# Metric horsepower: Wikis

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Horsepower (HP) is the name of several units of measurement of power. The most common definitions equal between 735.5 to 746 watts. The horsepower is not recognized in the International System of Units (SI).

The horsepower was originally defined to compare the output of steam engines with the power of draft horses. The unit was widely adopted to measure the output of piston engines, turbines, electric motors, and other machinery. The definition of the unit varied between 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 January 1st, 2010, the use of horsepower in the EU is only permitted as supplementary unit.

The definition of the horsepower also has varied between different applications:

• The mechanical horsepower of 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 735.499 watts.
• The boiler horsepower is used for rating steam boilers and is equivalent to 34.5 pounds of water evaporated per hour at 212 degrees Fahrenheit, or 9,809.5 watts.
• One horsepower for rating electric motors is equal to 746 watts.
• 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.[1][2]
• The Royal Automobile Club (RAC) horsepower or British tax horsepower is an estimate based on several engine dimensions.

## History of the unit

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 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.[3] 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). The wheel was 12 feet 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:

$power = \frac{work}{time} = \frac{force \times distance}{time} = \frac{(180 \mbox{ lbf})(2.4 \times 2 \pi \times 12 \mbox{ ft})}{1\ \mbox{min}}=32,572 \frac{\mbox{ft} \cdot \mbox{lbf}}{\mbox{min}}.$

This was rounded to an even 33,000 ft·lbf/min.[4]

Others recount that 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. Watt then judged a horse was 50% more powerful than a pony and thus arrived at the 33,000 ft·lbf/min figure.[citation needed]

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.[5]

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. Regardless, comparison with a horse proved to be an enduring marketing tool.[citation needed]

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[6] and 0.3 hp for a period of several hours.

### Horsepower from a horse

R. D. Stevenson and R. J. Wassersug published an article in Nature 364, 195-195 (15 July 1993) calculating the upper limit to an animal's power output. The peak power over a few seconds has been measured to be as high as 14.9 hp. However, for longer periods, an average horse produces less than one horsepower.

## Current definitions

The following definitions have been widely used:

 Mechanical horsepower hp(I) ≡ 33,000 ft-lbf/min = 550 ft·lbf/s = 745.6999 W Metric horsepower hp(M) ≡ 75 kgf·m/s ≡ 735.49875 W Electrical horsepower hp(E) ≡ 746 W Boiler horsepower hp(S) ≡ 33,475 BTU/h = 9,809.5 W Hydraulic horsepower = flow rate (US gal/min) × pressure ([[lbf/in2|psi]]) × 7/12,000 = 550 ft·lbf/s = 745.6999 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. The formula given above is for conversion to mechanical horsepower from the factors acting on a hydraulic system.

### Mechanical horsepower

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 = 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 lbf ≈ 4.448 N, 1 J = 1 N·m, 1 W = 1 J/s: 1 hp = 746 W

### Metric horsepower

Metric horsepower began in Germany in the 19th century and became popular across Europe and Asia. The various units used to indicate this definition (PS, CV, hk, pk, 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.

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.[citation needed]

#### PS

This unit (German: Pferdestärke = horse strength) is no longer a statutory unit, but is still commonly used in Europe, South America and Japan, especially by the automotive and motorcycle industry. It was adopted throughout continental Europe with designations equivalent to the English horsepower, but mathematically different from the British unit. It is defined by the Physikalisch-Technische Bundesanstalt (PTB)[7] in Braunschweig as exactly:

1 PS = 75 kilopond-meters per second
(75 kp·m/s)×(9.80665 N/kp) = 735.49875 N·m/s ≈ 735.5 N·m/s ≈ 735.5 W ≈ 0.7355 kW ≈ 0.98632 hp (SAE)

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.

#### pk, hk, hv, LE, k/ks, KM, CP

The Dutch paardenkracht (pk), the Swedish hästkraft (hk), the Finnish hevosvoima (hv), the Norwegian and Danish hestekraft (hk), the Hungarian lóerő (LE), the Czech koňská síla and Slovak koňská sila (k or ks), the Serbo-Croatian konjska snaga (k or ks), the Polish koń mechaniczny (KM) and the Romanian cal-putere (CP) all equal the German Pferdestärke (PS).

