Power-to-weight ratio
Template:Short description Template:Self-published 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. Template:Toclimit
Power-to-weight (specific power)
[edit]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" can be considered 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 Template:Convert and a mass of Template:Convert,<ref name="gmduramax">Template:Cite web</ref> 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 Template:Convert) and produces Template:Cvt<ref name="ssmetpb1">Template:Cite web</ref> for a power-to-weight ratio of 153 kW/kg (93 hp/lb).
Physical interpretation
[edit]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).
- <math>
P = \lim _{\Delta t\rightarrow 0} \tfrac{\Delta W(t)}{\Delta t} = \lim _{\Delta t\rightarrow 0} P_\mathrm{avg} = \frac{d}{dt}W(t)\, </math>
The typically used metric unit of the power-to-weight ratio is <math>\tfrac{\text{W}}{\text{kg}}\;</math> which equals <math>\tfrac{\text{m}^2}{\text{s}^3}\;</math>. 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
[edit]If the work to be done is rectilinear motion of a body with constant mass <math>m\;</math>, whose center of mass is to be accelerated along a (possibly non-straight) line to a speed <math>|\mathbf{v}(t)|\;</math> and angle <math>\phi\;</math> with respect to the centre and radial of a gravitational field by an onboard powerplant, then the associated kinetic energy is
- <math> E_K =\tfrac{1}{2} m|\mathbf{v}(t)|^2 </math>
where:
- <math>m\;</math> is mass of the body
- <math>|\mathbf{v}(t)|\;</math> 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 <math>\int_C \mathbf{F} \cdot d\mathbf{x} = \int_t^{t + \Delta t} \mathbf{F} \cdot \mathbf{v}(t) dt</math>, so the fundamental theorem of calculus has that power is given by <math>\mathbf{F}(t) \cdot \mathbf{v}(t) = m\mathbf{a}(t) \cdot \mathbf{v}(t) = \mathbf{\tau}(t) \cdot \mathbf{\omega}(t)</math>.
where:
- <math>\mathbf{a}(t) = \frac{d}{dt}\mathbf{v}(t)\;</math> is acceleration of the center of mass of the body, changing with time.
- <math>\mathbf{F}(t)\;</math> is linear force – or thrust – applied upon the center of mass of the body, changing with time.
- <math>\mathbf{v}(t)\;</math> is velocity of the center of mass of the body, changing with time.
- <math>\mathbf{\tau}(t)\;</math> is torque applied upon the center of mass of the body, changing with time.
- <math>\mathbf{\omega}(t)\;</math> 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
- <math> \mbox{P-to-W} = |\mathbf{a}(t)||\mathbf{v}(t)|\;</math>
where:
- <math>|\mathbf{v}(t)|\;</math> is linear speed of the center of mass of the body.
Engine power
[edit]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
[edit]Engines
[edit]Heat engines and heat pumps
[edit]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.
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Electric motors and electromotive generators
[edit]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.
