# Horsepower

Physical unit
Unit name Horsepower
Unit symbol ${\ displaystyle \ mathrm {hp}}$, ${\ displaystyle \ mathrm {HP}}$
Physical quantity (s) power
Formula symbol ${\ displaystyle P}$
dimension ${\ displaystyle {\ mathsf {K \; L \; T ^ {- 1}}}}$
system Anglo-American system of measurement
In SI units ${\ displaystyle \ mathrm {1 \, hp = 745 {,} 699 \, 871 \, 515 \, 585 \; W} = 745 {,} 699871515585 \, {\ frac {\ mathrm {kg} \, \ mathrm {m} ^ {2}} {\ mathrm {s} ^ {3}}}}$
Named after 1.5 times the average performance of a work horse
Derived from Pound power , foot , minute
hp

Horsepower is a unit of measurement from the Anglo-American system of measurement for power with the unit symbol hp . It is defined as a mass of 33,000  Anglo-American pounds over one foot in one minute. Assuming that the unspecified acceleration is the same as the normal fall acceleration , this corresponds to an output of around 745.7 watts. The name Horsepower can be as horsepower translated into German, Horsepower and but horsepower are different measurements, as they differ in the amount of accelerated mass and possibly the strength of the acceleration.

## definition

The definition of horsepower is incomplete because the definition lacks the necessary acceleration. A horsepower is defined as:

${\ displaystyle {1} \, {\ mathrm {hp}} = {\ frac {33000 \, \ mathrm {lb} \ cdot \ mathrm {ft}} {\ mathrm {min}}} = {\ frac {550 \, \ mathrm {lb} \ cdot \ mathrm {ft}} {\ mathrm {s}}}}$

If the standardized normal acceleration of the earth is used, the result is:

${\ displaystyle {1} \, \ mathrm {hp} = {\ frac {550 \, \ mathrm {lb} \ cdot \ mathrm {ft}} {\ mathrm {s}}} \ cdot {\ frac {9 { ,} 80665 \, \ mathrm {m}} {\ mathrm {s} ^ {2}}} = 745 {,} 699871515585 \, {\ frac {\ mathrm {kg} \ cdot \ mathrm {m} ^ {2 }} {\ mathrm {s} ^ {3}}}}$

In the literature, the 50th degree of latitude at sea level is often given as an alternative to this as the reference point for the acceleration, since London is close to the 50th degree of latitude and so the conversion to watts results in a natural number. At the 50th parallel, the acceleration due to gravity is less than the normal fall acceleration. Therefore the mass to be accelerated has to be increased to 550.22 Anglo-American pounds in order to achieve horsepower. The normal earth acceleration is still used as a calculation variable:

${\ displaystyle {1} \, \ mathrm {hp} = {\ frac {550 {,} 22 \, \ mathrm {lb} \ cdot \ mathrm {ft}} {\ mathrm {s}}} \ cdot {\ frac {9 {,} 80665 \, \ mathrm {m}} {\ mathrm {s} ^ {2}}} = 746 \, {\ frac {\ mathrm {kg} \ cdot \ mathrm {m} ^ {2 }} {\ mathrm {s} ^ {3}}}}$

The first definition is used in this article because it has become widely accepted.

## Conversion into other units of measurement

Conversion table
hp W. kp m / s PS BTU / s kcal / s
1 745.7 76.0402 1.0139 0.70678 0.17811
Source:

## history

Thomas Savery , who invented an early form of the steam engine in the early 18th century, is said to have been the first to use the term horsepower. As a definition, he stated that a steam engine that can perform the performance of two work horses in a certain period of time has an output of 10 horsepower, since the steam engine, unlike work horses, can work continuously; According to Savery, at least ten workhorses have to be kept available in order to permanently provide the performance of two work horses. James Watt , who invented the modern steam engine, apparently adopted the term horsepower from Savery. Watt based the definition of horsepower on foot pounds per minute, i.e. mass and length over time.

