Editing Horsepower (section)

==Definitions==

===Imperial horsepower===
Assuming the third [[General Conference on Weights and Measures|CGPM]] (1901, CR 70) definition of [[standard gravity]], {{nowrap|1=''g''<sub>n</sub> = 9.80665 m/s<sup>2</sup>}}, is used to define the pound-force as well as the kilogram force, and the [[international avoirdupois pound]] (1959), one imperial horsepower is:

:{|
|-
|1&nbsp;hp
|≡ 33,000&nbsp;ft·lbf/min
| colspan="2" |by definition
|-
|
|= 550&nbsp;ft⋅lbf/s
|since
|1 min = 60 s
|-
|
|= 550 × 0.3048 × 0.45359237 m⋅[[kilogram-force|kgf]]/s
|since
|1&nbsp;ft ≡ 0.3048 m and 1&nbsp;lb ≡ 0.45359237&nbsp;kg
|-
|
|= 76.0402249068&nbsp;kg<sub>f</sub>⋅m/s
|
|
|-
|
|= 76.0402249068 × 9.80665&nbsp;kg⋅m<sup>2</sup>/s<sup>3</sup>
|since
|''g'' = 9.80665&nbsp;m/s<sup>2</sup>
|-
|
|= 745.69987158227022 W ≈ 745.700 W
|since
|1 W ≡ 1 [[joule|J]]/s = 1 [[Newton (unit)|N]]⋅m/s = 1 (kg⋅m/s<sup>2</sup>)⋅(m/s)
|}

Or given that 1&nbsp;hp = 550&nbsp;ft⋅lbf/s, 1&nbsp;ft = 0.3048&nbsp;m, 1&nbsp;lbf&nbsp;≈ 4.448&nbsp;N, 1&nbsp;J = 1&nbsp;N⋅m, 1&nbsp;W = 1&nbsp;J/s: 1&nbsp;hp ≈ 745.7&nbsp;W

==={{anchor|Metric horsepower|Metric|PS|cv|hk|pk|ks|ch}} Metric horsepower (PS, KM, cv, hk, pk, k, ks, ch)===
[[File:Horsepower plain.svg|thumb|right|One ''metric horsepower'' is needed to lift 75&nbsp;[[kilogram]]s by 1&nbsp;[[metre]] in 1&nbsp;[[second]].]]

The various units used to indicate this definition (''PS'', '' KM'', ''cv'', ''hk'', ''pk'', ''k'', ''ks'' and ''ch'') all translate to ''horse power'' in English. British manufacturers often intermix metric horsepower and mechanical horsepower depending on the origin of the engine in question.<ref>{{cite web | url = https://ateupwithmotor.com/terms-technology-definitions/gross-versus-net-horsepower/ | archiveurl = https://web.archive.org/web/20221202230849/https://ateupwithmotor.com/terms-technology-definitions/gross-versus-net-horsepower/ | archivedate = 2022-12-02 | title = Understanding Gross Versus Net Horsepower Ratings | work = Ate Up With Motor | date = 2008-04-15 | first = Aaron | last = Severson }}</ref>

[[Deutsches Institut für Normung|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:<ref>{{cite web |url=http://www.ptb.de/cms/fileadmin/internet/Themenrundgaenge/hueterin_der_einheiten/einheiten_d.pdf |title=Die gesetzlichen Einheiten in Deutschland |language=de |page=6 |trans-title=List of units of measure in Germany |publisher=Physikalisch-Technische Bundesanstalt (PTB) |access-date=13 November 2012 }}</ref> {{nowrap|75&nbsp;kg × 9.80665&nbsp;m/s<sup>2</sup> × 1&nbsp;m / 1&nbsp;s}} = 75&nbsp;[[Kilogram-force|{{abbr|kgf|Kilogram-force}}]]⋅m/s = 1&nbsp;PS. This is equivalent to 735.49875&nbsp;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.<ref>{{cite web
|url=http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=DD:I:1971_III:31971L0354:EN:PDF | archive-url=https://web.archive.org/web/20210306071848/https://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX%3A31971L0354 | archive-date=2021-03-06
|title=Council Directive 71/354/EEC: On the approximation of the laws of the Member States relating to units of measurement |publisher=The Council of the European Communities
|date=18 October 1971 }}</ref>