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Fluid engines and fluid pumps
[edit]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 | Example use | |||
|---|---|---|---|---|---|---|---|
| SI | English | SI | English | SI | English | ||
| PlatypusPower Q2/200 hydroelectric turbine<ref name="platypuspower">Template:Cite web</ref> | 43 kg | 95 lb | 2 kW | 2.7 hp | 0.047 kW/kg | 0.029 hp/lb | |
| PlatypusPower PP20/200 hydroelectric turbine<ref name="platypuspower"/> | 330 kg | 728 lb | 20 kW | 27 hp | 0.060 kW/kg | 0.037 hp/lb | |
| Atlas Copco LZL 35 pneumatic motor<ref>Template:Cite web</ref> | 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<ref>Template:Cite web</ref> | 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<ref name="boschpneumatics">Template:Cite web</ref> | 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<ref>Template:Cite web</ref> | 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<ref name="boschpneumatics"/> | 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<ref>Template:Cite web</ref> | 300 kg | 661 lb | 250 kW | 335 hp | 0.83 kW/kg | 0.50 hp/lb | |
| SAI GM3 radial piston hydraulic motor<ref>Template:Cite web</ref> | 15 kg | 33 lb | 15 kW | 20 hp | 1 kW/kg | 0.61 hp/lb | |
| Denison GOLD CUP P14 axial piston hydraulic motor<ref>Template:Cite web</ref> | 110 kg | 250 lb | 384 kW | 509 hp | 3.5 kW/kg | 2.0 hp/lb | |
| Denison TB vane pump<ref>Template:Cite web</ref> | 7 kg | 15 lb | 40.2 kW | 53.9 hp | 5.7 kW/kg | 3.6 hp/lb | |
| Rexroth A2FM 16cc/rev, bent axis hydraulic motor (continuous output) | 5.4 kg | 11.9 lb | 81.8 kW | 109.7 hp | 15.1 kW/kg | 9.21 hp/lb | Concrete mixers, combine harvesters |
| Hydroleduc M18, bent axis hydraulic motor (continuous output)<ref name="Hydroleduc">Template:Cite web</ref> | 5.5 kg | 12.1 lb | 92 kW | 123 hp | 16.7 kW/kg | 10.2 hp/lb | Vehicle transmissions, forestry equipment |
Thermoelectric generators and electrothermal actuators
[edit]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
[edit](Closed cell) batteries
[edit]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.<ref>Template:Cite journal</ref>
| Battery type | Volts | Template:Abbr | Energy-to-weight ratio | Power-to-weight ratio |
|---|---|---|---|---|
| Energizer 675 Mercury Free zinc–air battery<ref>Template:Cite web</ref> | 1.4 V | 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<ref>Template:Cite web</ref> | 54.2 V | -40–65 °C | 342 kJ/kg to 37.8 V | 15.8 W/kg C/6 (76 A) |
| Panasonic R03 AAA Zinc–carbon battery<ref>Template:Cite web</ref><ref>Template:Cite web Template:Dead link</ref> | 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 60 Ah 22-cell nickel–hydrogen battery<ref>Template:Cite web Template:Dead linkTemplate:Cbignore</ref> | 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 400 Ah lithium-ion battery<ref>Template:Cite web</ref><ref name="claytonpower">Template:Cite web</ref> | 12 V | 617 kJ/kg | 85.7 W/kg C/1 (175 A) | |
| Energizer 522 Prismatic Zn–MnO2 alkaline battery<ref>Template:Cite web</ref> | 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 9.25 Ah nickel–metal hydride battery<ref>Template:Cite web</ref> | 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 1418 Ah replaceable anode aluminium–air battery model<ref>Template:Cite journal</ref><ref>Template:Cite journal</ref> | 244.8 V | 60 °C | 4680 kJ/kg | 130.3 W/kg (142 A) |
| LG Chemical/CPI E2 6 Ah LiMn2O4 Lithium-ion polymer battery<ref>Template:Cite web</ref><ref>Template:Cite web</ref> | 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<ref>Template:Cite web</ref> | 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 1.8 Ah nickel–cadmium battery<ref>Template:Cite web</ref> | 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<ref name="firefly_oasis">Template:Cite web</ref> | 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 7.2 V | 234 W/kg CCA (625 A) | ||
| 0 °C | 9 kJ/kg CA to 7.2 V | 300 W/kg CA (800 A) | ||
| Panasonic CGA103450A 1.95 Ah LiCoO2 Lithium-ion battery<ref name="panasonicliion">Template:Cite web</ref> | 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 120 Ah zinc–air fuel cell<ref>Template:Cite web</ref> | 630 kJ/kg | 500 W/kg C/1 | ||
