/lb Boeing 777
PWR RS-24 (SSME) Block II H2 Brayton turbopump[16][17] 63,384 kW 85,000 hp 138 kW/kg 84 hp/lb Space Shuttle (STS-110 and later) [•]
PWR RS-24 (SSME) Block I H2 Brayton turbopump[2] 53,690 kW 72,000 hp 153 kW/kg 93 hp/lb Space Shuttle
  1. Full vehicle power-to-weight ratio shown below

Electric motors/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 Example Use
SI English SI English kW/kg hp/lb
Panasonic MSMA202S1G AC servo motor[18] 6.5 kg 14 lb 2 kW 2.7 hp 0.31 kW/kg 0.19 hp/lb Conveyor belts, Robotics
Toshiba 660 MVA water cooled 23kV AC turbo generator 1,342 t 2,959,000 lb 660 MW 890,000 hp 0.49 kW/kg 0.30 hp/lb Bayswater, Eraring Coal Power stations
Canopy Tech. Cypress 32 MW 15 kV AC PM generator[19] 33,557 kg 73,981 lb 32 MW 43,000 hp 0.95 kW/kg 0.58 hp/lb Electric Power stations
Toyota Brushless AC Nd Fe B PM motor[20] 36.3 kg 80 lb 50 kW 67 hp 1.37 kW/kg 0.84 hp/lb Toyota Prius[•] 2004
Himax HC6332-250 Brushless DC motor[21] 0.45 kg 0.99 lb 1.7 kW 2.3 hp 3.78 kW/kg 2.30 hp/lb Radio controlled cars
Hi-Pa Drive HPD40 Brushless DC wheel hub motor[22] 25 kg 55 lb 120 kW 160 hp 4.8 kW/kg 2.92 hp/lb Mini QED HEV, Ford F150 HEV
ElectriFly GPMG4805 Brushless DC[23] 1.48 kg 3.3 lb 8.4 kW 11.3 hp 5.68 kW/kg 3.45 hp/lb Radio-controlled aircraft
YASA-400 Brushless AC[24] 24 kg 53 lb 165 kW 221 hp 6.875 kW/kg 4.18 hp/lb Electric Vehicle, Drive eO
ElectriFly GPMG5220 Brushless DC[25] 0.133 kg 0.29 lb 1.035 kW 1.388 hp 7.78 kW/kg 4.73 hp/lb Radio-controlled aircraft
Remy HVH250-090-POC3 Brushless DC[26] 33.5 kg 74 lb 297 kW 398 hp 8.87 kW/kg 5.39 hp/lb Electric Vehicle
EMRAX268 Brushless AC[27] 19.9 kg 44 lb 200 kW 270 hp 10.05 kW/kg 6.12 hp/lb Battery Electric Air Plane
  1. 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
SI English SI English SI English
PlatypusPower Q2/200 hydroelectric turbine[28] 43 kg 95 lb 2 kW 2.7 hp 0.047 kW/kg 0.029 hp/lb
PlatypusPower PP20/200 hydroelectric turbine[28] 330 kg 728 lb 20 kW 27 hp 0.060 kW/kg 0.037 hp/lb
Atlas Copco LZL 35 pneumatic motor[29] 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[30] 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[31] 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[32] 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[31] 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[33] 300 kg 661 lb 250 kW 335 hp 0.83 kW/kg 0.50 hp/lb
SAI GM3 radial piston hydraulic motor[34] 15 kg 33 lb 15 kW 20 hp 1 kW/kg 0.61 hp/lb
Denison GOLD CUP P14 axial piston hydraulic motor[35] 110 kg 250 lb 384 kW 509 hp 3.5 kW/kg 2.0 hp/lb
Denison TB vane pump[36] 7 kg 15 lb 40.2 kW 53.9 hp 5.7 kW/kg 3.6 hp/lb

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.

