Definitions of term[edit]
One metric horsepower is needed to lift 75 kilograms (avg. body weight of a person) by 1 meter (3.28 feet) in 1 second.
Units called "horsepower" have differing definitions:
The mechanical horsepower, also known as imperial horsepower, of exactly 550 foot-pounds per second is approximately equivalent to 745.7 watts.
The metric horsepower of 75 kgf-m per second is approximately equivalent to 735.5 watts or 98.6% of an imperial mechanical horsepower.
The Pferdestärke PS (German translation of horsepower) is a name for a group of similar power measurements used in Germany around the end of the 19th century, all of about one metric horsepower in size.[4][5][6]
The boiler horsepower is used for rating steam boilers and is equivalent to 34.5 pounds (about 15.6 kg) of water evaporated per hour at 212 degrees Fahrenheit (100 degrees Celsius), or 9809.5 watts.
One horsepower for rating electric motors is equal to 746 watts.
Continental European electric motors used to have dual ratings, using a conversion rate of 0.735 kW for 1 hp
British Royal Automobile Club (RAC) horsepower is one of the tax horsepower systems adopted around Europe which make an estimate based on several engine dimensions.
History of the unit[edit]
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…[7]
The idea was later used by James Watt to help market his improved steam engine. He had previously agreed to take royalties of one third of the savings in coal from the older Newcomen steam engines.[8] 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).[9] The wheel was 12 feet (3.6576 meters) in radius; therefore, the horse travelled 2.4·2π·12 feet in one minute. Watt judged that the horse could pull with a force of 180 pounds. So:
P = \frac{W}{t} = \frac{F\cdot d}{t} = \frac{180\,\mathrm{lbf}\cdot 2.4 \cdot 2\, \pi \cdot 12\, \mathrm{ft}}{1\,\mathrm{min}} = 32,572 \cdot \frac{\mathrm{ft} \cdot \mathrm{lbf}}{\mathrm{min}}.
Watt defined and calculated the horsepower as 32,572 ft·lbf/min, which was rounded to an even 33,000 ft·lbf/min.[10]
Watt determined that a pony could lift an average 220 lbf (0.98 kN) 100 ft (30 m) per minute over a four-hour working shift.[11] Watt then judged a horse was 50% more powerful than a pony and thus arrived at the 33,000 ft·lbf/min figure.[12][better source needed] Engineering in History recounts that John Smeaton initially estimated that a horse could produce 22,916 foot-pounds per minute.[citation needed] John Desaguliers had previously suggested 44,000 foot-pounds per minute and Tredgold 27,500 foot-pounds per minute. "Watt found by experiment in 1782 that a 'brewery horse' could produce 32,400 foot-pounds per minute." James Watt and Matthew Boulton standardized that figure at 33,000 the next year.[13]
Most observers familiar with horses and their capabilities estimate that Watt was either a bit optimistic or intended to underpromise and overdeliver; few horses can maintain that effort for long.[citation needed] Regardless, comparison with a horse proved to be an enduring marketing tool.
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, but tried to cheat by taking the strongest horse he had and driving it to the limit. Watt, while aware of the trick, accepted the challenge and built a machine which was actually even stronger than the figure achieved by the brewer, and it was the output of that machine which became the horsepower.[14]
In 1993, R. D. Stevenson and R. J. Wassersug published an article calculating the upper limit to an animal's power output.[15] The peak power over a few seconds has been measured to be as high as 14.9 hp.[15] However, Stevenson and Wassersug observe that for sustained activity, a work rate of about 1 hp per horse is consistent with agricultural advice from both 19th and 20th century sources.[15]
When considering human-powered equipment, a healthy human can produce about 1.2 hp briefly (see orders of magnitude) and sustain about 0.1 hp indefinitely; trained athletes can manage up to about 2.5 hp briefly[16] and 0.3 hp for a period of several hours.
Calculating power[edit]
When torque T is in pound-foot units, rotational speed (N) is in rpm and power is required in horsepower:
P \mathrm{(hp)} = \frac{T\,\mathrm{ft}\cdot\mathrm{lbf} \times N\,\mathrm{rpm}}{5252}
The constant 5252 is the rounded value of (33,000 ft·lbf/min)/(2π rad/rev).
When torque T is in inch pounds:
P \mathrm{(hp)} = \frac{T\,\mathrm{in}\cdot\mathrm{lbf} \times N\,\mathrm{rpm}}{63{,}025}
The constant 63,025 is the approximation of
33{,}000\,\frac{\mathrm{ft}\cdot\mathrm{lbf}}{\mathrm{min}} \cdot \frac{ 12\,\frac{\mathrm{in}}{\mathrm{ft}}} {2\,\pi\mathrm{rad}} \approx 63{,}025.
If torque and rotational speed are expressed in coherent SI units, the power is calculated by ;
P = \tau\cdot\omega
where P is power in watts when \tau is torque in newton-metres, and \omega is angular speed in radians per second. When using other units or if the speed is in revolutions per unit time rather than radians, a conversion factor has to be included.
