Horsepower (hp or HP) is the name of several non-metric units of power. In scientific discourse, the term "horsepower" is rarely used because of its various definitions and the already existent SI unit for power, the watt (W). However, use of the term "horsepower" persists as a legacy in many languages and industries, particularly as a unit of measurement of the maximum power output of internal-combustion engines of automobiles; and often of trucks, buses, and ships. The use of 'HP' is being slowly replaced by kW (kilowatt) and MW (megawatt).
There are two important factors to consider when evaluating the measurement of "horsepower":
These factors can be combined in unexpected ways — the power output for an engine rated at "100 horsepower" might not be what a reader expects. For this reason, various groups have attempted to standardize not only the definition of "horsepower" but the measurement of "horsepower". In the interim, more confusion may surface.
Others recount that Watt determined that a pony could lift an average 220 pounds 100 feet (30 m) per minute over a four-hour working shift. Watt then judged a horse was 50% more powerful than a pony and thus arrived at the 33,000 ft·lbf/min figure.
Engineering in History recounts that John Smeaton initially estimated that a horse could produce 22,916-foot-pounds per minute. John Desaguliers increased that to 27,500-foot-pounds per minute. "Watt found by experiment in 1782 that a 'brewery horse' was able to produce 32,400-foot-pounds per minute". James Watt and Matthew Boulton standardized that figure at 33,000 the next year.
Put into perspective, a healthy human can produce about 1.2 hp briefly (see Orders of magnitude (power)) and sustain about 0.1 hp indefinitely, and trained athletes can manage up to about 0.3 horsepower for a period of several hours.
Most observers familiar with horses and their capabilities estimate that Watt was either a bit optimistic or intended to under promise and over deliver; few horses can maintain that effort for long. Regardless, comparison to a horse proved to be an enduring marketing tool.
|Mechanical horsepower||≡ 33,000 ft·lbf/min = 550 ft·lbf/s|
= 745.6999 W
|Metric horsepower||≡ 75 kgf·m/s|
= 735.49875 W (exactly)
|Electrical horsepower||≡746 W|
|Boiler horsepower||≡ 33,475 Btu/h =9809.5 W|
|Hydraulic horsepower||=Flow Rate(US gal/min) * Pressure(psi) / 1714|
Additionally, the term "horsepower" has been applied to calculated (estimated rather than measured) metrics:
|1 hp||≡ 33,000 ft·lbf/min||by definition|
|= 550 ft·lbf/s||since||1 min||= 60 s|
|= 550 × 0.3048 × 0.45359237 m·kgf/s||since||1 ft||= 0.3048 m and|
|= 76.0402249068 kgf·m/s||1 lb||= 0.45359237 kg|
|= 76.0402249068 × 9.80665 kg·m²/s³||g||= 9.80665 m/s²|
|= 745.69987158227022 W||since||1 W||≡ 1 J/s = 1 N·m/s = 1 (kg·m/s²)·(m/s)|
Or given that 1 hp = 550 ft·lbf/s, 1 ft = 0.3048 m, 1 lb = 4.448 N, 1 J = 1 N·m, 1 W = 1 J/s: 1 hp = 746 W
cross multiply and cancel out:
| 550 || 0.3048 || 4.448 || 1 ||1 W|
|1 hp|| 1 || 1 ||1 ||1 |
Metric horsepower, as a rule, is defined as 0.73549875 kW, or roughly 98.6% of mechanical horsepower. This was a minor issue in the days when measurement systems varied widely and engines produced less power, but has become a major sticking point today. Exotic cars from Europe like the McLaren F1 and Bugatti Veyron are often quoted using the wrong definition, and their power output is sometimes even converted twice because of confusion over whether the original "horsepower" number was metric or mechanical.
The PS was adopted by the Deutsches Institut für Normung (DIN) and then by the automotive industry throughout most of Europe, under varying names. In 1992, the PS was rendered obsolete by EEC directives, when it was replaced by the kilowatt as the official power measuring unit. It is still in use for commercial and advertising purposes, as many customers are not familiar with the use of kilowatts for engines.
In Italian ("Cavalli"), Spanish ("Caballos"), and Portuguese ("Cavalos"), 'CV' is the equivalent to the German 'PS'. It is also used as the French term for the Pferdestärke, but in French, this should be written in lowercase letters as 'cv'.
In addition, the capital form 'CV' is a French unit for tax horsepower, short for chevaux vapeur ("steam horses") or cheval-vapeur. CV is a non-linear rating of a motor vehicle for tax purposes. The CV rating, or fiscal power, is , where P is the maximum power in kilowatts and U is the amount of CO2 emitted in grams per kilometre. The fiscal power has found its way into naming of automobile models, such as the popular Citroën deux-chevaux. The cheval-vapeur (ch) unit should not be confused with the French cheval fiscal (CV).