Other names for the metric horsepower are the Italian {{lang|it|cavallo vapore (cv)}}, Dutch {{lang|nl|paardenkracht (pk)}}, the French {{lang|fr|cheval-vapeur (ch)}}, the Spanish {{lang|es|caballo de vapor}} and Portuguese {{lang|pt|cavalo-vapor (cv)}}, the Russian {{lang|ru|лошадиная сила (л.&nbsp;с.)}}, the Swedish {{lang|sv|hästkraft (hk)}}, the Finnish {{lang|fi|hevosvoima (hv)}}, the Estonian {{lang|et|hobujõud (hj)}}, the Norwegian and Danish {{lang|da|hestekraft (hk)}}, the Hungarian {{lang|hu|lóerő (LE)}}, the Czech {{lang|cs|koňská síla}} and Slovak {{lang|sk|konská sila (k}} or {{lang|sk|ks}}), the Serbo-Croatian {{lang|sh|konjska snaga (KS)}}, the Bulgarian {{lang|bg|конска сила}}, the Macedonian {{lang|mk|коњска сила (KC)}}, the Polish {{lang|pl|koń mechaniczny (KM)}} ({{literal translation|mechanical horse}}), Slovenian {{lang|sl|konjska moč (KM)}}, the Ukrainian {{lang|uk|кінська сила (к.&nbsp;с.)}}, the Romanian {{lang|ro|cal-putere (CP)}}, and the German {{lang|de|Pferdestärke (PS)}}.

In the 19th century, [[French Revolution|revolutionary-era France]] had its own unit used to replace the ''cheval vapeur'' (horsepower); based on a 100 [[kilogram-force|kgf]]⋅m/s standard, it was called the [[poncelet]] and was abbreviated ''p''.

===Tax horsepower===
{{Main|Tax horsepower}}

Tax or fiscal horsepower is a non-linear rating of a motor vehicle for tax purposes.<ref>{{cite web |url=http://www.numericana.com/answer/units.htm |title=Measurements, Units of Measurement, Weights and Measures |website=numericana.com |access-date=2011-07-18 }}</ref> Tax horsepower ratings were originally more or less directly related to the size of the engine; but as of 2000, many countries changed over to systems based on {{CO2}} emissions, so are not directly comparable to older ratings.{{Citation needed|date=December 2023}} The [[Citroën 2CV]] is named for its French fiscal horsepower rating, "deux chevaux" (2CV).{{Citation needed|date=December 2023}}

===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. Wattage is calculated by multiplying voltage by amperage and power factor.<ref>{{cite book |first=H. Wayne |last=Beatty |title=Handbook of Electric Power Calculations |edition=3rd |publisher=McGraw Hill |year=2001 |isbn=0-07-136298-3 |pages=6–14}}</ref>

===Hydraulic horsepower===
Hydraulic horsepower can represent the power available within [[hydraulic machinery]], power through the down-hole nozzle of a [[drilling rig]],<ref name="Schlumberger, Hydraulic horsepower" >{{cite web |title=Hydraulic Horsepower |work=Oilfield Glossary |publisher=Schlumberger |url=http://www.glossary.oilfield.slb.com/Terms/h/hydraulic_horsepower.aspx }}</ref> or can be used to estimate the mechanical power needed to generate a known hydraulic flow rate.

It may be calculated as<ref name="Schlumberger, Hydraulic horsepower" />
: <math>\text{hydraulic power} = \frac{\text{pressure} \times \text{volumetric flow rate}}{1714},</math>
where pressure is in psi, and flow rate is in [[US gallon]]s per minute.

Drilling rigs are powered mechanically by rotating the drill pipe from above. Hydraulic power is still needed though, as 1 500 to 5 000 W are required to push [[drilling mud|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]].<ref name="Schlumberger, Hydraulic horsepower" />

When using SI units, the equation becomes coherent and there is no dividing constant.

: <math>\text{hydraulic power} = \text{pressure} \times \text{volumetric flow rate}</math>
where pressure is in pascals (Pa), and flow rate is in [[cubic metre]]s per second (m<sup>3</sup>).