| Sion Power 2.5 Ah lithium–sulfur battery<ref>Template:Cite web</ref> | 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<ref>Template:Cite journal</ref> | 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<ref>Template:Cite journal</ref> | 45 °C | 980 W/kg | ||
| Toshiba SCiB cell 4.2 Ah Li2TiO3 lithium-ion battery<ref>Template:Cite web</ref><ref>Template:Cite web</ref> | 2.4 V | 25 °C | 242 kJ/kg | 67.2 W/kg C/1 |
| Ionix Power Systems LiMn2O4 lithium-ion battery lab model<ref>Template:Cite web</ref> | lab | 270 kJ/kg | 1700 W/kg | |
| lab | 29 kJ/kg | 4900 W/kg | ||
| A123 Systems 26650 Cell 2.3 Ah LiFePO4 lithium-ion battery<ref>Template:Cite web</ref><ref>Template:Cite web</ref> | 3.3 V | -20 °C | 347 kJ/kg C/1 to 2 V | 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 6 Ah lithium-ion battery<ref>Template:Cite web</ref> | 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 | 3289 W/kg 58.3C (350 A) | |||
| 34 kJ/kg 267C to 2.5 V | 7388 W/kg 267C (1.6 kA) | |||
| 4.29 kJ/kg 333C to 2.5 V | 9706 W/kg 333C (2 kA) |
Electrostatic, electrolytic and electrochemical capacitors
[edit]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 nanoporous 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 | Template:Abbr | Energy-to-weight ratio | Power-to-weight ratio |
|---|---|---|---|---|---|
| ACT Premlis lithium-ion capacitor<ref>Template:Cite web</ref> | 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<ref>Template:Cite web Template:Dead link</ref> | 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<ref>Template:Cite web</ref> @ 2,547 A | ||||
| EEStor EESU barium titanate supercapacitor<ref name="USPTO-7466536">Template:Ref patent</ref> | 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<ref>Template:Cite web</ref> | 20.5 mF | 3300 V | (unknown) | 2.3 kJ/kg | (unknown)Template:Clarify |
Fuel cell stacks and flow cell batteries
[edit]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 | Example use |
|---|---|---|---|
| Redflow Power+BOS ZB600 10kWh ZBB<ref>Template:Cite web</ref> | 900 kg | 5.6 W/kg (9.3 W/kg peak) | Rural Grid support |
| Ceramic Fuel Cells BlueGen MG 2.0 CHP SOFC<ref>Template:Cite web</ref> | 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 25 W DMFC<ref>Template:Cite web</ref> | 1.7 kg | 14.7 W/kg | Portable military electronics |
| UTC Power PureCell 400 kW PAFC<ref>Template:Cite web</ref> | 27,216 kgTemplate:Clarify | 14.7 W/kg | |
| GEFC 50V50A-VRB Vanadium redox battery<ref>Template:Cite web</ref> | 80 kg | 31.3 W/kg (125 W/kg peak) | |
| Ballard Power Systems Xcellsis HY-205 205 kW PEMFC<ref>Template:Cite web</ref> | 2,170 kg | 94.5 W/kg | Mercedes-Benz Citaro O530BZTemplate:Cref2 |
| UTC Power/NASA 12 kW AFC<ref>Template:Cite web</ref> | 122 kg | 98 W/kg | Space Shuttle orbiterTemplate:Cref2 |
| Ballard Power Systems FCgen-1030 1.2 kW CHP PEMFC<ref name="ballardfuelcells">Template:Cite web</ref> | 12 kg | 100 W/kg | Residential cogeneration |
| Ballard Power Systems FCvelocity-HD6 150 kW PEMFC<ref name="ballardfuelcells"/> | 400 kg | 375 W/kg | Bus and heavy duty |
| NASA Glenn Research Center 50 W SOFC<ref name="nasafuelcells">Template:Cite web</ref> | 0.071 kg | 700 W/kg | |
| Honda 2003 43 kW FC Stack PEMFC<ref>Template:Cite web</ref>Template:Cref2 | 43 kg | 1000 W/kg | Honda FCX ClarityTemplate:Cref2 |
| Lynntech PEMFC lab prototype<ref>Template:Cite conference</ref> | 0.347 kg | 1,500 W/kg | |
| PowerCell S3 125 kW commercial PEMFC<ref>Template:Cite web</ref> | 43 kg | 2,900 W/kg |
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Photovoltaics
[edit]| Photovoltaic Panel type | Power-to-weight ratio |
|---|---|
| Thyssen-Solartec 128 W nanocrystalline Si triple-junction PV module<ref>Template:Cite web</ref> | 6 W/kg |
| Suntech/UNSW HiPerforma PLUTO220-Udm 220 W Ga-F22 polycrystalline Si PERC PV module<ref>Template:Cite web Template:Dead link</ref> | 13.1 W/kg STP |
| 9.64 W/kg nominal | |
| Global Solar PN16015A 62 W CIGS polycrystalline thin-film PV module<ref>Template:Cite web</ref> | 40 W/kg |
| Able (AEC) PUMA 6 kW GaInP2/GaAs/Ge-on-Ge Triplejunction PV array<ref>Template:Cite web</ref> | 65 W/kg |
| Current spacecraft grade | ~77 W/kg<ref name=rocket>Template:Cite book</ref> |
Vehicles
[edit]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.<ref name="vam">Template:Cite web</ref>
Locomotives
[edit]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.