Thermoelectric Powerplant type Dry Weight Peak Power Output Power-to-weight ratio Example Use
Teledyne 238Pu GPHS-RTG 1980[37][38] 56 kg 123 lb 285 W 0.39 hp 5.09 W/kg 0.003 hp/lb Galileo probe, New Horizons probe
Boeing 238Pu MMRTG MSL[38] 44.1 kg 97.2 lb 123 W 0.16 hp 2.79 W/kg 0.002 hp/lb Mars Science Laboratory
HZ-20 thermoelectric module 0.115 kg 0.254 lb 19 W 0.025 hp 165 W/kg 0.098 hp/lb Hi-Z Technology Inc.

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.[39]

Battery type Volts Temp. Energy-to-weight ratio Power-to-weight ratio
Energizer 675 Mercury Free Zinc-air battery[40] 1.4V 21 °C 1,645 kJ/kg to 0.9 V 1.65 W/kg 2.24 mA
GE Durathon™ NaMx A2 UPS Molten salt battery[41] 54.2V -40–65 °C 342 kJ/kg to 37.8 V 15.8 W/kg C/6 (76 A)
Panasonic R03 AAA Zinc–carbon battery[42][43] 1.5 V 20±2 °C 47 kJ/kg 20 mA to 0.9 V 3.3 W/kg 20 mA
88 kJ/kg 150 mA to 0.9 V 24 W/kg 150 mA
Eagle-Picher SAR-10081 60Ah 22-cell Nickel–hydrogen battery[44] 27.7 V 10 °C 192 kJ/kg C/2 to 22 V 23 W/kg C/2
165 kJ/kg C/1 to 22 V 46 W/kg C/1
ClaytonPower 400Ah Lithium-ion battery[45][46] 12V 617 kJ/kg 85.7 W/kg C/1 (175 A)
Energizer 522 Prismatic Zn–MnO2 Alkaline battery[47] 9 V 21 °C 444 kJ/kg 25 mA to 4.8 V 4.9 W/kg 25 mA
340 kJ/kg 100 mA to 4.8 V 19.7 W/kg 100 mA
221 kJ/kg 500 mA to 4.8 V 99 W/kg 500 mA
Panasonic HHR900D 9.25Ah Nickel–metal hydride battery[48] 1.2 V 20 °C 209.65 kJ/kg to 0.7 V 11.7 W/kg C/5
58.2 W/kg C/1
116 W/kg 2C
URI 1418Ah replaceable anode Aluminium–air battery model[49][50] 244.8 V 60 °C 4680 kJ/kg 130.3 W/kg (142 A)
LG Chemical/CPI E2 6Ah LiMn2O4 Lithium-ion polymer battery[51][52] 3.8 V 25 °C 530.1 kJ/kg C/2 to 3.0 V 71.25 W/kg
513 kJ/kg 1C to 3.0 V 142.5 W/kg
Saft 45E Fe Super-Phosphate Lithium iron phosphate battery[53] 3.3 V 25 °C 581 kJ/kg C to 2.5 V 161 W/kg
560 kJ/kg 1.14 C to 2.0 V 183 W/kg
0.73 kJ/kg 2.27 C to 1.5 V 367 W/kg
Energizer CH35 C 1.8Ah Nickel–cadmium battery[54] 1.2 V 21 °C 152 kJ/kg C/10 to 1 V 4 W/kg C/10
147.1 kJ/kg 5C to 1 V 200 W/kg 5 C
Firefly Energy Oasis FF12D1-G31 6-cell 105Ah VRLA battery[55] 12 V 25 °C 142 kJ/kg C/10 to 7.2 V 4 W/kg C/10
-1 8 °C 7 kJ/kg CCA to 7.2V 234 W/kg CCA (625A)
0 °C 9 kJ/kg CA to 7.2 V 300 W/kg CA (800 A)
Panasonic CGA103450A 1.95Ah LiCoO2 Lithium-ion battery[56] 3.7 V 20 °C 666 kJ/kg C/5.3 to 2.75 V 35 W/kg C/5.3
0 °C 633 kJ/kg C/1 to 2.75 V 176 W/kg C/1
20 °C 655 kJ/kg C/1 to 2.75 V 182 W/kg C/1
20 °C 641 kJ/kg 2C to 2.75 V 356 W/kg 2C
Electric Fuel Battery Corp. UUV 120Ah Zinc–air fuel cell[57] 630 kJ/kg 500 W/kg C/1
Sion Power 2.5Ah Li–S Lithium-ion battery[58] 2.15 V 25 °C 1260 kJ/kg 70 W/kg C/5
1209 kJ/kg 672 W/kg 2C
Stanford Prussian Blue durable Potassium-ion battery[59] 1.35 V room 54 kJ/kg 13.8 W/kg C/1
50 kJ/kg 138 W/kg 10C
39 kJ/kg 693 W/kg 50C
Maxell / Yuasa / AIST Nickel–metal hydride lab prototype[60] 45 °C 980 W/kg
Toshiba SCiB cell 4.2Ah Li2TiO3 Lithium-ion battery[61][62] 2.4 V 25 °C 242 kJ/kg 67.2 W/kg C/1
218 kJ/kg 4000 W/kg 12C
Ionix Power Systems LiMn2O4 Lithium-ion battery lab model[63] lab 270 kJ/kg 1700 W/kg
lab 29 kJ/kg 4900 W/kg
A123 Systems 26650 Cell 2.3Ah LiFePO4 Lithium ion battery[64][65] 3.3 V -20 °C 347 kJ/kg C/1 to 2V 108 W/kg C/1
0 °C 371 kJ/kg C/1 to 2 V 108 W/kg C/1
25 °C 390 kJ/kg C/1 to 2 V 108 W/kg C/1
25 °C 390 kJ/kg 27C to 2 V 3300 W/kg 27C
25 °C 57 kJ/kg 32C to 2 V 5657 W/kg 32C
Saft VL 6Ah Lithium-ion battery[66] 3.65 V -20 °C 154 kJ/kg 30C to 2.5 V 41.4 W/kg 30C (180 A)
182 kJ/kg 1C to 2.5 V 67.4 W/kg 1C
25 °C 232 kJ/kg 1C to 2.5 V 64.4 W/kg 1C
233 kJ/kg 58.3C to 2.5 V 3757 W/kg 58.3C (350A)
34 kJ/kg 267C to 2.5 V 17176 W/kg 267C (1.6kA)
4.29 kJ/kg 333C to 2.5 V 21370 W/kg 333C (2kA)

