Horsepower

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Horsepower

This article is about the unit of measurement. For the machine which used horses to generate power, see horse power (machine). For other uses of hp, see HP (disambiguation).

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:

Various definitions for the unit itself
Various standards for measuring the value

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:

Mechanical horsepower — 0.74569987158227022 kW (33,000 ft·lbf per minute)
Metric horsepower — 0.73549875 kW
Electrical horsepower — 0.746 kW
Boiler horsepower — 9.8095 kW

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

RAC horsepower is based solely on the dimensions of a piston engine

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)^* 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^*.
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:

\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:

\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?

$P / {\rm hp} = =32,572 \frac{\mbox{ft} \cdot \mbox{lbf}}{\mbox{min}}$ 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 1.2hp briefly (see Orders of magnitude (power)) 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 = g_n × 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

External links

"What is Horsepower?" (picture)
"What's the difference between horsepower and torque?" at the Straight Dope
"Torque and Horsepower - A Primer" (addressed to automotive enthusiasts)

Imperial units | Units of power | Customary units in the United States

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