# Horsepower

The horsepower (hp) is the name of several non-metric units of power. In scientific discourse the term "horsepower" is rarely used due to the various definitions and the existence of an SI unit for power, the watt (W). However, the idea of horsepower persists as a legacy term in many languages, particularly in the automotive industry for listing the maximum rate of power application of internal-combustion engines.

There are two important factors to consider when evaluating a "horsepower" figure:

These factors can be combined in unexpected ways — the true power output for an engine rated at "100 horsepower" might vary significantly from a reader's expectations. For this reason, various groups have attempted to standardize both the definition and measurement system, often leading to even more confusion. Although the SI watt is not subject to varying definitions, it can still vary based on the measurement conditions.

## Definition

There have been many definitions for the term over the years since James Watt first coined the term in 1782. The following metrics have been widely used:

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

### Mechanical horsepower

See History of the term "horsepower"

The most-common definition of horsepower for engines is the one originally proposed by James Watt in 1782. Under this system, one horsepower is defined as:

1 hp = 33,000 ft·lbf·min−1 = exactly 0.74569987158227022 kW

A common memory aid is based on the fact that Christopher Columbus first sailed to the Americas in 1492. The memory aid states that 1 hp = 1/2 Columbus or 746 W.

In fourteen hundred and ninety-two
Columbus sailed the ocean blue.
Divide that son-of-a-gun by two
And that's the number of watts in a horsepower too.

### 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. Companies of the United Kingdom 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 due to confusion over whether the original "horsepower" number was metric or mechanical.

#### PS

This unit (German: Pferdestärke = horse strength) is no longer a lawful 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 "horse power", but mathematically different from the British unit. It is defined by the Physikalisch-Technische Bundesanstalt (PTB)[1] in Braunschweig as exactly:

1 PS = 75 kp·m/s = 0.73549875 kW = 0.9863201652997627 hp (SAE)

The PS was adopted by the Deutsches Institut für Normung (DIN) and then by the automotive industry throughout most of Europe, and is always measured at the wheels, as opposed to most factory horsepower figures, which are rated at the crank (which is measured right off the motor, not accounting to any drivetrain loss, which is especially considerable in an All wheel Drive configuration).

In the 19th century, the French did not use this German unit, but had their own, the Poncelet. In 1992, the PS was rendered obsolete by EEC directives, when it was replaced by the kilowatt as the official power measuring unit, but it continued to be used for commercial and advertising purposes, as customers were not familiar with the use of kilowatts for combustion engines.

#### pk and hk

A Dutch paardenkracht equals the German Pferdestärke hence

1 pk = 0.73549875 kW

A Swedish hästkraft and Norwegian and Danish hestekraft (hk) also equals the German Pferdestärke.

#### CV and cv

Often the French name for the Pferdestärke. Also a French unit for tax horsepower, short for chevaux vapeur ("steam horses") or cheval-vapeur.
CV is a nonlinear rating of a motor vehicle for tax purposes[2].
The CV rating, or fiscal power, is (P/40)1.6+ U/45,
where P is the maximum power in kW and U is the amount of CO2 emitted in g/km. The fiscal power has found its way into naming of automobile models, such as the popular Citroën deux-chevaux.

In Italian ("Cavalli"), Spanish ("Caballos"), and Portuguese ("Cavalos"), 'CV' is the equivalent to the German 'PS'. In France this should be written as 'cv'.

#### ch

This is an Afghan 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'. Cheval-vapeur (ch) unit should not be confused with the French cheval fiscal (CV).

### 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 an hour./

### Electrical horsepower

The electrical horsepower is used by the electrical industry for electric motors and is defined to be exactly 746 W (at 100% efficiency).

### 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:

$P / {\rm hp} = {[\tau / ({\rm ft \cdot lbf})] [\omega / ({\rm r/min})] \over 5252}$.

This is based on Watt's definition of the mechanical horsepower. The constant 5252 is rounded; the exact value is 16,500/π. See torque.

### Drawbar horsepower (dbhp)

Drawbar horsepower is the power a railroad 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 railroad 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; this is normally a second locomotive with its brakes applied, in addition to a static load.

If the drawbar force is measured pounds-force ($F / {\rm lbf}$) and speed is measured in miles per hour ($v / ({\rm mi/h})$), then the drawbar power in horsepower ($P / {\rm hp}$) is:

$P / {\rm hp} = {[F / {\rm lbf}] [v / ({\rm mi/h})] \over 375}$.

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

$P / {\rm hp} = {{2025 \times 5 } \over 375} = 27$.

The constant "375" is because 1 hp = 375 lbf·mi/h. 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 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 "40/50hp", 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

This is equal to the displacement in cubic inches divided by 10π then divided again by the stroke in inches. [3]

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 true 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 both the measurement system and definition used.

In general:

Indicated or gross horsepower (theoretical capability of the engine)
minus frictional losses within the engine (bearings, rods, etc), equals
Brake or net horsepower (power delivered directly by the engine)
minus frictional losses in the transmission (bearings, gears, etc.), equals
Shaft horsepower (power delivered to the driveshaft)
minus shaft losses (friction, slip, cavitation, etc), equals
Effective or wheel horsepower

### Indicated horsepower (ihp)

Indicated horsepower is the theoretical power of a reciprocating engine assuming that 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.