There are different representations of how watt determines what performance a horse can produce. According to one illustration, Watt had workhorses from the Barclay & Perkins brewery lift a weight out of a hole with a rope stretched over a pulley. Watt found that a weight with a mass of 100 Anglo-American pounds could be lifted while a horse was running at a speed of 2.5 miles per hour. This is equivalent to 22,000 foot pounds per minute. Watt increased this value by 50% to 33,000 foot pounds per minute in order to compensate for possible friction losses and to improve the performance values ​​of his steam engines. Another illustration says that Watt measured the number of times an hour a workhorse capable of pulling 180 Anglo-American pounds could turn a mill wheel 24 feet in diameter. Watt found that a workhorse could turn the mill wheel 144 times an hour. This is equivalent to 32,572 foot pounds per minute, which rounded watts up to 33,000 foot pounds per minute.

At the international electricians' congress in Paris in 1889, the recommendation was made for the first time to replace horsepower on a broad basis with more suitable units of power such as watt and kilowatt. The International Electrotechnical Commission in Turin and the standardization commission of the American Institute of Electrical Engineers each recommended in 1911 that Horsepower should be finally replaced by kilowatts. In electrical engineering, watts or kilowatts have therefore been used as a unit of measure for power since the early 20th century. In the case of machines that perform mechanical work, especially internal combustion engines, however, horsepower is still used today in the English-speaking world.

## Differentiation from horsepower

33,000 foot pounds per minute is equivalent to 550 foot pounds per second. The name Horsepower has been translated into various languages, although the respective definitions did not always use 550 foot pounds per second. The values ​​fluctuated between about 430 and 600 foot pounds per second, depending on the definition. This corresponds to values ​​between 75 and a little more than 76 kilogram meters per second. With the introduction of the metric system, this value was set at 75 kilogram meters per second in many countries, while the definition of 550 foot pounds per second continued in the Anglo-American language area. Therefore, the performance of a horsepower is greater than that of a horsepower, which is based on the definition of 75 kilograms per second. In order to differentiate between “English Horsepower” or “Mechnical Horsepower”, “Metric Horsepower” is used for horsepower.

## Weakness of definition

A weak point in the definition of horsepower is the unclear definition of acceleration. Strictly speaking, neither a foot pound nor a kilogram meter of torque or work is considered, since it does not take into account how strong the acceleration is. This problem did not exist for James Watt at first, as he could assume that the acceleration on earth is roughly the same everywhere (9.80665 meters per square second). In fact, the acceleration depends on several factors such as latitude and altitude. Horsepower is therefore a location-dependent unit of measurement. Since a horsepower corresponds to approximately 746 watts, the 50th parallel at sea level is often used as a reference point. If 550 Anglo-American pounds are accelerated with the standardized earth's normal acceleration of 9.80665 meters per square second, then at the 50th parallel, because of the lower acceleration there, the accelerated mass per second must be 550.22 Anglo-American pounds so that the power still corresponds to horsepower.

Assuming that the acceleration of the 50th degree of latitude at sea level is chosen as the reference point, the accelerated mass at Horsepower must be adapted to the location as follows:

Latitude Above sea level 0 ft 5000 ft 10,000 ft 0 ° 30 ° 45 ° 60 ° 90 ° 551.7 lb. 550.97 lb 550.24 lb 549.52 lb. 548.79 lb 551.86 lb 551.13 lb 550.41 lb 549.68 lb 548.95 lb 552.03 lb. 551.30 lb 550.57 lb 549.85 lb 549.12 lb Source:

In order to get around this definition problem, the literature suggests using watts or kilowatts, since the definition of watts is not dependent on location.