#### CV and cv

In Italian (Cavalli), Spanish (Caballos de vapor), 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 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.[8] 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 CO2 emitted in grams per kilometre. The term for CO2 measurements has only been included in the definition 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).

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.

#### ch

This is a French unit for automobile power. The symbol ch is short for chevaux (horses). It has the same definition as the German PS, and is approximatively equal to 735.5 W.

### Boiler horsepower

A boiler horsepower is used for boilers in various industrial applications, however it is considered an antiquated term and is not used in modern power plants. It is equal to a boiler thermal output of 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 term 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 lb/h of water, based on feedwater at 100 °F (38 °C), and saturated steam generated at 70 psi (480 kPa) gauge pressure. This original definition is equivalent to a boiler heat output of 33,485 BTU/h. In 1884, the ASME re-defined the boiler horsepower as the thermal output equal to the evaporation of 34.5 lb/h 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/h, which is very close to the original and revised definitions.

The amount of power that can be obtained by a steam engine or steam turbine based on boiler horsepower varies so widely that use of the term is entirely obsolete for these purposes. The term makes no distinction as to the steam pressure or temperature which is produced (both of which significantly influence engine/turbine output), it merely defines a thermal output of a boiler. Smaller steam engines often require several boiler horsepower to make one horsepower, and modern steam turbines can make power with as little as about 0.15 hp (boiler) thermal output per actual horsepower developed.

### Electrical horsepower

The electrical horsepower is used by the electrical industry for electrical machines and is defined as exactly 746 W. The nameplates on electrical motors show their power output, not their power input.

### Relationship with torque

For a given torque and speed, the power may be calculated. The standard equation relating torque in foot-pounds, rotational speed in RPM and horsepower is:

$P [ {\rm hp}] = {(\Tau [{\rm ft \cdot lbf}]) (\omega [{\rm RPM}]) \over 5252}$

Where P is power, Τ is torque, and ω is rotations per minute. The constant 5252 comes from (33,000 ft·lbf/min)/(2π rad./rev.).

See torque.

### Drawbar horsepower

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 ($\scriptstyle F$) is measured in pound-force (lbf) and speed ($\scriptstyle v$) is measured in miles per hour (mph), then the drawbar power ($\scriptstyle P$) in horsepower (hp) is:

$P = {Fv\over 375}$

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

$P = {{2025 \times 5 } \over 375} = 27$

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 $\scriptstyle P = Fv$.

### RAC horsepower (taxable horsepower)

This measure was instituted by the Royal Automobile Club in Britain 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.

$RAC h.p. = {D^2 * n}/2.5 \,$
where
D is the diameter (or bore) of the cylinder in inches
n is the number of cylinders [9]

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 3.4-litre XK engine of the 1950s had six cylinders with a bore of 83 mm (3.27 in) and a stroke of 106 mm (4.17 in),[10] where most American automakers had long since moved to oversquare (wide bore, short stroke) V-8s (see, for example, the early Chrysler Hemi).

## Measurement

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.

In general:

Nominal is derived from the size of the engine and the piston speed and is only accurate at a pressure of 48 kPa (7 psi).[11]
Indicated or gross horsepower (theoretical capability of the engine)
minus frictional losses within the engine (bearing drag, rod and crankshaft windage losses, oil film drag, etc.), equals
Brake / net / crankshaft horsepower (power delivered directly to and measured at the engine's crankshaft)
minus frictional losses in the transmission (bearings, gears, oil drag, windage, etc.), equals
Shaft horsepower (power delivered to and measured at the output shaft of the transmission, when present in the system)
minus frictional losses in the universal joint/s, differential, wheel bearings, tire and chain, (if present), equals
Effective, True (thp) or commonly referred to as wheel horsepower (whp)

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 brake mean effective pressure (BMEP). This is a coefficient of theoretical brake horsepower and cylinder pressures during combustion.

### Nominal horsepower

Nominal horsepower (nhp) is an early Nineteenth Century rule of thumb used to estimate the power of steam engines.

