# Horsepower

Physical unit
Unit name Horsepower
Unit symbol ${\ displaystyle \ mathrm {PS}}$
Physical quantity (s) power
dimension ${\ displaystyle {\ mathsf {K \; L \; T ^ {- 1}}}}$
system Technical measurement system
In SI units ${\ displaystyle \ mathrm {1 \, PS = 735 {,} 498 \, 75 \; W} = 735 {,} 49875 \, {\ frac {\ rm {{{kg} \, {\ rm {{m} ^ {2}}}}} {\ rm {{s} ^ {3}}}}}$
Named after Average performance of a workhorse
Derived from Kilopond meter , second
Illustration of unity horse power

The horse power is a unit of the technical unit system for the quantity power . PS is used as the unit symbol . It is defined as a mass of 75 kilograms (75 kg · m · s −1 · 9.80665 m · s −2 ) accelerated over a period of one second over a length of one meter under normal acceleration conditions and corresponds exactly to 735.49875 watts . Today the unit of measure horsepower is considered obsolete.

Horsepower goes back to the horsepower unit introduced by James Watt . The definitions of horsepower and horsepower are similar, with the difference that the mass of the Horsepower is 550 lb over a length of 1 ft per second, which corresponds to around 76.04 kg · m / s. With the introduction of the metric system in continental Europe, this value for horsepower was changed to 75 kg · m / s, so that today horsepower and horsepower are different.

In the International System of Units (SI system), the unit watt (according to James Watt) is standardized today instead of horse power. The watt was prescribed in 1970 in the German Democratic Republic and on January 1, 1978 in the Federal Republic of Germany as a unit of measurement for power. The watt has been used in electrical engineering since the early 20th century.

## use

Although the horse power has not been an official legal unit in metrology in Germany since 1978 due to Directive 80/181 / EEC , it is still used mainly in internal combustion engines , especially in motor vehicles . The additional use of PS is still permitted by Directive 2009/3 / EC . The sole performance of PS and all other non-SI units are no longer permitted in the entire EU in business and official dealings. The SI unit (here watt or its decimal multiple ) must be emphasized here. In German law, this requirement was implemented in Section 3 of the Unit Ordinance.

## historical development

Historically, horsepower was understood as the average usable continuous power of a work horse , for example when driving a mill . In the course of the introduction of steam engines, it has proven to be advantageous to introduce a power unit comparable to the horse drive so that the new drives could be designed accordingly.

In the literature there are different statements about what James Watt chose as a reference for his unit. It is widespread that he chose the performance of a pit horse as a benchmark because he wanted to rent out his steam engines to mine operators . Assuming that a strong horse is twice as strong as a pit pony, he concluded that a strong horse would pull 550 Anglo-American pounds over a foot in a second, or 33,000 foot-pounds per minute. Another version of the story says that he used as a basis the horses that used ropes and pulleys to pull sacks of coal out of the pits for days. A horse would lift an average of 330 Anglo-American pounds of coal in its ten hour shift at a rate of 100 feet per minute, which is also 33,000 foot-pounds per minute. Other sources assume that Watt determined his unit using a typical horse peg. If the horse is 24 feet in diameter, it will pull 180 pounds and make 144 cycles per hour, or about 2.4 per minute. The horse was thus running at a speed of 181 feet per minute (55 meters per minute). Watt multiplied that distance by the 180 pounds of force and came up with 32,580 ft × lb / min. That was rounded up to 33,000 ft x lb / min.

33,000 ft × lb / min is equivalent to 550 ft × lb / s or 76.04 kg m / s. With the introduction of the metric system in continental Europe, this value was changed to 75 kg m / s, which is why horsepower different from Horsepower.

## definition

1 PS is defined in DIN 66036 as the power that must be provided in order to move a body with a mass of m = 75 kg against the gravitational field of the earth (with standard acceleration 9,80665 m / s²) at a speed of 1 m / s .

${\ displaystyle \ left [P \ right] = \ left [{\ frac {W} {t}} \ right] = \ left [m \ cdot g \ cdot v \ right] = 1 \, {\ rm {{ PS} = 75 \, {\ rm {{kg} \ times 9 {,} 80665 \, {\ frac {\ rm {m}} {\ rm {s ^ {2}}}} \ times 1 \, { \ frac {\ rm {m}} {\ rm {s}}} = 735 {,} 49875 \, {\ frac {\ rm {{kg} \, {\ rm {{m} ^ {2}}} }} {\ rm {{s} ^ {3}}}}}}}}}$

1 hp = 75 kpm / s = 735.49875 W.

Converted, this corresponds roughly to the power that a draft horse has to use to pull a cart with a mass of 500 kg up a 10 percent incline at walking speed (5.4 km / h). With a light draft horse of around 750 kg mass, there is an additional 1.5 HP that the horse has to muster to move its own mass.

For comparison, the continuous power of an adult, average-sized person is given as 0.14 PS (100 watts), although with appropriate training, 440 watts for over an hour and 910 watts for 6 seconds (corresponds to about 1.2 PS) are possible .

The performance of a horse can vary considerably depending on the breed , level of training or current level of exertion: a horse can briefly produce over 20 hp , for example when galloping or jumping , while it produces around 1 hp on average during the day.

## Conversion PS ↔ kW

1 HP = 75 m × kp / s = 0.73549875 kW

The following applies to the usual conversion:

• 1 kW = 1.36 hp; 1 hp = 0.735 kW.

The following applies to the rough calculation :

• 1 kW = 4/3 HP; 1 HP = 3/4 kW.

