Horsepower (hp) is a unit of measurement of power, or the rate at which work is done, usually in reference to the output of engines or motors. There are many different standards and types of horsepower. Two common definitions used today are the imperial horsepower, abbreviated hp or bhp, which is about , and the metric horsepower, also represented as cv or PS, which is approximately . The electric horsepower, hpE, is exactly , while the boiler horsepower is 9809.5 or 9811 watts, depending on the exact year.
The term was adopted in the late 18th century by Scottish engineer James Watt to compare the output of steam engines with the power of draft horses. It was later expanded to include the output power of other power-generating machinery such as piston engines, turbines, and electric motors. The definition of the unit varied among geographical regions. Most countries now use the SI unit watt for measurement of power. With the implementation of the EU Directive 80/181/EEC on 1 January 2010, the use of horsepower in the EU is permitted only as a supplementary unit.
History
The development of the steam engine provided a reason to compare the output of horses with that of the engines that could replace them. In 1702, Thomas Savery wrote in The Miner's Friend:
So that an engine which will raise as much water as two horses, working together at one time in such a work, can do, and for which there must be constantly kept ten or twelve horses for doing the same. Then I say, such an engine may be made large enough to do the work required in employing eight, ten, fifteen, or twenty horses to be constantly maintained and kept for doing such a work...
The idea was later used by James Watt to help market the Watt steam engine, an improved Newcomen steam engine. He had previously agreed to take royalties of one-third of the savings in coal from the older Newcomen steam engines. This royalty scheme did not work with customers who did not have existing steam engines but used horses instead.
Watt determined that a horse could turn a mill wheel 144 times in an hour (or 2.4 times a minute).Hart-Davis, Adam (2012). Engineers. Dorling Kindersley. p. 121. The wheel was in radius; therefore, the horse travelled feet in one minute. Watt judged that the horse could pull with a force of . So:
Engineering in History recounts that John Smeaton initially estimated that a horse could produce per minute. John Desaguliers had previously suggested per minute, and Thomas Tredgold suggested per minute. "Watt found by experiment in 1782 that a 'brewery horse' could produce per minute." James Watt and Matthew Boulton standardized that figure at per minute the next year.
A common legend states that the unit was created when one of Watt's first customers, a brewer, specifically demanded an engine that would match a horse, and chose the strongest horse he had and driving it to the limit. In that legend, Watt accepted the challenge and built a machine that was actually even stronger than the figure achieved by the brewer, and the output of that machine became the horsepower.
In 1993, R. D. Stevenson and R. J. Wassersug published correspondence in Nature summarizing measurements and calculations of peak and sustained work rates of a horse. Citing measurements made at the 1925 Iowa State Fair, they reported that the peak power over a few seconds has been measured to be as high as and also observed that for sustained activity, a work rate of about per horse is consistent with agricultural advice from both the 19th and 20th centuries and also consistent with a work rate of about four times the basal rate expended by other vertebrates for sustained activity.
When considering human-powered equipment, a healthy human can produce about briefly (see orders of magnitude) and sustain about indefinitely; trained athletes can manage up to about brieflyEugene A. Avallone et al., (ed), Marks' Standard Handbook for Mechanical Engineers 11th Edition , Mc-Graw Hill, New York 2007, , page 9-4. and for a period of several hours. The Jamaican sprinter Usain Bolt produced a maximum of 0.89 seconds into his 9.58 second sprint world record in 2009.
In 2023 a group of engineers modified a dynamometer to be able to measure how much power a horse can produce. This horse was measured to .
Calculating power When torque is in pound-foot units, rotational speed is in rpm, the resulting power in horsepower is
The constant 5252 is the rounded value of (33,000 ft⋅lbf/min)/(2π rad/rev).
When torque is in inch-pounds,
The constant 63,025 is the approximation of
Definitions
Imperial horsepower Assuming the third CGPM (1901, CR 70) definition of standard gravity, , is used to define the pound-force as well as the kilogram force, and the international avoirdupois pound (1959), one imperial horsepower is:
|1 hp |≡ 33,000 ft·lbf/min | colspan="2" |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 1 lb ≡ 0.45359237 kg
|= 76.0402249068 kgf⋅m/s
|= 76.0402249068 × 9.80665 kg⋅m2/s3 |since |g = 9.80665 m/s2
|= 745.69987158227022 W ≈ 745.700 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 lbf ≈ 4.448 N, 1 J = 1 N⋅m, 1 W = 1 J/s: 1 hp ≈ 745.7 W
Metric horsepower (PS, KM, cv, hk, pk, k, ks, ch)
The various units used to indicate this definition (PS, KM, cv, hk, pk, k, ks and ch) all translate to horsepower in English. British manufacturers often intermix metric horsepower and mechanical horsepower depending on the origin of the engine in question.