Utility and practical vehicles
[edit]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
[edit]Template:Original research section
Common power
[edit]Performance luxury, roadsters and mild sports
[edit]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.
Sports vehicles
[edit]Power-to-weight ratio is an important vehicle characteristic that affects the acceleration of sports vehicles.
Early vehicles
[edit]Aircraft
[edit]Propeller aircraft depend on high power-to-weight ratios to generate sufficient thrust to achieve sustained flight, and then for speed.
| Aircraft | Power | Template:Abbr | Power-to-weight ratio |
|---|---|---|---|
| Hughes H-4 Hercules Spruce Goose | {{#expr:8*2,640}} kW / {{#expr:8*3,000}} hp | Template:Convert | {{#expr:8*2640/180round0}} W/kg / {{#expr:(8*3)/400round2}} hp/lb |
| Boeing B-29 Superfortress | {{#expr:4*1,600}} kW / {{#expr:4*2,200}} hp | Template:Convert | {{#expr:4*1600/60.555round0}} W/kg / {{#expr:(4*2.2)/133.5round2}} hp/lb |
| Boeing B-17 Flying Fortress | {{#expr:4*895}} kW / {{#expr:4*1,200}} hp | Template:Convert | {{#expr:4*895/29.700round0}} W/kg / {{#expr:(4*1.2)/65.5round2}} hp/lb |
| Cessna 337D Super Skymaster | Template:Convert | Template:Convert | {{#expr:320/1.996round0}} W/kg / {{#expr:420/4400round2}} hp/lb |
| Antonov An-22 | {{#expr:4*11,186}} kW / {{#expr:4*15,000}} hp | Template:Convert | {{#expr:4*11186/250round0}} W/kg / {{#expr:(4*15)/551.16round2}} hp/lb |
| Lockheed C-130 Hercules | Template:Convert | Template:Convert | {{#expr:13691/70.307round0}} W/kg / {{#expr:18360/155000round2}} hp/lb |
| Lockheed Martin C-130J Super Hercules | Template:Convert | Template:Convert | {{#expr:13831/70.307round0}} W/kg / {{#expr:18548/155000round2}} hp/lb |
| Antonov An-28 | {{#expr:2*720}} kW / {{#expr:2*960}} hp | Template:Convert | {{#expr:2*720/6.500round0}} W/kg / {{#expr:(2*960)/14330round2}} hp/lb |
| Airbus A400M Atlas | Template:Convert | Template:Convert | {{#expr:32811/141.000round0}} W/kg / {{#expr:44000/310852round2}} hp/lb |
| North American P-51 Mustang Fighter aircraft 1941 | Template:Convert | Template:Convert | {{#expr:1280/5.488round0}} W/kg / {{#expr:1720/12100round2}} hp/lb |
| Tupolev Tu-95 | Template:Convert | Template:Convert | {{#expr:44000/188.000round0}} W/kg / {{#expr:60000/414469round2}} hp/lb |
| Tupolev Tu-142 | Template:Convert | Template:Convert | {{#expr:44130/185.000round0}} W/kg / {{#expr:59180/407855round2}} hp/lb |
| Lockheed P-38 Lightning | Template:Convert | Template:Convert | {{#expr:2400/7.938round0}} W/kg / {{#expr:3200/21600round2}} hp/lb |
| Bombardier Dash 8 Q400 turboprop airliner | Template:Convert | Template:Convert | {{#expr:2*3781/30.481round0}} W/kg / {{#expr:(2*5071)/67200round2}} hp/lb |
| Mitsubishi A6M Zero Fighter aircraft 1939 | Template:Convert | Template:Convert | {{#expr:710/2.796round0}} W/kg / {{#expr:950/6164round2}} hp/lb |