#### SAE gross horsepower

Prior to 1972 most American automakers rated their engines in terms of SAE gross horsepower (defined under SAE standards J245 and J1995). Gross hp was measured using a blueprinted test engine running on a stand without accessories, mufflers, or emissions control devices. It therefore reflected a maximum, theoretical value, not the power of an installed engine in a street car. Gross horsepower figures were also subject to considerable adjustment by carmakers: the power ratings of mass-market engines were often exaggerated, while those for the highest-performance muscle car engines were frequently underrated.

### Brake horsepower (bhp)

Brake horsepower (bhp) is the measure of an engine's horsepower without the loss in power caused by the gearbox, generator, differential, water pump and other auxiliaries. The actual horsepower delivered to the driving wheels is less. An engine would have to be retested to obtain a rating in another system.

#### hp (SAE)

In the United States the term "bhp" fell into disuse after the American Society of Automotive Engineers (SAE) recommended manufacturers use hp (SAE) to indicate the net power of the engine, given that particular car's complete engine installation. It measures engine power at the flywheel, not counting drivetrain losses.

Starting in 1971 automakers began to quote power in terms of SAE net horsepower (as defined by standard J1349). This reflected the rated power of the engine in as-installed trim, with all accessories and standard intake and exhaust systems. By 1972 U.S. carmakers quoted power exclusively in SAE net hp. The change was meant to 'deflate' power ratings to assuage the auto insurance industry and environmental and safety lobbies, as well as to obfuscate the power losses caused by emissions-control equipment.

SAE net ratings, while more accurate than gross ratings, still represent the engine's power at the flywheel. Contrary to some reports, it does not measure power at the drive wheels.

Because SAE gross ratings were applied liberally, at best, there is no precise conversion from gross to net. Comparison of gross and net ratings for unchanged engines show a variance of anywhere from 40 to 150 horsepower. The Chrysler 426 Hemi, for example, in 1971 carried a 425 hp gross rating (often considered to be underrated) and a net rating of 375 hp.

#### SAE-certified horsepower

In 2005, the Society of Automotive Engineers introduced a new test procedure (J2723) for engine horsepower and torque. The procedure eliminates some of the areas of 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, often with surprising results. The rated output of Cadillac's supercharged Northstar V8 jumped from 440 hp (328 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 (157 kW) to 190 hp (142 kW). 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 (373 kW) to 505 hp (377 kW).

#### hp (DIN)

DIN horsepower is the power measured according to the German standard DIN 70020. It is measured at the flywheel, and is in practical terms equivalent to the SAE net figure. However, be aware that DIN "horsepower" is often expressed in metric (Pferdestärke) rather than mechanical horsepower.

#### hp (ECE)

ECE R24 is another standard for measuring net horsepower. It is quite similar to the DIN 70020 standard, but the requirement for connecting an engine's fan during testing varies. ECE is seen as slightly more liberal than DIN, and ECE figures tend to be slightly higher than DIN. John Deere is one strong adherent to ECE testing.

#### 9768-EC

9768-EC is a standard from the European Union. Generally, ISO-14396 and 9768-EC metrics are very similar.

#### ISO 14396

ISO 14396[4] is a new method from the International Standards Organization for all engines not intended for on-road use. Generally, ISO-14396 and 9768-EC metrics are very similar. New Holland is an adherent of ISO-14396 testing.

### Shaft horsepower (shp)

Shaft horsepower is the power delivered to the propellor shaft of a ship or turboprop airplane. 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, through drivetrain losses can be significant.

### Effective horsepower (ehp)

Effective horsepower is the power converted to useful work. In the case of a vehicle this is the power actually turned into forward motion.

In automobiles, effective horsepower is often referred to as wheel horsepower. Most automotive dynamometers measure wheel horsepower and then apply a conversion factor to calculate net or brake horsepower at the engine. Wheel horsepower will often be 5-15% lower than the bhp ratings due to a loss through the drivetrain.

## History of the term "horsepower"

The term "horsepower" was invented 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[5]. 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, thus in a minute the horse travelled 2.4 × 2π × 12 feet. Watt judged that the horse could pull with a force of 180 pounds (just 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:

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

This was rounded to an even 33,000 ft·lbf/min[6].

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[7].

Put into perspective, a healthy human can produce about 1.2hp briefly and sustain about 0.1hp 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 underpromise and overdeliver; 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 Jul 1993) calculating the upper limit to an animals 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.

### Conversion of historical definition to watts

The historical value of 33,000 ft·lbf/min may be converted to the SI unit of watts by using the following conversion of units factors:

• 1 ft = 0.3048m
• 1 lbf = gn × 1 lb = 9.80665 m/s2 × 1 lb × 0.45359237 kg/lb = 4.44822 kg·m/s2 = 4.44822 N
• 60 seconds = 1 minute
$33,000 \frac{\mbox{ft} \cdot \mbox{lbf}}{\mbox{min}} \times \frac{0.3048 \mbox{ m}}{\mbox{ft}} \times \frac{4.44822 \mbox{ N}}{\mbox{lbf}} \times \frac{\mbox{min}}{60 \mbox{ s}}=745.69987158227022 \ \frac{\mbox{N} \cdot \mbox{m}}{\mbox{s}}$

And the watt is defined as $1\ \mbox{W} = 1 \frac{\mbox{N} \cdot \mbox{m}}{\mbox{s}}$ so the historical figure of 33,000 ft·lbf/min converts exactly to the modern definition.

## References

• H.W.Dickenson, James Watt - Craftsman and Engineer, Cambridge University Press, 1936, p 145.
• Richard Shelton Kirby, et al, Engineering in History, Courier Dover Publications, 1990, p 171, ISBN 0486264122