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 48 kPa (7 psi) and for the piston speed to be of the order of 54–75 m/min.[11]

### Indicated horsepower

Indicated horsepower (ihp) is the theoretical power of a reciprocating engine if it is completely frictionless in converting the expanding gas energy (piston pressure × displacement) in the cylinders. It is calculated from the pressures developed in the cylinders, measured by a device called an engine indicator – hence indicated horsepower. As the piston advances throughout its stroke, the pressure against the piston generally decreases, and the indicator device usually generates a graph of pressure vs stroke within the working cylinder. From this graph the amount of work performed during the piston stroke may be calculated. It was the figure normally used for steam engines in the 19th century but is misleading because the mechanical efficiency of an engine means that the actual power output may only be 70% to 90% of the indicated horsepower.

### Brake horsepower

Brake horsepower (bhp) is the measure of an engine's horsepower without the loss in power caused by the gearbox, alternator, differential, water pump, and other auxiliary components such as power steering pump, muffled exhaust system, etc. Brake refers to a device which was used to load an engine and hold it at a desired RPM. During testing, the output torque and rotational speed were measured to determine the brake horsepower. Horsepower was originally measured and calculated by use of the indicator (a James Watt invention of the late 18th century), and later by means of a De Prony brake connected to the engine's output shaft. More recently, an engine dynamometer is used instead of a De Prony brake. The output delivered to the driving wheels is less than that obtainable at the engine's crankshaft.

### British horsepower

The acronym bhp may also be used for British horsepower, which has the same definition as the American SAE gross brake horsepower: 33,000 lb·ft/min. More information on American SAE horsepower measurements is below.

### SAE horsepower

#### SAE gross crankshaft horsepower

Prior to the 1972 model year, American automakers rated and advertised their engines in brake horsepower (bhp), frequently referred to as SAE gross horsepower, because it was measured in accord with the protocols defined in SAE standards J245 and J1995. As with other brake horsepower test protocols, SAE gross hp was measured using a stock test engine, generally running with few belt-driven accessories and sometimes fitted with long tube (test headers) in lieu of the OEM exhaust manifolds. The atmospheric correction standards for barometric pressure, humidity and temperature for testing were relatively idealistic.

#### SAE net crankshaft horsepower

In the United States, the term bhp fell into disuse in 1971-72, as automakers began to quote power in terms of SAE net horsepower in accord with SAE standard J1349. Like SAE gross and other brake horsepower protocols, SAE Net hp is measured at the engine's crankshaft, and so does not account for transmission losses. However, the SAE net hp testing protocol calls for standard production-type belt-driven accessories, air cleaner, emission controls, exhaust system, and other power-consuming accessories. This produces ratings in closer alignment with the power produced by the engine as it is actually configured and sold.

#### SAE certified crankshaft horsepower

In 2005, the SAE introduced a new test protocol for engine horsepower and torque.[12] The new protocol eliminates some of the flexibility in power measurement, and requires an independent observer present when engines are measured. The test is voluntary, but engines completing it can be advertised as SAE-certified.

A few manufacturers such as Honda and Toyota switched to the new ratings immediately, with multi-directional results; the rated output of Cadillac's supercharged Northstar V8 jumped from 440 hp (330 kW) to 469 hp (350 kW) under the new tests, while the rating for Toyota's Camry 3.0 L 1MZ-FE V6 fell from 210 hp (160 kW) to 190 horsepower (140 kW). The ES330 and Camry SE V6 were previously rated at 225 hp but the ES330 dropped to 218 hp while the Camry declined to 210 hp. 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 500 hp (370 kW) to 505 hp (377 kW).

### DIN horsepower

DIN horsepower is the power measurement protocol in the German DIN standard 70020. Because the German word for horsepower is Pferdestärke, in Germany it is commonly abbreviated to PS. DIN hp is measured at the engine's output shaft, and is usually expressed in metric (Pferdestärke) rather than mechanical horsepower.

### ECE hp

ECE R24 is the European standard for measuring engine output.[13] It is quite similar to the DIN 70020 standard, but with different requirements for connecting an engine's fan during testing. ECE is seen as slightly more liberal than DIN, and ECE figures tend to be slightly higher than DIN.[citation needed]

### 97/68/EC

97/68/EC is a European Union standard, generally very similar to ISO-14396.

### ISO 14396

ISO 14396 is a new standard from the ISO for all engines not intended for on-road use.