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 Capacity Volts Temp. Energy-to-weight ratio Power-to-weight ratio
ACT Premlis Lithium ion capacitor[67] 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[68] 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[69] @ 2,547A
EEStor EESU barium titanate supercapacitor[70] 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[71] 20.5 mF 3300 V ? °C 2.3 kJ/kg 6.8 MW/kg @ 100 kA

Fuel cell stacks and flow cell batteries

Fuel cells and flow cells, although perhaps using similar chemistry to batteries, have the distinction of not containing 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 Example Use
Redflow Power+BOS ZB600 10kWh ZBB[72] 900 kg 5.6 W/kg (9.3 W/kg peak) Rural Grid support
Ceramic Fuel Cells BlueGen MG 2.0 CHP SOFC[73] 200 kg 10 W/kg
15 W/kg CHP
MTU Friedrichshafen 240 kW MCFC HotModule 2006 20,000 kg 12 W/kg
Smart Fuel Cell Jenny 600S 25W DMFC[74] 1.7 kg 14.7 W/kg Portable military electronics
UTC Power PureCell 400 kW PAFC[75] 27,216 kg 14.7 W/kg
GEFC 50V50A-VRB Vanadium redox battery[76] 80 kg 31.3 W/kg (125 W/kg peak)
Ballard Power Systems Xcellsis HY-205 205 kW PEMFC[77] 2,170 kg 94.5 W/kg Mercedes-Benz Citaro O530BZ[•]
UTC Power/NASA 12 kW AFC[78] 122 kg 98 W/kg Space Shuttle orbiter[•]
Ballard Power Systems FCgen-1030 1.2 kW CHP PEMFC[79] 12 kg 100 W/kg Residential cogeneration
Ballard Power Systems FCvelocity-HD6 150 kW PEMFC[79] 400 kg 375 W/kg Bus and heavy duty
NASA Glenn Research Center 50 W SOFC[80] 0.071 kg 700 W/kg
Honda 2003 43 kW FC Stack PEMFC[81][•] 43 kg 1000 W/kg Honda FCX Clarity[•]
Lynntech, Inc. PEMFC lab prototype[82] 0.347 kg 1,500 W/kg
  1. Full vehicle power-to-weight ratio shown below

