Definitions

# Horsepower

[hawrs-pou-er]

Horsepower (hp or HP) is the name of several non-metric units of power. In scientific discourse, the term "horsepower" is rarely used because of its various definitions and the already existent SI unit for power, the watt (W). However, use of the term "horsepower" persists as a legacy in many languages and industries, particularly as a unit of measurement of the maximum power output of internal-combustion engines of automobiles; and often of trucks, buses, and ships. The use of 'HP' is being slowly replaced by kW (kilowatt) and MW (megawatt).

There are two important factors to consider when evaluating the measurement of "horsepower":

• The inconsistent definitions of the "horsepower" unit itself
• The various standards used in measuring the value of "horsepower"

These factors can be combined in unexpected ways — the power output for an engine rated at "100 horsepower" might not be what a reader expects. For this reason, various groups have attempted to standardize not only the definition of "horsepower" but the measurement of "horsepower". In the interim, more confusion may surface.

## History of the term "horsepower"

The development of the steam engine provided a reason to equate the output of horses with 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 term "horsepower" was coined later 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. 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 (assuming that the measurements of mass were equivalent to measurements of force in pounds-force, which were not well-defined units at the time). So:
$power = frac\left\{work\right\}\left\{time\right\} = frac\left\{force times distance\right\}\left\{time\right\} = frac\left\{\left(180 mbox\left\{ lbf\right\}\right)\left(2.4 times 2 pi times 12 mbox\left\{ ft\right\}\right)\right\}\left\{1 mbox\left\{min\right\}\right\}=32,572 frac\left\{mbox\left\{ft\right\} cdot mbox\left\{lbf\right\}\right\}\left\{mbox\left\{min\right\}\right\}.$
This was rounded to an even 33,000 ft·lbf/min.

Others recount that Watt determined that a pony could lift an average 220 pounds 100 feet (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.

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.

Put into perspective, a healthy human can produce about 1.2 hp briefly (see Orders of magnitude (power)) and sustain about 0.1 hp indefinitely, and trained athletes can manage up to about 0.3 horsepower for a period of several hours.

Most observers familiar with horses and their capabilities estimate that Watt was either a bit optimistic or intended to under promise and over deliver; few horses can maintain that effort for long. Regardless, comparison to a horse proved to be an enduring marketing tool.

### Horsepower from a horse

R. D. Stevenson and R. J. Wasserzug 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 ≡ 33,000 ft·lbf/min = 550 ft·lbf/s
= 745.6999 W
Metric horsepower ≡ 75 kgf·m/s
= 735.49875 W (exactly)
Electrical horsepower ≡746 W
Boiler horsepower ≡ 33,475 Btu/h =9809.5 W
Hydraulic horsepower =Flow Rate(US gal/min) * Pressure(psi) / 1714
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.

Additionally, the term "horsepower" has been applied to calculated (estimated rather than measured) metrics:

• RAC horsepower is based solely on the dimensions of a piston engine (1 litre of engine displacement is equal to 10 RAC horsepower)

### Mechanical horsepower

The term "horsepower" was coined by the engineer James Watt in 1782 while working in the performance of steam engines. This occurred while using a mine pony to lift coal out of a coal mine. He conceived the idea of defining the power exerted by these animals to accomplish this work. He found that, on the average, a mine pony could pull (lift by means of a pulley) 22,000 foot-pounds per minute. Rather than call this "pony" power, he increased these test results by 50 percent, and called it horsepower i.e. 33,000 foot-pounds of work per minute.

Assuming the third CGPM (1901, CR 70) definition of standard gravity, g, and the international avoirdupois pound (1958), 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 lb = 4.448 N, 1 J = 1 N·m, 1 W = 1 J/s: 1 hp = 746 W

cross multiply and cancel out:

550 ft-lb/s 0.3048 m 4.448 N 1 J 1 W
1 hp 1 ft 1 lb 1 N-m 1 J/s
= 745.66272 W or 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", "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.

#### PS

This unit (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) in Braunschweig as exactly:

1 PS = 75 kilopond·metre/second ~= 735.5 newton·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, and hv

The Dutch paardenkracht (pk), the Swedish hästkraft (hk), the Finnish hevosvoima (hv), the Norwegian and Danish hestekraft (hk), and the Hungarian lóerő (LE) all equal the German Pferdestärke (PS).

#### CV and cv

In Italian ("Cavalli"), Spanish ("Caballos"), 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 a French unit for tax horsepower, short for chevaux vapeur ("steam horses") or cheval-vapeur. CV is a non-linear rating of a motor vehicle for tax purposes. The CV rating, or fiscal power, is $left\left(tfrac\left\{P\right\}\left\{40\right\}right\right)^\left\{1.6\right\} + tfrac\left\{U\right\}\left\{45\right\}$, where P is the maximum power in kilowatts and U is the amount of CO2 emitted in grams per kilometre. 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"). Some sources give it as 0.7355 kW, but it is generally used interchangeably with the German 'PS'.

### Boiler horsepower

A boiler horsepower is used for boilers in power plants. It is equal to 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.

### Electrical horsepower

The electrical horsepower is used by the electrical industry for electrical machines and is defined to be exactly 746 W at 100% efficiency. Electric motors can never run at 100% efficiency. The nameplates on electrical motors show their power output, not their power input.