===Boiler horsepower===
Boiler horsepower is a [[steam boiler|boiler]]'s capacity to deliver [[steam]] to a [[steam engine]] and is not the same unit of power as the 550&nbsp;ft lb/s definition. One boiler horsepower is equal to the thermal energy rate required to evaporate {{convert|34.5|lb}} of fresh water at {{convert|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.<ref>{{citation | first=Robert | last=McCain Johnston | title=Elements of Applied Thermodynamics | publisher=Naval Institute Press | date=1992 | isbn=1557502269 | page=503 }}</ref>

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 {{convert|30|lb}} of water per hour, based on feed water at {{convert|100|°F}}, and saturated steam generated at {{cvt|70|psi}}. This original definition is equivalent to a boiler heat output of {{cvt|33,485|Btu/h|kW}}.{{cn|date=January 2025}} A few years later in 1884, the [[American Society of Mechanical Engineers|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" {{convert|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 {{cvt|33,469|Btu/h|kW}}.{{cn|date=January 2025}} Present industrial practice is to define "boiler horsepower" as a boiler thermal output equal to {{cvt|33,475|Btu/h|kW}},{{cn|date=January 2025}} 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===
{{See also|Power at rail}}

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 the locomotive keeps a continuous record of the [[drawbar (haulage)|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 ({{mvar|F}}) is measured in pounds-force (lbf) and speed ({{mvar|v}}) is measured in miles per hour (mph), then the drawbar power ({{mvar|P}}) in horsepower (hp) is

<math display=block>\{P\}_\mathrm{hp} = \frac{\{F\}_\mathrm{lbf} \{v\}_\mathrm{mph}}{375}.</math>

Example: How much power is needed to pull a drawbar load of 2,025 pounds-force at 5 miles per hour?

<math display=block>\{P\}_\mathrm{hp} = \frac{2025 \times 5}{375} = 27.</math>

The constant 375 is because 1&nbsp;hp = 375&nbsp;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 {{math|1=''P'' = ''Fv''}}.

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?

<math display=block>\{P\}_\mathrm{hp} = \frac{4000 \times 400}{375} = 4266.7.</math>

===RAC horsepower (taxable horsepower)===
{{See also|Tax 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 horsepower|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.<ref>{{citation | url=https://books.google.com/books?id=JOg2WxEye1QC&pg=PA409 | title=Official Year Book of the Commonwealth of Australia | volume=44 | date=1958 | page=409 | first=S.R. | last=Carver | publisher=Commonwealth Bureau of Census and Statistics | location=Canberra }}</ref><ref>{{citation | url=https://books.google.com/books?id=wkP3icv3ilcC&pg=RA12-PA39 | title=Motor-Vehicle Taxation and Regulations in Foreign Countries | work=The Balance of International Payments of the United States in 1922- | first=C.E. | last=Haynes | publisher=Bureau of Foreign and Domestic Commerce | date=1923 | volume=Trade Information Bulletin no. 463 | pages=39–42 }}</ref> The RAC formula was sometimes applied in British colonies as well, such as [[Kenya Colony|Kenya (British East Africa)]].<ref>{{harvp|Haynes|1923|p=[https://books.google.com/books?id=wkP3icv3ilcC&pg=RA12-PA43 43]}}</ref>

: <math>\text{RAC h.p.} = \frac{D \times D \times n}{2.5}</math>

where

: ''D'' is the diameter (or [[Bore (engine)|bore]]) of the cylinder in inches,
: ''n'' is the number of cylinders.<ref>{{Cite web |url=http://www.designchambers.com/wolfhound/wolfhoundRACHP.htm |title=The RAC HP (horsepower) Rating - Was there any technical basis? |first=Richard |last=Hodgson |website=WolfHound.org.uk |access-date=2007-08-11 }}</ref>

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 (bore smaller than stroke), which tended to impose an artificially low limit on [[rotational speed]], 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 Cars|Jaguar's]] 3.4-litre XK engine of the 1950s had six cylinders with a bore of {{convert|83|mm|in|abbr=on|sigfig=3}} and a stroke of {{convert|106|mm|in|abbr=on|sigfig=3}},<ref>{{Cite web |first=Dan |last=Mooney |url=http://www.classicjaguar.com/xkengine.html |title=The XK engine by Roger Bywater |website=ClassicJaguar.com |access-date=2010-03-13 |url-status=dead |archive-url=https://web.archive.org/web/20100223052130/http://www.classicjaguar.com/xkengine.html |archive-date=2010-02-23 }}</ref> where most American automakers had long since moved to oversquare (large bore, short stroke) [[V8 engine]]s. See, for example, the early [[Chrysler Hemi engine#First generation: FirePower|Chrysler Hemi engine]].