| Tupolev Tu-114 | Template:Convert | Template:Convert | {{#expr:44130/177.000round0}} W/kg / {{#expr:59180/376990round2}} hp/lb |
| Messerschmitt Bf 109 Fighter aircraft 1935 | Template:Convert | Template:Convert | {{#expr:1085/3.4round0}} W/kg / {{#expr:1455/7495round2}} hp/lb |
| Bell Boeing V-22 Osprey | {{#expr:2*4,590}} kW / {{#expr:2*6,150}} hp | Template:Convert | {{#expr:2*4590/27.4round0}} W/kg / {{#expr:(2*6150)/60500round2}} hp/lb |
| Supermarine Spitfire Fighter aircraft 1936 | Template:Convert | Template:Convert | {{#expr:1096/3.049round0}} W/kg / {{#expr:1470/6700round2}} hp/lb |
| Republic XF-84H Thunderscreech 1955 | Template:Convert | Template:Convert | {{#expr:4365/12.293round0}} W/kg / {{#expr:5850/27046round2}} hp/lb |
| de Havilland Hornet Fighter aircraft 1946 | Template:Convert | Template:Convert | {{#expr:3087/8.278round0}} W/kg / {{#expr:(2*2070)/18250round2}} hp/lb |
| Supermarine S.6 | Template:Convert | Template:Convert | {{#expr:1400/2.618round0}} W/kg / {{#expr:(1*1900)/5771round2}} hp/lb |
| Supermarine S.6B | Template:Convert | Template:Convert | {{#expr:1750/2.761round0}} W/kg / {{#expr:(1*2350)/6086round2}} hp/lb |
Thrust-to-weight ratio
[edit]Template:Main Jet aircraft produce thrust directly.
| Aircraft | Thrust | Template:Abbr | Thrust-to-weight ratio |
|---|---|---|---|
| Airbus A300-600F | 2 × Template:Cvt | 170.5 t / 375,888 lb | {{#expr:2*61000/375888round3}} |
| McDonnell Douglas MD-11 | 3 × Template:Cvt | 273.3 t / 602,500 lb | {{#expr:3*62000/602500round3}} |
| Boeing 707-320B/C | 4 × Template:Cvt | 151.3 t / 333,600 lb | {{#expr:4*19000/333600round3}} |
| Antonov An-225 Mriya | 6 × Template:Cvt | 640 t / 1,410,958 lb | {{#expr:6*51600/1410958round3}} |
| McDonnell Douglas DC-10-10 | 3 × Template:Cvt | 195 t / 430,000 lb | {{#expr:3*40000/430000round3}} |
| Messerschmitt Me 262 | 2 × Template:Cvt | 7.13 t / 15,719 lb | {{#expr:2*1980/15719round3}} |
| Airbus A380 | 4 × Template:Cvt | 575 t / 1,267,658 lb | {{#expr:4*80210/1267658round3}} |
| Airbus A320 | 2 × Template:Cvt | 78 t / 172,000 lb | {{#expr:2*27000/172000round3}} |
| Lockheed P-80 Shooting Star | 1 × Template:Cvt | 7.65 t / 16,856 lb | {{#expr:1*4600/16856round3}} |
| Boeing 737 MAX 7 | 2 × Template:Cvt | 80.29 t / 177,000 lb | {{#expr:2*29317/177000round3}} |
| Tupolev Tu-154M | 3 × Template:Cvt | 102 t / 225,000 lb | {{#expr:2*23000/225000round3}} |
| Northrop Grumman B-2 Spirit | 4 × Template:Cvt | 170.6 t / 376,000 lb | {{#expr:4*17300/376000round3}} |
| Northrop YB-49 | 8 × Template:Cvt | 87.97 t / 193,938 lb | {{#expr:8*4000/193938round3}} |
| Boeing 757-200 | 2 × Template:Cvt | 115.66 t / 255,000 lb | {{#expr:2*43500/255000round3}} |
| Boeing 747-300 | 4 × Template:Cvt | 378 t / 833,000 lb | {{#expr:4*56900/833000round3}} |