Photovoltaics

Photovoltaic Panel type Power-to-weight ratio
Thyssen Solartec 128W Nanocrystalline Si Triplejunction PV module[83] 6 W/kg
Suntech/UNSW HiPerforma PLUTO220-Udm 220W Ga-F22 Polycrystalline Si PV module[84] 13.1 W/kg STP
9.64 W/kg nominal
Global Solar PN16015A 62W CIGS polycrystalline thin film PV module[85] 40 W/kg
Able (AEC) PUMA 6 kW GaInP2/GaAs/Ge-on-Ge Triplejunction PV array[86] 65 W/kg
Current spacecraft grade ~77 W/kg[87]
ITO/InP on Kapton foil 2000 W/kg[88]

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.[89]

Utility and practical vehicles

Most vehicles are designed to meet passenger comfort and cargo carrying requirements. Different 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. Rail locomotives require high mass to maintain adhesive traction on the rails, therefore improving the power-to-weight ratio by reducing mass is not necessarily beneficial. However choice of rail locomotive traction system (i.e. AC VFD over DC) can support improved power-to-weight ratio by reducing mass for the same adhesion.

Notable low ratio
Vehicle Power Weight Power to Weight ratio
Benz Patent Motorwagen 954 cc 1886[90] 560 W / 0.75 bhp 265 kg / 584 lb 2.1 W/kg / 779 lb/hp
Stephenson's Rocket 0-2-2 steam locomotive with tender 1829[91] 15 kW / 20 bhp 4,320 kg / 9524 lb 3.5 W/kg / 476 lb/hp
CBQ Zephyr streamliner diesel locomotive with railcars 1934[92] 492 kW / 660 bhp 94 t / 208,000 lb 5.21 W/kg / 315 lb/hp
Alberto Contador's Verbier climb 2009 Tour de France on Specialized bike[89] 420 W / 0.56 bhp 62 kg / 137 lb 6.7 W/kg / 245 lb/hp
Force Motors Minidor Diesel 499 cc auto rickshaw[93][94] 6.6 kW / 8.8 bhp 700 kg / 1543 lb 9 W/kg / 175 lb/hp
PRR Q2 4-4-6-4 steam locomotive with tender 1944 5,956 kW / 7,987 bhp 475.9 t / 1,049,100 lb 12.5 W/kg / 131 lb/hp
Mercedes-Benz Citaro O530BZ H2 fuel cell bus 2002[95] 205 kW / 275 bhp 14,500 kg / 32,000 lb 14.1 W/kg / 116 lb/hp
TGV BR Class 373 high-speed Eurostar Trainset 1993 12,240 kW / 16,414 bhp 816 t / 1,798,972 lb 15 W/kg / 110 lb/hp
General Dynamics M1 Abrams Main battle tank 1980[96] 1,119 kW / 1500 bhp 55.7 t / 122,800 lb 20.1 W/kg / 81.9 lb/hp
BR Class 43 high-speed diesel electric locomotive 1975 1,678 kW / 2,250 bhp 70.25 t / 154,875 lb 23.9 W/kg / 69 lb/hp
GE AC6000CW diesel electric locomotive 1996 4,660 kW / 6,250 bhp 192 t / 423,000 lb 24.3 W/kg / 68 lb/hp
BR Class 55 Napier Deltic diesel electric locomotive 1961 2,460 kW / 3,300 bhp 101 t / 222,667 lb 24.4 W/kg / 68 lb/hp
International CXT 2004[97] 164 kW / 220 bhp 6,577 kg / 14500 lb 25 W/kg / 66 lb/hp
Ford Model T 2.9 L flex-fuel 1908 15 kW / 20 bhp 540 kg / 1,200 lb 28 W/kg / 60 lb/hp