In the 19th century the French had their own unit, which they used instead of the CV or horsepower. It was called the poncelet and was abbreviated 'p'.
This is a French unit for automobile power. The symbol ch is short for chevaux ("horses"). Some sources give it as 0.7355 kW, but it is generally used interchangeably with the German 'PS'.
A boiler horsepower is used for boilers in power plants. It is equal to 33,475 Btu/h (9.8095 kW), which is the energy rate needed to evaporate 34.5 lb (15.65 kg) of water at 212 °F (100 °C) in one hour.
The electrical horsepower is used by the electrical industry for electrical machines and is defined to be exactly 746 W at 100% efficiency. Electric motors can never run at 100% efficiency. The nameplates on electrical motors show their power output, not their power input.
Where is power, is torque, and is rotations per minute. Outside the United States, most countries use the newton meter as the unit of torque. Most automobile specifications worldwide have torque listed in newton meters. The standard equation relating torque in newton meters, rotational speed in RPM and power in kilowatts is:
These are based on Watt's definition of the mechanical horsepower. The constants 5252 and 9549 are rounded.
5252 comes from 33,000 (ft.lbf/min) / 2π (radians/revolution),
and 9549 comes from 60 (s/min) x 1000 (W/kW) / 2π (radians/revolution).
If the drawbar force () is measured in (lbf) and speed () is measured in miles per hour (mph), then the drawbar power () in horsepower (hp) is:
Example: How much power is needed to pull a drawbar load of 2025 pounds-force at 5 miles per hour?
The constant "375" is because 1 hp = 375 lbf·mph. If other units are used, the constant is different. When using a coherent system of units, such as SI (watts, newtons, and metres per second), no constant is needed, and the formula becomes .
Taxable horsepower does not reflect developed horsepower; rather, it is a calculated figure based on the engine's bore size, number of cylinders, and a (now archaic) presumption of engine efficiency. As new engines were designed with ever-increasing efficiency, it was no longer a useful measure, but was kept in use by UK regulations which used the rating for tax purposes.
This is equal to the displacement in cubic inches divided by 10π then divided again by the stroke in inches.
Since taxable horsepower was computed based on bore and number of cylinders, not based on actual displacement, it gave rise to engines with 'undersquare' dimensions, i.e. relatively narrow bore, but long stroke; this tended to impose an artificially low limit on rotational speed (rpm), hampering the potential power output and efficiency of the engine.
The situation persisted for several generations of four- and six-cylinder British engines: for example, Jaguar's 3.8-litre XK engine had six cylinders with a bore of 87 mm (3.43 inches) and a stroke of 106 mm (4.17 inches), where most American automakers had long since moved to oversquare (wide bore, short stroke) V-8s]
The power of an engine may be measured or estimated at several points in the transmission of the power from its generation to its application. A number of names are used for the power developed at various stages in this process, but none is a clear indicator of either the measurement system or definition used.
In the case of an engine dynamometer, power is measured at the engine's flywheel (i.e., at the crankshaft output). With a chassis dynamometer or "rolling road", power output is measured at the driving wheels. This accounts for the significant power loss through the drive train. As an example, an early-production BL Mini engine produced about at the flywheel, of which only reached the driving wheels.
All the above assumes that no power inflation factors have been applied to any of the readings.
Engine designers use expressions other than horsepower to denote objective targets or performance, such as BMEP (Brake Mean Effective pressure). This is a coefficient of theoretical brake horsepower and cylinder pressures during combustion.
nhp = 7 x area of piston x equivalent piston speed/33,000
For paddle ships the piston speed was estimated as 129.7 x (stroke)1/3.35
For the nominal horsepower to equal the actual power it would be necessary for the mean steam pressure in the cylinder during the stroke to be 7 psi and for the piston speed to be of the order of 180-248 ft/s.
No pre-1972 engine in its unaltered, production line stock form, as installed in the vehicle, has ever yielded documented, qualified third party validated power figures that equal or exceed its original gross rating. Claims that such engines were "under-rated" are therefore dubious; for example, the 1969 427 ZL1 Chevrolet, rated at , is frequently cited as an "under-rated" high performance engine, yet it produced only .
Because SAE gross ratings were applied liberally, there is no precise conversion from gross to net. Comparison of gross and net ratings for unchanged engines shows a variance of anywhere from 40 to 150 horsepower. The Chrysler 426 Hemi, for example, in 1971 carried a 425 hp gross rating and a net rating of 350 hp, while the same company's 225 Slant 6 carried a rating of 145 bhp but 110 net hp.
Many manufacturers began switching to the new rating immediately, with multi-directional results; the rated output of Cadillac's supercharged Northstar V8 jumped from to under the new tests, while the rating for Toyota's Camry 3.0 L 1MZ-FE V6 fell from to . The first engine certified under the new program was the 7.0 L LS7 used in the 2006 Chevrolet Corvette Z06. Certified power rose slightly from to .