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## Horsepower

Horsepower (hp) is the name of several units of measurement of power, the rate at which work is done. The most common conversion factor, especially for electrical power, is 1 hp = 746 watts. 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 types of piston engines, as well as turbines, electric motors and other machinery.[1][2] 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 1, 2010, the use of horsepower in the EU is only permitted as supplementary unit.

## Definitions of term

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 735.499 watts.
• The Pferdest rke 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.[3][4][5]
• 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.
• 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

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[6]: "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.[7] 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 2 12 feet in one minute. Watt judged that the horse could pull with a force of 180 pounds. So:

\mathit{power} = \frac{\mathit{work}}{\mathit{time}} = \frac{\mathit{force} \times \mathit{distance}}{\mathit{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.[8]

Others recount that Watt determined that a pony could lift an average 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.[9] 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.[10]

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.

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[11] [12] and 0.3 hp for a period of several hours.

### Horsepower from a horse

In 1993, R. D. Stevenson and R. J. Wassersug published an article calculating the upper limit to an animal's power output.[13] The peak power over a few seconds has been measured to be as high as 14.9 hp. 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.

## Current definitions

The following definitions have been widely used:

 Mechanical horsepower hp(I) 33,000 ft-lbf/min = 550 ft lbf/s = 745.699872 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 (psi) 7/12,000 or = flow rate (US gal/min) pressure (psi) / 1714 = 550 ft lbf/s = 745.699872 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 |colspan=3|by definition |- | |= 550 ft lbf/s |since |align=right|1 min  |= 60 s |- | |= 550 0.3048 0.45359237 m kgf/s  |since |align=right|1 ft |= 0.3048 m and |- | |= 76.0402249068 kgf m/s | |align=right|1 lb |= 0.45359237 kg |- | |= 76.0402249068 9.80665 kg m2/s3 | |align=right|g |= 9.80665 m/s2 |- | |= 745.69987158227022 W |since |align=right|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, 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.

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. Car companies constantly compete in a 'power war' with each other, and measurement methods are often points of argument.

#### PS

This unit ( = horse strength) is no longer a statutory unit, but is still commonly used in Europe, South America, Japan and India 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.

DIN 66036 defines one 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;[14] this is equivalent to 735.49875 W. Similar definitions were already common to the time of James Watt.

The PS was adopted by the Deutsches Institut f r 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, in addition to the kW rating, as many customers are still not familiar with the use of kilowatts for engines.

#### pk, ch, hk, hv, LE, k/ks, , KS, KM, CP, PS

The Dutch paardenkracht (pk), the French chevaux (ch), the Swedish h stkraft (hk), the Finnish hevosvoima (hv), the Norwegian and Danish hestekraft (hk), the Hungarian l er (LE), the Czech ko sk s la and Slovak konsk sila (k or ks), the Bosnian/Croatian/Serbian konjska snaga (KS),the Bulgarian " ", the Macedonian (KC), the Polish ko mechaniczny and Slovenian konjska mo (KM) and the Romanian cal-putere (CP) all equal the German Pferdest rke (PS), and are approximately equal to 735.5 W.

#### CV and cv

In French (Cheval-vapeur), Italian (Cavalli Vapore), Spanish (Caballos de vapor), and Portuguese (Cavalo-vapor), CV is the equivalent to the German, PS. It is also used as the French term for the Pferdest rke, 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.[15] 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 Citro n 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.

### Boiler horsepower

One boiler horsepower unit, or BHP, is equal to a boiler thermal output of , which is the energy rate needed to evaporate of water at in one hour. The unit is not current outside of North America.

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 , and saturated steam generated at gauge pressure. This original definition is equivalent to a boiler heat output of . In 1884, the ASME redefined 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 . 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.

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 horsepower used for electrical machines 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 relationship between torque in foot-pounds, rotational speed in rpm and horsepower is:

P / {\rm hp} = {\tau / ({\rm ft {\cdot} lbf}) \times f / ({\rm rpm}) \over 5252}

Where P is power, \tau is torque, and f is rotations per minute. The constant 5252 is the truncated value of (33,000 ft lbf/min)/(2  rad/rev).

The standard equation relating torque in inch pounds, rotational speed in rpm and horsepower is:

P / {\rm hp} = {\tau / ({\rm in {\cdot} lbf}) \times f / ({\rm rpm}) \over 63{,}025}

Where P is power, \tau is torque, and f is rotations per minute. The constant 63,025 is the truncated value of (33,000 ft lbf/min) (12 in/ft)/(2  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 (F) is measured in pounds-force (lbf) and speed (v) is measured in miles per hour (mph), then the drawbar power (P) in horsepower (hp) is:

P / {\rm hp} = {(F / {\rm lbf}) (v / {\rm mph}) \over 375}

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

P / {\rm hp} = {{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 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 [16]

This is equal to the displacement in cubic inches divided by 10 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 (bore smaller than 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 and a stroke of ,[17] where most American automakers had long since moved to oversquare (large 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. 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 .[18]
Indicated or gross horsepower (theoretical capability of the engine) [ PLAN/ 33000]
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 19th 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 and for the piston speed to be of the order of 54 75 m/min.[18]

### 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 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 before 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. Although the output delivered to the driving wheels is less than that obtainable at the engine's crankshaft, a chassis dynamometer gives an indication of an engine's 'real world' horsepower after losses in the drive train and gearbox. This gives a reasonably accurate indication of how a wheeled vehicle engine will perform once on the road.