TH!NK City 2008[98] 30 kW / 40 bhp 1038 kg / 2,288 lb 28.9 W/kg / 56.9 lb/hp
Messerschmitt KR200 Kabinenroller 191 cc 1955 6 kW / 8.2 bhp 230 kg / 506 lb 30 W/kg / 50 lb/hp
Wright Flyer 1903 9 kW / 12 bhp 274 kg / 605 lb 33 W/kg / 50 lb/hp
Tata Nano 624 cc 2008 26 kW / 35 bhp 635 kg / 1,400 lb 41.0 W/kg / 40 lb/hp
Bombardier JetTrain high-speed gas turbine-electric locomotive 2000[99] 3,750 kW / 5,029 bhp 90,750 kg / 200,000 lb 41.2 W/kg / 39.8 lb/hp
Suzuki MightyBoy 543 cc 1988 23 kW / 31 bhp 550 kg / 1,213 lb 42 W/kg / 39 lb/hp
Mitsubishi i MiEV 2009[100] 47 kW / 63 bhp 1,080 kg / 2,381 lb 43.5 W/kg / 37.8 lb/hp
Holden FJ 2,160 cc 1953[101] 44.7 kW / 60 bhp 1,021 kg / 2,250 lb 43.8 W/kg / 37.5 lb/hp
Chevrolet Kodiak/GMC Topkick LYE 6.6 L 2005[1][102] 246 kW / 330 bhp 5126 kg / 11,300 lb 48 W/kg / 34.2 lb/hp
DOE/NASA/0032-28 Chevrolet Celebrity 502 cc ASE Mod II 1985[5] 62.3 kW / 83.5 bhp 1,297 kg / 2,860 lb 48.0 W/kg / 34.3 lb/hp
Suzuki Alto 796 cc 2000 35 kW / 46 bhp 720 kg / 1,587 lb 49 W/kg / 35 lb/hp
Land Rover Defender 2.4 L 1990[103] 90 kW / 121 bhp 1,837 kg / 4,050 lb 49 W/kg / 33 lb/hp
Common power
Vehicle Power Weight Power to Weight ratio
Toyota Prius 1.8 L 2010 (petrol only)[104] 73 kW / 98 bhp 1,380 kg / 3,042 lb 53 W/kg / 31 lb/hp
Bajaj Platina Naked 100 cc 2006[105] 6 kW / 8 bhp 113 kg / 249 lb 53 W/kg / 31 lb/hp
Subaru R2 type S 2003[106] 47 kW / 63 bhp 830 kg / 1,830 lb 57 W/kg / 29 lb/hp
Ford Fiesta ECOnetic 1.6 L TDCi 5dr 2009[107] 66 kW / 89 bhp 1,155 kg / 2,546 lb 57 W/kg / 29 lb/hp
Volvo C30 1.6D DRIVe S/S 3dr Hatch 2010[108] 80 kW / 108 bhp 1,347 kg / 2,970 lb 59.4 W/kg / 27.5 lb/hp
Ford Focus ECOnetic 1.6 L TDCi 5dr Hatch 2009[109] 81 kW / 108 bhp 1,357 kg / 2,992 lb 59.7 W/kg / 27 lb/hp
Ford Focus 1.8 L Zetec S TDCi 5dr Hatch 2009[110] 84 kW / 113 bhp 1,370 kg / 3,020 lb 61 W/kg / 27 lb/hp
Honda FCX Clarity 4 kg Hydrogen 2008[111] 100 kW / 134 bhp 1,600 kg / 3,528 lb 63 W/kg / 26 lb/hp
Hummer H1 6.6 L V8 2006[112] 224 kW / 300 bhp 3,559 kg / 7,847 lb 63 W/kg / 26 lb/hp
Audi A2 1.4 L TDI 90 type S 2003[113] 66 kW / 89 bhp 1,030 kg / 2,270 lb 64 W/kg / 25 lb/hp
Opel/Vauxhall/Holden/Chevrolet Astra 1.7 L CTDi 125 2010[114] 92 kW / 123 bhp 1,393 kg / 3,071 lb 66 W∕kg / 24.9 lb∕hp
Mini (new) Cooper 1.6D 2007[115] 81 kW / 108 bhp 1,185 kg / 2,612 lb 68 W/kg / 24 lb/hp
Toyota Prius 1.8 L 2010 (electric boost)[104] 100 kW / 134 bhp 1,380 kg / 3,042 lb 72 W/kg / 23 lb/hp
Ford Focus 2.0 L Zetec S TDCi 5dr Hatch 2009[116] 100 kW / 134 bhp 1,370 kg / 3,020 lb 73 W/kg / 23 lb/hp
General Motors EV1 electric car Gen II 1998[117] 102.2 kW / 137 bhp 1,400 kg / 3,086 lb 73 W/kg / 23 lb/hp