Current definitions[edit]
The following definitions have been widely used:
Mechanical horsepower
hp(I) ≡ 33,000 ft-lbf/min
= 550 ft·lbf/s
≈ 17696 lbm·ft2/s3
= 745.69987158227 W
Metric horsepower
hp(M) - also PS, ''cv, hk, pk, ks or ch ≡ 75 kgf·m/s
≡ 75 kg · 9.80665 m/s2 · 1 m/s
≡ 735.49875 W
Electrical horsepower
hp(E) ≡ 746 W
Boiler horsepower
hp(S) ≡ 33,475 BTU/h
= 9,812.5 W
Hydraulic horsepower = flow rate (US gal/min) × pressure (psi) × 7/12,000
or
= flow rate (US gal/min) × pressure (psi) / 1714
= 550 ft·lbf/s
= 745.69987158227 W
Air horsepower = flow rate ( cubic feet / minute) × pressure (inches water column) / 6,356
or
= 550 ft·lbf/s
= 745.69987158227 W
In certain situations it is necessary to distinguish between the various definitions of horsepower and thus a suffix is added: hp(I) for mechanical (or imperial) horsepower, hp(M) for metric horsepower, hp(S) for boiler (or steam) horsepower and hp(E) for electrical horsepower.
Hydraulic horsepower is equivalent to mechanical horsepower.[citation needed] The formula given above is for conversion to mechanical horsepower from the factors acting on a hydraulic system.
Mechanical horsepower[edit]
Assuming the third CGPM (1901, CR 70) definition of standard gravity, gn=9.80665 m/s2, is used to define the pound-force as well as the kilogram force, and the international avoirdupois pound (1959), one mechanical horsepower is:
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 1 lb = 0.45359237 kg
= 76.0402249068 kgf·m/s
= 76.0402249068×9.80665 kg·m2/s3 since g = 9.80665 m/s2
= 745.69987158227 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 ≈ 746 W
Metric horsepower (PS, cv, hk, pk, ks, ch)[edit]
The various units used to indicate this definition (PS, cv, hk, pk, ks and ch) all translate to horse power in English, so it is common to see these values referred to as horsepower or hp in the press releases or media coverage of the German, French, Italian, and Japanese automobile companies. British manufacturers often intermix metric horsepower and mechanical horsepower depending on the origin of the engine in question. Sometimes the metric horsepower rating of an engine is conservative enough so that the same figure can be used for both 80/1269/EEC with metric hp and SAE J1349 with imperial hp.
DIN 66036 defines one metric horsepower 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;[17] this is equivalent to 735.49875 W or 98.6% of an imperial mechanical horsepower.
In 1972, the PS was rendered obsolete by EEC directives, when it was replaced by the kilowatt as the official power measuring unit.[18] It is still in use for commercial and advertising purposes, in addition to the kW rating, as many customers are still not familiar with the use of kilowatts for engines.
Other names for the metric horsepower are the Dutch paardenkracht (pk), the French cheval (ch), the Portuguese cavalo-vapor (cv), the Russian Лошадиная сила (лс), the Swedish hästkraft (hk), the Finnish hevosvoima (hv), the Norwegian and Danish hestekraft (hk), the Hungarian lóerő (LE), the Czech koňská síla and Slovak konská sila (k or ks), the Bosnian/Croatian/Serbian konjska snaga (KS), the Bulgarian Конска сила, the Macedonian Коњска сила (KC), the Polish koń mechaniczny (KM), Slovenian konjska moč (KM) and the Romanian cal-putere (CP), which all equal the German Pferdestärke (PS).
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.
French and Italian tax horsepower (CV)[edit]
Main article: Tax horsepower
In addition, the capital form CV is used in Italy and France as a unit for tax horsepower, short for, respectively, cavalli vapore and chevaux vapeur (steam horses). CV is a non-linear rating of a motor vehicle for tax purposes.[19] The CV rating, or fiscal power, is \scriptstyle\left(\tfrac{P}{40}\right)^{1.6} + \tfrac{U}{45}, where P is the maximum power in kilowatts and U is the amount of carbon dioxide (CO2) emitted in grams per kilometre. The term for CO2 measurements has been included in the definition only since 1998, so older ratings in CV are not directly comparable. 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).
Electrical horsepower[edit]
The horsepower used for electrical machines is defined as exactly 746 W.[20] In the US, nameplates on electrical motors show their power output in hp, not their power input. Outside the United States watts or kilowatts are generally used for electric motor ratings and in such usage it is the output power that is stated.
Boiler horsepower[edit]
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 34.5 lb of fresh water at 212 °F 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.[21]
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 30 pounds of water per hour, based on feed water at 100 °F, and saturated steam generated at 70 PSIG. This original definition is equivalent to a boiler heat output of 33,485 Btu/hr. Years later in 1884, the ASME re-defined the boiler horsepower as the thermal output equal to the evaporation of 34.5 pounds per hour of water "from and at" 212 °F. 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 33,469 Btu/hr. Present industrial practice is to define "Boiler Horsepower" as a boiler thermal output equal to 33,475 Btu/hr, which is very close to the original and revised definitions.
Boiler horsepower is still used to measure boiler output in industrial boiler engineering in Australia, the US, and New Zealand. Boiler horsepower is abbreviated BHP, not to be confused with brake horsepower, below, which is also called BHP.
Drawbar horsepower[edit]
See also: Power at rail
Drawbar horsepower (dbhp) 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 the locomotive keeps a continuous record of the drawbar pull exerted, and the 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 (F) is measured in pounds-force (lbf) and speed (v) is measured in miles