### Shaft horsepower

Shaft horsepower (shp) is the power delivered to the propeller shafts of a steamship (or one powered by diesel engines or nuclear power), or an aircraft powered by a piston engine or a gas turbine engine, and the rotors of a helicopter. This shaft horsepower can be measured with instruments, or estimated from the indicated horsepower and a standard figure for the losses in the transmission (typical figures are around 10%). This measure is not commonly used in the automobile industry, because there, drive train losses can become significant.

## Engine power test codes

Engine power test codes determine how the power and torque of an automobile engine is measured and corrected. Correction factors are used to adjust power and torque measurements to standard atmospheric conditions to provide a more accurate comparison between engines as they are affected by the pressure, humidity, and temperature of ambient air.[19] There exist several standards for this purpose, some described below.

### Society of Automotive Engineers

#### SAE gross power

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 power

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 power 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 power

In 2005, the SAE introduced "SAE Certified Power" with SAE J2723.[20] This test is voluntary and is in itself not a separate engine test code but a certification of either J1349 or J1995 after which the manufacturer is allowed to advertise "Certified to SAE J1349" or "Certified to SAE J1995" depending on which test standard have been followed. To attain certification the test must follow the SAE standard in question, take place in a ISO9000/9002 certified facility and be witnessed by an SAE approved third party.

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 under the new tests, while the rating for Toyota's Camry 3.0 L 1MZ-FE V6 fell from . The company's Lexus ES 330 and Camry SE V6 were previously rated at but the ES330 dropped to while the Camry declined 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 .

While Toyota and Honda are retesting their entire vehicle lineups, other automakers generally are retesting only those with updated powertrains. For example, the 2006 Ford Five Hundred is rated at 203 horsepower, the same as that of 2005 model. However, the 2006 rating does not reflect the new SAE testing procedure as Ford is not going to spend the extra expense of retesting its existing engines. Over time, most automakers are expected to comply with the new guidelines.

SAE tightened its horsepower rules after some engineers noticed parts of the old test could be subjected to different interpretations. Under the old testing procedures, there were small factors that required a judgment call: how much oil was in the crankcase, how the engine controls were calibrated and whether a vehicle was tested with premium fuel. In some cases, such can add up to a change in horsepower ratings. A road test editor at Edmunds.com, John Di Pietro, said decreases in horsepower ratings for some '06 models are not that dramatic. For vehicles like a midsize family sedan, it is likely that the reputation of the manufacturer will be more important.[21]

### Deutsches Institut f r Normung 70020

DIN 70020 is a standard from German DIN regarding road vehicles. Because the German word for horsepower is Pferdest rke, in Germany it is commonly abbreviated to PS. DIN hp is measured at the engine's output shaft, and is usually expressed in metric (Pferdest rke) rather than mechanical horsepower.

### Economic Commission for Europe R24

ECE R24 is a UN standard for the approval of compression ignition engine emissions, installation and measurement of engine power.[22] It is similar to DIN 70020 standard, but with different requirements for connecting an engine's fan during testing causing it to absorb less power from the engine.[23]

### Economic Commission for Europe R85

ECE R85 is a UN standard for the approval of internal combustion engines with regard to the measurement of the net power.[24]

### 80/1269/EEC

80/1269/EEC of 16 December 1980 is a European Union standard for road vehicle engine power.

### International Organization for Standardization

• ISO 14396 specifies the additional and method requirement for determinating the power of reciprocating internal combustion engines when presented for an ISO 8178 exhaust emission test. It applies to reciprocating internal combustion engines for land, rail and marine use excluding engines of motor vehicles primarily designed for road use.[25]
• ISO 1585 is an engine net power test code intended for road vehicles.[26]
• ISO 2534 is an engine gross power test code intended for road vehicles[27]
• ISO 4164 is an engine net power test code intended for mopeds.[28]
• ISO 4106 is an engine net power test code intended for motorcycles.[29]
• ISO 9249 is an engine net power test code intended for earth moving machines.[30]

### Japanese Industrial Standard D 1001

JIS D 1001 is a Japanese net, and gross, engine power test code for automobiles or trucks having a spark ignition, diesel engine, or fuel injection engine.[31]

## References

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