DIN 66036 defines one metric horsepower (Pferdestärke, or PS) as the power to raise a mass of 75 kilograms against the Earth's gravitational force over a distance of one metre in one second: = 75 ⋅m/s = 1 PS. This is equivalent to 735.49875 W, or 98.6% of an imperial horsepower. In 1972, the PS was replaced by the kilowatt as the official power-measuring unit in EEC directives.
Other names for the metric horsepower are the Italian , Dutch , the French , the Spanish and Portuguese , the Russian , the Swedish , the Danish and Norwegian , the Finnish , the Estonian , the Hungarian , the Czech and Slovak or ), the Serbo-Croatian , the Bulgarian , the Macedonian , the Polish (), Slovenian , the Ukrainian , the Romanian , and the German .
In the 19th century, revolutionary-era France had its own unit used to replace the cheval vapeur (horsepower); based on a 100 kgf⋅m/s standard, it was called the poncelet and was abbreviated p.
Tax horsepower
Tax, or fiscal, horsepower is a non-linear rating of a motor vehicle for tax purposes. Tax-horsepower ratings were originally more or less directly related to engine displacements, but, , many countries have changed over to systems based on emissions so the current systems are not directly comparable to old tax horsepower. The Citroën 2CV is named for its French fiscal horsepower rating, (2CV).
Electrical horsepower Nameplates on electrical motors show their available shaft power output, not the electrical power input. This power output is ordinarily stated in watts or kilowatts. In the United States, the power output is stated in horsepower.
Hydraulic horsepower Hydraulic horsepower can be the power available within hydraulic machinery or power through the down-hole nozzle of a drilling rig, or it can be used as an estimate of the mechanical power needed to generate a given hydraulic flow rate.
It may be calculated as
where pressure is in psi and flow rate is in US gallons per minute.
Drilling rigs are powered mechanically by rotating the bit from above. Hydraulic power is still needed, though, as are required to push mud through the drill bit to clear waste rock. Additional hydraulic power may also be used to drive a down-hole mud motor to power directional drilling.
When using SI units, the equation becomes coherent and there is no dividing constant.
where pressure is in pascals (Pa), and flow rate is in cubic metres per second (m3/s).
Boiler horsepower Boiler horsepower is a boiler's capacity to deliver steam to a steam engine and is not the same unit of power as the 550 ft⋅lb/s definition. One boiler horsepower is equal to the thermal energy rate required to evaporate of fresh water at in one hour. In the early days of steam use, the boiler horsepower was roughly comparable to the horsepower of engines fed by the boiler.
The term boiler horsepower was originally developed at the Philadelphia Centennial Exhibition in 1876, where the best steam engines of that period were tested. The average steam consumption of those engines (per output horsepower) was determined to be the evaporation of of water per hour, based on feed water at , and saturated steam generated at . This original definition is equivalent to a boiler heat output of . A few years later in 1884, the ASME redefined the boiler horsepower as the thermal output equal to the evaporation of 34.5 pounds per hour of water "from and at" . This considerably simplified boiler testing, and provided more accurate comparisons of the boilers at that time. This revised definition is equivalent to a boiler heat output of . Present industrial practice is to define boiler horsepower as a boiler thermal output equal to , which is very close to the original and revised definitions.
Boiler horsepower is still used to measure boiler output in industrial boiler engineering in the US. Boiler horsepower is abbreviated BHP, which is also used in many places to symbolize brake horsepower.
Drawbar power
Drawbar power (dbp) is the power a railway locomotive has available to haul a train or an agricultural tractor to pull an implement. This is a measured figure rather than a calculated one. A special railway car called a dynamometer car coupled behind a locomotive keeps a continuous record of drawbar tension and speed. From these, the power generated can be calculated. To determine the maximum power available, a controllable load is required; it is normally a second locomotive with its brakes applied, in addition to a static load.
If the drawbar force () is measured in pounds-force (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 2,025 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 coherent SI units (watts, newtons, and metres per second), no constant is needed, and the formula becomes .
This formula may also be used to calculate the power of a jet engine, using the speed of the jet and the thrust required to maintain that speed.
Example: how much power is generated with a thrust of 4000 pounds at 400 miles per hour?
RAC horsepower (taxable horsepower)
This measure was instituted by the Royal Automobile Club and was used to denote the power of early 20th-century British cars. Many cars took their names from this figure (hence the Austin Seven and Riley Nine), while others had names such as "40/50 hp", which indicated the RAC figure followed by the true measured power.
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. The United Kingdom was not the only country that used the RAC rating; many states in Australia used RAC hp to determine taxation. The RAC formula was sometimes applied in British colonies as well, such as Kenya (British East Africa).
where
D is the diameter (or bore) of the cylinder in inches, n is the number of cylinders.