## Information provided by the horsepower

Depending on the intended use, there are various options for specifying the horsepower. They do not differ in the definition of the unit of measurement horsepower, but in the point at which a machine's power is measured or how it is calculated. The most common are:

• Nominal Horsepower ; (nhp): Approximate performance of a steam engine, is calculated based on the cylinder size and the piston speed. At a vapor pressure of 7 lb f · in −2 (48 kPa) this corresponds roughly to the effective power.
• Indicated Horsepower (hp i ): Theoretical machine power calculated on the basis of various parameters using an indicator.
• Brake Horsepower (bhp, hp): Power measured on the machine's flywheel (with an eddy current brake).
• Shaft Horsepower (shaft power or effective power) (shp, hp e , e shp): Power measured on the gear output shaft of a gear unit flanged to the machine.

Source:

## Other units of measure with similar names

There are other units of measurement that have the term “horsepower” in their names, but which are defined differently from horsepower:

• Horsepower (PS): Unit of measure of power. Also based on mass, length and time. Instead of 550 Anglo-American pounds, 75 kilograms are used.
• Electric Motor Horsepower: Unit of measure of power. Corresponds to horsepower or horsepower, depending on the definition.
• Drawbar Horsepower: Unit of measure of power. Corresponds to 375 Anglo-American pounds accelerated with normal fall acceleration over a length of one country mile within a period of one hour (375 lb f · mi · h −1 ) and is therefore equal to horsepower.
• RAC Horsepower : A measure of the taxation of motor vehicles. RAC Horsepower was determined based on the cylinder bore and number of cylinders and is therefore not related to physical performance .
• Hydraulic Horsepower: Unit of measure of power. A measure of the kinetic energy transferred to a liquid per unit of time at 100% pump efficiency. Defined as the mass of one Anglo-American pound per square inch multiplied by the normal fall acceleration and the flow rate of one US liquid gallon per minute divided by 1714 (1 lb f · in −2 · US gal · 1714 −1 ). Approximately equivalent to one horsepower.
• Air Horsepower: unit of measure of power. Like Hydraulic Horsepower, but with air instead of a liquid.
• Boiler Horsepower: Unit of measure for thermal output. Corresponds to the power required to completely vaporize water with a mass of 34.5 Anglo-American pounds in one hour at a temperature of 212 ° F. Equals 9.3 British thermal units per second or 13.16 horsepower.

Source:

## Remarks

1. Work or torque is mass × square length ÷ square time, expressed in SI base units kg · m² / s², or expressed in derived units N · m (Newton meter). Since acceleration was neglected in the definition of horsepower, acceleration in the sections "History" and "Differentiation from horsepower" is omitted in this article for reasons of presentation.

## Individual evidence

1. a b c U.S. Government Printing Office (Ed.): The Relation of the Horsepower to the Kilowatt , Nos. 34 and 35, 1915, p. 12
2. ^ Robert Bosch GmbH (ed.): Kraftfahrtechnisches Taschenbuch. 25th edition, Springer, Wiesbaden 2003, ISBN 978-3-528-23876-6 , p. 35.
3. US Government Printing Office (Ed.): The Relation of the Horsepower to the Kilowatt , No. 34 and 35, 1915, p. 10
4. ^ A b Steven A. Treese: History and Measurement of the Base and Derived Units , Springer, 2018, ISBN 978-3-319-77576-0 , p. 964
5. US Government Printing Office (Ed.): The Relation of the Horsepower to the Kilowatt , No. 34 and 35, 1915, p. 9
6. US Government Printing Office (Ed.): The Relation of the Horsepower to the Kilowatt , No. 34 and 35, 1915, p. 11
7. US Government Printing Office (Ed.): The Relation of the Horsepower to the Kilowatt , No. 34 and 35, 1915, p. 13
8. US Government Printing Office (Ed.): The Relation of the Horsepower to the Kilowatt , No. 34 and 35, 1915, p. 15
9. Eduard Sozaev, John Tredrea: Russian Warships in the Age of Sail 1696-1860: Design, Construction, Careers and Fates , Seaforth Publishing, 2010, ISBN 9781473853225 , p 1871
10. United States Bureau of Naval Personnel (Ed.): Principles of Naval Engineering , 1970, p. 87