### Relationship with torque

For a given torque, the equivalent power may be calculated. The standard equation relating torque in foot-pounds, rotational speed in RPM and horsepower is:
$P \left[\left\{rm hp\right\}\right] = \left\{\left[Tau / \left(\left\{rm ft cdot lbf\right\}\right)\right] \left[omega / \left(\left\{rm r/min\right\}\right)\right] over 5252\right\}$

Where $P$ is power, $tau$ is torque, and $omega$ is rotations per minute. Outside the United States, most countries use the newton meter as the unit of torque. Most automobile specifications worldwide have torque listed in newton meters. The standard equation relating torque in newton meters, rotational speed in RPM and power in kilowatts is:

$P \left[\left\{rm kW\right\}\right] = \left\{\left[Tau / \left(\left\{rm N cdot m \right\}\right)\right] \left[omega / \left(\left\{rm r/min\right\}\right)\right] over 9549\right\}$

These are based on Watt's definition of the mechanical horsepower. The constants 5252 and 9549 are rounded.

5252 comes from 33,000 (ft.lbf/min) / 2π (radians/revolution),

and 9549 comes from 60 (s/min) x 1000 (W/kW) / 2π (radians/revolution).

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; is normally a second locomotive with its brakes applied, in addition to a static load.

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

$P = \left\{Fvover 375\right\}$

Example: How much power is needed to pull a drawbar load of 2025 pounds-force at 5 miles per hour?

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

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.

$RAC h.p. = \left\{D^2 * n\right\}/2.5 ,$

where

D is the diameter (or bore) of the cylinder in inches
n is the number of cylinders

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 3.8-litre XK engine had six cylinders with a bore of 87 mm (3.43 inches) and a stroke of 106 mm (4.17 inches), where most American automakers had long since moved to oversquare (wide bore, short stroke) V-8s]

## 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. As an example, an early-production BL Mini engine produced about at the flywheel, of which only reached the driving wheels.

In general:

Nominal is derived from the size of the engine and the piston speed and is only accurate at a pressure of 7 lbf/in².

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 BMEP (Brake Mean Effective pressure). 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 7 psi and for the piston speed to be of the order of 180-248 ft/s.

### Indicated horsepower

Indicated horsepower (ihp) is the theoretical power of a reciprocating engine if it is completely efficient in converting the energy contained in the expanding gases in the cylinders. It is calculated from the pressures developed in the cylinders, measured by a device called an engine indicator - hence indicated horsepower. 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 (abbreviated bhp) is the measure of an engine's horsepower without the loss in power caused by the gearbox, generator, differential, water pump, and other auxiliary components such as alternator, power steering pump, muffled exhaust system, etc. "Brake" refers to how horsepower was originally measured and calculated, 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/minute. More information on American SAE horsepower measurements is below.

### SAE horsepower

#### SAE gross 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 blueprinted test engine running on a stand with no belt-driven accessories, air cleaner, mufflers, or emission control devices 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 were relatively idealistic. The resulting gross power and torque figures therefore reflected a maximum, theoretical value and not the power of an installed engine in a street car. Gross horsepower figures were also subject to considerable adjustment by the manufacturer's advertising and marketing staff under the direction of product managers. The power ratings of mass-market engines were often exaggerated beyond their actual gross output, while those of the highest-performance muscle car engines often tended to be closer in actual output to their advertised, gross ratings.

No pre-1972 engine in its unaltered, production line stock form, as installed in the vehicle, has ever yielded documented, qualified third party validated power figures that equal or exceed its original gross rating. Claims that such engines were "under-rated" are therefore dubious; for example, the 1969 427 ZL1 Chevrolet, rated at , is frequently cited as an "under-rated" high performance engine, yet it produced only .

#### SAE net 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. The change to net hp effectively deflated power ratings to assuage the auto insurance industry and environmental and safety lobbies.

Because SAE gross ratings were applied liberally, there is no precise conversion from gross to net. Comparison of gross and net ratings for unchanged engines shows a variance of anywhere from 40 to 150 horsepower. The Chrysler 426 Hemi, for example, in 1971 carried a 425 hp gross rating and a net rating of 350 hp, while the same company's 225 Slant 6 carried a rating of 145 bhp but 110 net hp.

#### SAE certified horsepower

In 2005, the SAE introduced a new test protocol for engine horsepower and torque. 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".

Many manufacturers began switching to the new rating immediately, with multi-directional results; the rated output of Cadillac's supercharged Northstar V8 jumped from to under the new tests, while the rating for Toyota's Camry 3.0 L 1MZ-FE V6 fell from 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 to .

### DIN hp

DIN horsepower is the power measurement protocol in the German DIN standard 70020. It is sometimes abbreviated as "PS", which stands for Pferdestärke, which is the German word for horsepower. 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. 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.

### 9768-EC

9768-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 airplane 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 metric is uncommon in the automobile industry, though drivetrain losses can be significant.

### Effective (true, wheel) hp

Effective horsepower (ehp), True horsepower (thp) or wheel horsepower (whp) is the power 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. Thp is generally 10% to 20% less than the engine's bhp rating due to drivetrain losses.