Toyota Venza I4 2.7 L FWD 2009[118] 136 kW / 182 bhp 1,706 kg / 3,760 lb 80 W/kg / 20.7 lb/hp
Ford Focus 2.0 L Zetec S 5dr Hatch 2009[119] 107 kW / 143 bhp 1,327 kg / 2,926 lb 81 W/kg / 20 lb/hp
Fiat Grande Punto 1.6 L Multijet 120 2005[120] 88 kW / 118 bhp 1,075 kg / 2,370 lb 82 W/kg / 20 lb/hp
Mini (classic) 1275GT 1969 57 kW / 76 bhp 686 kg / 1,512 lb 83 W/kg / 20 lb/hp
Opel/Vauxhall/Holden/Chevrolet Astra 2.0 L CTDi 160 2010[121] 118 kW / 158 bhp 1,393 kg / 3,071 lb 85 W∕kg / 19.4 lb∕hp
Ford Focus 2.0 auto 2007[122] 104.4 kW / 140 bhp 1,198 kg / 2,641 lb 87.1 W/kg / 19 lb/hp
Subaru Legacy/Liberty 2.0R 2005[123] 121 kW / 162 bhp 1,370 kg / 3,020 lb 88 W/kg / 19 lb/hp
Subaru Outback 2.5i 2008[124] 130.5 kW / 175 bhp 1,430 kg / 3,153 lb 91 W/kg / 18 lb/hp
Smart Fortwo 1.0 L Brabus 2009[125] 72 kW / 97 bhp 780 kg / 1,720 lb 92 W/kg / 18 lb/hp
Toyota Venza V6 3.5 L AWD 2009[118] 200 kW / 268 bhp 1,835 kg / 4,045 lb 109 W/kg / 15 lb/hp
Toyota Venza I4 2.7 L FWD 2009[118] with Lotus mass reduction[126] 136 kW / 182 bhp 1,210 kg / 2,667 lb 112.2 W/kg / 14.7 lb/hp
Toyota Hilux V6 DOHC 4 L 4×2 Single Cab Pickup ute 2009[127] 175 kW / 235 bhp 1,555 kg / 3,428 lb 112.5 W/kg / 14.6 lb/hp
Toyota Venza V6 3.5 L FWD 2009[118] 200 kW / 268 bhp 1,755 kg / 3,870 lb 114 W/kg / 14.4 lb/hp
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 Power Weight Power to Weight ratio
Honda Accord sedan V6 2011 202 kW / 271 bhp 1630 kg / 3593 lb 124 W/kg / 13.26 lb/hp
Mini (new) Cooper 1.6T S JCW 2008[128] 155 kW / 208 bhp 1205 kg / 2657 lb 129 W/kg / 13 lb/hp
Mazda RX-8 1.3 L Wankel 2003 173 kW / 232 bhp 1309 kg / 2888 lb 132 W/kg / 12 lb/hp
Holden Statesman/Caprice / Buick Park Avenue / Daewoo Veritas 6 L V8 2007[129] 270 kW / 362 bhp 1891 kg / 4170 lb 143 W/kg / 12 lb/hp
Kawasaki KLR650 Gasoline DualSport 650 cc 26 kW / 35 bhp 182 kg / 401 lb 143 W/kg / 11 lb/hp
NATO HTC M1030M1 Diesel/Jet fuel DualSport 670 cc[130] 26 kW / 35 bhp 182 kg / 401 lb 143 W/kg / 11 lb/hp
Harley-Davidson FLSTF Softail Fat Boy Cruiser 1,584 cc 2009[131] 47 kW / 63 bhp 324 kg / 714 lb 145 W/kg / 11.3 lb/hp
BMW 7 Series 760Li 6 L V12 2006[132] 327 kW / 439 bhp 2250 kg / 4960 lb 145 W/kg / 11 lb/hp
Subaru Impreza WRX STi 2.0 L 2008[133] 227 kW / 304 bhp 1530 kg / 3373 lb 148 W/kg / 11 lb/hp
Honda S2000 roadster 1999 183.88 kW / 240 bhp 1250 kg / 2723 lb 150 W/kg / 11 lb/hp
GMH HSV Clubsport / GMV VXR8 / GMC CSV CR8 / Pontiac G8 6 L V8 2006[134] 317 kW / 425 bhp 1831 kg / 4037 lb 173 W/kg / 9.5 lb/hp
Tesla Roadster 2011[135] 215 kW / 288 bhp 1235 kg / 2723 lb 174 W/kg / 9.5 lb/hp