| Airbus A340-500 | 4 × Template:Cvt | 380 t / 840,000 lb | {{#expr:4*61902/840000round3}} |
| Boeing 777-300ER | 2 × Template:Cvt | 351.53 t / 775,000 lb | {{#expr:2*115300/775000round3}} |
| McDonnell Douglas DC-9-15 | 2 × Template:Cvt | 41.14 t / 90,700 lb | {{#expr:2*15500/90700round3}} |
| Messerschmitt Me 163 Komet | 1 × Template:Cvt | 4.31 t / 9,500 lb | {{#expr:1*3307/9500round3}} |
| Saunders-Roe SR.53 | 1 × Template:Cvt | 8.35 t / 18,400 lb | {{#expr:1*9640/18400round3}} |
| Lockheed T-33 | 1 × Template:Cvt | 6.832 t / 15,061 lb | {{#expr:2*4600/15061round3}} |
| Concorde | 4 × Template:Cvt | 185.07 t / 408,010 lb | {{#expr:4*38050/408010round3}} |
| Lockheed SR-71 Blackbird | 2 × Template:Cvt | 78 t / 172,000 lb | {{#expr:2*25000/172000round3}} |
| Saunders-Roe SR.A/1 | 2 × Template:Cvt | 8.63 t / 19,033 lb | {{#expr:2*3850/19033round3}} |
| Bell X-1E | 1 × Template:Cvt | 6.69 t / 14,750 lb | {{#expr:1*6000/14750round3}} |
| Lockheed F-117A Nighthawk | 2 × Template:Cvt | 23.813 t / 52,500 lb | {{#expr:2*10600/52500round3}} |
| Boeing 2707 SST<ref>Template:Cite web</ref> | 4 × Template:Cvt | 306.175 t / 675,000 lb | {{#expr:4*63200/675000round3}} |
| Lockheed L-2000 SST | 4 × Template:Cvt | 267.62 t / 590,000 lb | {{#expr:4*65000/590000round3}} |
| McDonnell Douglas MD-83 | 2 × Template:Cvt | 72.6 t / 160,000 lb | 0.263 |
| Lockheed F-104 Starfighter | 1 × Template:Cvt | 13.16 t / 29,027 lb | {{#expr:1*15600/29027round3}} |
| Lockheed Martin F-35 Lightning II | 1 × Template:Cvt | 31.751 t / 70,000 lb | {{#expr:1*43000/70000round3}} |
| Grumman F-14 Tomcat | 2 × Template:Cvt | 33.725 t / 74,350 lb | {{#expr:2*23400/74350round3}} |
| Boeing F/A-18E/F Super Hornet | 2 × Template:Cvt | 29.937 t / 66,000 lb | {{#expr:2*22000/66000round3}} |
| General Dynamics F-16 Fighting Falcon | 1 × Template:Cvt | 19.187 t / 42,300 lb | {{#expr:1*29500/42300round3}} |
| McDonnell Douglas F-15 Eagle | 2 × Template:Cvt | 30.844 t / 68,000 lb | {{#expr:2*23770/68000round3}} |
| Eurofighter Typhoon | 2 × Template:Cvt | 23.5 t / 51,809 lb | {{#expr:2*20000/51809round3}} |
| McDonnell Douglas F-15E Strike Eagle | 2 × Template:Cvt | 36.741 t / 81,000 lb | {{#expr:2*23770/81000round3}} |
| Saunders-Roe SR.177 | 1 × Template:Cvt | 12.78 t / 28,174 lb | {{#expr:1*24000/28174round3}} |
| Hawker Siddeley P.1127 | 1 × Template:Cvt | 7.71 t / 17,000 lb | {{#expr:1*15000/17000round3}} |
| Lockheed Martin F-22 Raptor | 2 × Template:Cvt | 38 t / 83,500 lb | {{#expr:2*37000/83500round3}} |
| Tupolev Tu-160 | 4 × Template:Cvt | 275 t / 606,271 lb | {{#expr:2*55000/606271round3}} |
| North American X-15 | 1 × Template:Cvt | 15.42 t / 34,000 lb | {{#expr:1*70400/34000round3}} |
Human
[edit]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 five-second maximum.<ref>Template:Cite web</ref>
See also
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