### Shaft horsepower

Shaft horsepower (shp) is the power delivered to the propeller shaft of a ship or an aircraft powered by a piston engine or a turbine engine (the combination of turbine engine and propeller commonly called a turboprop). This may be measured, or estimated from the indicated horsepower given a standard figure for the losses in the transmission (typical figures are around 10%). This measure is uncommon in the automobile industry, because drive train losses can be significant.

### True / Effective horsepower (chassis dynamometer)

True horsepower (THP), Effective horsepower (EHP) and wheel horsepower (whp) are the brake horsepower converted to useful work. In the case of a road vehicle this is the power actually turned into forward motion as measured on a chassis dynamometer. Power available at the road is generally 10% to 20% less than the engine's actual bhp crankshaft rating due to vehicle related parasitic losses, much of which is due to the vehicle's rubber tires rather than true transmission losses. Aside from adding simple dyno parasitic drag, there are no additional power adding factors and power is corrected using appropriate atmospheric correction factors.[14]

For railway locomotives the terms drawbar horsepower or equivalent drawbar horsepower (EDHP) refer to the power available to haul a train. This is synonymous with the Effective horsepower.[15] This figure takes into account the horsepower needed to move the locomotive, which is not available for hauling the train. The rail horsepower is the power at the wheels of a locomotive, directly comparable to the wheel horsepower of a road vehicle.

### Dynojet horsepower / DJHP (chassis dynamometer)

Dynojet horsepower is a marketing hp scale that was created to read higher than True / Effective horsepower.[16] They were successful in getting the magazines to accept the inflated numbers and are now the de facto standard for retail magazines. In the 100 djhp area, djhp is about 15% higher than True and in the 200 djhp, it's 18% to 20% higher.[14] Most chassis dyno results that are published by magazines are djhp, causing confusion, as there is True hp, djhp and "estimated djhp". Commonly, the wide range of power sometimes reported is due to the error of djhp vs "estimated djhp" vs. the actual, unmodified True hp. DJHP is not "RWP" or "wheel power", it has its own factored up hp scale. Dynojet hp is always an inertia loaded sweep test.

Front-wheel drive cars (provided a transverse engine layout is used) suffer slightly lower coastdown losses due to the absence of the beveled crown and pinion gears used to change the drive direction in the back axle of a rear-wheel drive car.[17]

## References

1. ^ Horsepower, retrieved 2009 Feb 5
2. ^ "Conversion Factors", page F-313 of Handbook of Chemistry and Physics, 58th Edition, CRC Press Inc., Clevland, Ohio ISBN 0-8493-0458-X, 1977, Robert C. Weast (Ed.)
3. ^ "Math Words — horsepower". pballew.net/. Retrieved 2007-08-11.
4. ^ Tully, Jim (September 2002), Philadelphia Chapter Newsletter, American Society of Mechanical Engineers, retrieved 2007-08-11  (see the AMSE puzzler answer)
5. ^ Richard Shelton Kirby (August 1, 1990). Engineering in History. Dover Publications. p. 171. ISBN 0486264122. Retrieved 2007-08-11.
6. ^
7. ^ Die gesetzlichen Einheiten in Deutschland (in German) on PTB.de
8. ^ Measurements, Units of Measurement, Weights and Measures - numericana.com
9. ^ Richard Hodgson. "The RAC HP (horsepower) Rating - Was there any technical basis?". wolfhound.org.uk. Retrieved 2007-08-11.
10. ^ Dan Mooney. "The XK engine by Roger Bywater". Classicjaguar.com. Retrieved 2010-03-13.
11. ^ a b Brown, DK Before the ironclad, pub Conway, 1990, p188.
12. ^ SAE J2723 Certified Power
13. ^ ECE Regulation 24, Revision 2, Annex 10
14. ^ a b "True Rear Wheel Horsepower". Factorypro.com. Retrieved 2010-03-13.
15. ^ Clough, David; Beckett, Martin (1988) [1988]. BR Motive Power Performance. London, UK: Ian Allan Ltd. ISBN 0 7110 1718 2.
16. ^ "Dynojet horsepower explained V Max Factory Pro compete". Factorypro.com. Retrieved 2010-03-13.
17. ^ "Coastdown Losses". pumaracing.co.uk/. Retrieved 2009-01-23.