Sports vehicles and aircraft

Power-to-weight ratio is an important vehicle characteristic that affects the acceleration and handling - and therefore the driving enjoyment - of any sports vehicle. Aircraft also depend on high power-to-weight ratio to achieve sufficient lift.

Vehicle Power Weight Power to Weight ratio
Lotus Elise SC 2008 163 kW / 218 bhp 910 kg / 2006 lb 179 W/kg / 9.20 lb/hp
Ferrari Testarossa 1984 291 kW / 390 bhp 1506 kg / 3320 lb 193 W/kg / 8.51 lb/hp
Citroën DS3 WRC rally car 2011[136] 235 kW / 315 bhp 1200 kg / 2,645.5 lb 196 W/kg / 8.40 lb/hp
Artega GT[137] 220 kW / 300 bhp 1100 kg / 2425 lb 200 W/kg / 8.08 lb/hp
Lotus Exige GT3 2006[138] 202.1 kW / 271 bhp 980 kg / 2160 lb 206 W/kg / 7.97 lb/hp
Chevrolet Corvette C6 2008[139] 321 kW / 430 bhp 1441 kg / 3177 lb 223 W/kg / 7.39 lb/hp
Nissan GT-R R35 3.6L Turbo V6[140] 406 kW / 545 bhp 1779 kg / 3922 lb[141] 228 W/kg / 7.20 lb/hp
Dodge Charger SRT Hellcat 6.2L Hemi V8[142] 527 kW / 707 bhp 2075 kg / 4575 lb 254 W/kg / 6.47 lb/hp
Suzuki V-Strom 650 V-twin DualSport 650 cc 50 kW / 67 bhp 194 kg / 427 lb 258 W/kg / 6.4 lb/hp
Chevrolet Corvette C6 Z06[139] 376 kW / 505 bhp 1421 kg / 3133 lb 265 W/kg / 6.2 lb/hp
Porsche 911 GT2 2007 390 kW / 523 bhp 1440 kg / 3200 lb 271 W/kg / 6.1 lb/hp
Lamborghini Murciélago LP 670-4 SV 2009[143] 493 kW / 661 bhp 1550 kg / 3417 lb 318 W/kg / 5.17 lb/hp
Mercedes-Benz C-Coupé DTM touring car 2012[144] 343 kW / 460 bhp 1110 kg / 2,447 lb 309 W/kg / 5.32 lb/hp
Sector111 Drakan Spyder[145] 321 kW / 430 bhp 907 kg / 2000 lb 354 W/kg / 4.65 lb/hp
McLaren F1 GT 1997[146] 467.6 kW / 627 bhp 1220 kg / 2690 lb 403 W/kg / 4.3 lb/hp
BAC Mono 2011[147] 213 kW / 285 bhp 540 kg / 1190 lb 394 W/kg / 4.18 lb/hp
Porsche 918 Spyder[148] 661 kW / 887 bhp 1656 kg / 3650 lb 399 W/kg / 4.16 lb/hp
Lancia Delta S4 group B 1985[149] 350 kW / 480 bhp 890 kg / 1,962 lb 393 W/kg / 4.08 lb/hp
Ariel Atom 3S 2014[150] 272 kW / 365 bhp 639 kg / 1400 lb 426 W/kg / 3.84 lb/hp
Bombardier Dash 8 Q400 turboprop airliner[151] 7,562 kW / 10,142 bhp 17,185 kg / 37,888 lb 440 W/kg / 3.7 lb/hp
Ferrari LaFerrari[152] 708 kW / 950 bhp 1585 kg / 3495 lb 447 W/kg / 3.68 lb/hp
McLaren P1 2013[153] 673 kW / 903 bhp 1490 kg / 3280 lb 452 W/kg / 3.63 lb/hp
Supermarine Spitfire Fighter aircraft 1936 1,096 kW / 1,470 bhp 2,309 kg / 5,090 lb 475 W/kg / 3.46 lb/hp
Messerschmitt Bf 109 Fighter aircraft 1935 1,085 kW / 1,455 bhp 2,247 kg / 4,954 lb 483 W/kg / 3.40 lb/hp
Thunderbolt Land speed record car 3504 kW / 4700 bhp 7 t / 15432 lb 500 W/kg / 3.28 lb/hp
Ferrari FXX 2005 597 kW / 801 bhp 1155 kg / 2546 lb 517 W/kg / 3.18 lb/hp
Polaris Industries Assault Snowmobile 2009[154] 115 kW / 154 bhp 221 kg / 487 lb 523 W/kg / 3.16 lb/hp
Audi R10 TDI Le Mans Prototype 2006[155] 485 kW / 650 bhp 925 kg / 2,039 lb 524 W/kg / 3.13 lb/hp
Ultima GTR 720 2006[156] 536.9 kW / 720 bhp 920 kg / 2183 lb 583 W/kg / 3.03 lb/hp
Honda CBR1000RR 2009 133 kW / 178 bhp 199 kg / 439 lb 668 W/kg / 2.46 lb/hp
Ariel Atom 500 V8 2011 372 kW / 500 bhp 550 kg / 1212 lb 676.3 W/kg / 2.47 lb/hp
BMW S1000RR 2009 144 kW / 193 bhp 207.7 kg / 458 lb 693.3 W/kg / 2.37 lb/hp
Peugeot 208 T16 Pikes Peak 2013 652 kW / 875 bhp 875 kg / 1930 lb 745 W/kg / 2.21 lb/hp
Koenigsegg One:1 2015 1000 kW / 1341 bhp 1310 kg / 2888 lb 763 W/kg / 2.15 lb/hp
Nissan R90C Group C 1990[157] 746 kW / 1000 bhp 900 kg / 1984 lb 829W/kg / 1.98 lb/hp
Ducati 1199 Panigale R (WSB) 2012 151 kW / 202 bhp 165 kg / 364 lb 915 W/kg / 1.80 lb/hp
KillaCycle Drag racing electric motorcycle 260 kW / 350 bhp 281 kg / 619 lb 925 W/kg / 1.77 lb/hp
MTT Turbine Superbike 2008[158] 213.3 kW / 286 bhp 227 kg / 500 lb 940 W/kg / 1.75 lb/hp
Vyrus 987 C3 4V V supercharged motorcycle 2010[159] 157.3 kW / 211 bhp 158 kg / 348.3 lb 996 W/kg / 1.65 lb/hp
Kawasaki H2R Motorcycle 2015[160] 223 kW / 300 bhp 216 kg / 476 lb 1032 W/kg / 1.43 lb/hp
BMW Williams FW27 Formula One 2005[161] 690 kW / 925 bhp 600 kg / 1323 lb 1150 W/kg / 1.58 lb/hp
Honda RC211V MotoGP 2004-6 176.73 kW / 237 bhp 148 kg / 326 lb 1194 W/kg / 1.37 lb/hp
Boeing 747-300[11] at Mach 0.84 cruise, 35,000 ft altitude 245 MW / 328,656 bhp 178.1 t / 392,800 lb 1376 W/kg / 1.20 lb/hp
John Force Racing Funny Car NHRA Drag Racing 2008[162] 5,963.60 kW / 8,000 bhp 1043 kg / 2,300 lb 5717 W/kg / 0.30 lb/hp

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 they maintain that power. A professional cyclist can produce over 20 W/kg as a 5-second maximum. [163]

See also

References

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