## Standards for determining performance

The performance data, especially for vehicle engines, are not always comparable internationally, as different measurement methods were used. In Germany, for example, the power given by the engine to the gearbox when installed was given ("DIN-PS", measured according to DIN 70020). In Italy the " Cuna-PS " (without air filter and silencer) was used, which was 5 to 10% higher than the DIN output. In the United States , engine power was determined according to the SAE J1995 and J245 standards until the 1970s. The engine output was determined without the operation of the fan , water pump , alternator , air filter and silencer . A performance determined according to SAE standards is between 10 and 25% greater than the performance determined according to DIN 70020.

### DIN-PS

The performance of motor vehicle engines was measured on the flywheel in accordance with DIN 70020 and given in PS (DIN PS).

According to DIN 70020 “Motor vehicle construction; Common Terms; Definition and Explanation ”of August 1954, the net power was measured“ on the coupling of the in-line engine in all parts including the intake and exhaust system under normal operating conditions ”and stated in HP. The maximum useful power that the motor can continuously deliver without exceeding the permissible thermal stress was specified as continuous power, and that which the motor can deliver for at least 15 minutes as short power; after that he must be able to continue working properly with continuous power. Normal operating conditions include serial adjustments and commercial fuel; The fan, water pump, cooling air fan, fuel pump, injection pump and the unloaded alternator must be driven by the engine during the test. The measured power is converted to 760  Torr (= 1013 mbar) and 20 ° C, the humidity is not taken into account. A deviation of ± 5% is permissible for re-inspections. Useful power must always be specified in connection with the associated speed in 1 / min.

In February 1957, this standard was split up, the specifications for power, speeds and acceleration came in Part 3. The measurement conditions for the useful power remained unchanged, the continuous power was renamed "greatest useful power" and must be achieved in the "thermal steady state", the short power has been dropped.

In December 1973, the “Performance” section of DIN 70020-3 was replaced by the pre-standard DIN 70020-4, June 1972 edition, which provides for the reference state 25 ° C and 1000 mbar instead of 20 ° C and 1013 mbar = 760 Torr. These new purchase conditions resulted in a reduction in nominal output of 2 to 4%. In order to avoid this competitive disadvantage and disadvantages in compliance with a minimum engine power required in Section 35 of the StVZO , DIN returned in November 1976 with the issue of the DIN 70020-6 standard “Motor vehicle construction; Power ”back to the old reference values, recommending the units kW or PS for the net power and min −1 for speeds. This standard was replaced in April 1997 by DIN ISO 1585 “Road vehicles - method for determining the net power of engines (ISO 1585: 1992)” for the purpose of international harmonization .

### ECE-PS

ECE R 24 is another standard that comes very close to DIN 70020. However, the measurements only apply to diesel engines and vary according to the connection of the cooling fan.

### Cuna-PS

The Italian Cuna PS was used before kW was introduced in Italy and is based on kg and m (hence metric). When determining engine power according to the Cuna standard, the engine power is specified without air filter and silencer.

### SAE-HP (USA)

#### Gross SAE

Until 1972, SAE gross horsepower ("gross SAE-HP") were specified according to the standards J245 and J1995 of the Society of Automotive Engineers , which were measured on the engine test bench without the fan , water pump , alternator , air filter and silencer being operated. Due to this unpractical method, which was up to 25% higher than the European performance values, the pure numerical values ​​could exaggerate the engine performance.

#### Net SAE

Since 1972 the SAE net horsepower (“net SAE-HP”) according to the guidelines SAE J1349 and SAE J2723, which are similar to DIN 70020, have been in force in the USA . The numerical values ​​of the SAE gross decreased significantly, for example in the Chrysler 426 Hemi from 1971 from 425 hp gross to 350 hp net . In SAE J2723, the method is described how the performance of the combustion engine is to be determined and how the ancillary units or which ancillary units must be operated. SAE J1349 specifies the equations for calculating how the engine power determined on the test bench must be converted to a reference condition standardized according to SAE. The reference states of the European directive and the SAE directive do not differ. However, the SAE correction factor contains an efficiency correction value, so that there are slight differences in the performance values. In Europe, the EU guideline 80/1269 of December 16, 1980 is used to correct the engine power of cars; the corresponding guideline for motorcycles is 95/1 / EC of February 2, 1995.

## Measures for the taxation of motor vehicles

### Displacement HP

With the Reichsstempelgesetz of June 7th, 1906 it was stipulated in § 53 that motor vehicles “may only be used to drive on public roads and places if a permit of the kind specified in the tariff has been obtained from the competent authority against payment of the tax amount has been. "the payable annual tax allowance of 25 marks to 150 marks straightened up in Germany after the engine power for which the displacement was placed in a fixed relation to the transaction. In Section 7 of the Road Traffic Act of May 3, 1909, strict liability for the operation of motor vehicles was included. For the commissioning of the motor vehicle there was now also an insurance obligation, which was proven by a license plate and the carrying of the permit card.

Following technical progress, with more modern designs the calculated and technically effective performance soon diverged widely. Double information then became common in vehicle advertising. The Mercedes 28/60 hp (from 1912 to 1920) with 7240 cm³ displacement with 28 displacement and 60 power hp was offered.

Examples of engine displacement for motorcycles and cars in Germany from 1906 to 1922 (extracts):

Cubic capacity
in cm³
PS
(motorcycle)
HP
(car)
175 1 12
250 2 14
500 3 12
750 6th
1000 8th 4th
1500 6th
2000 8th
2600 10
4000 16

The British Royal Automobile Club took on RAC Horsepower (from 1906 to January 1947) as did the American Association of Licensed Automobile Manufacturers (ALAM) (from around 1907) and its successor organization, the National Automobile Chamber of Commerce (NACC) (from 1913 ), only the square of the cylinder diameter and the number of cylinders as the basis for the abstract calculation of the power:

${\ displaystyle {\ text {hp}} = {\ frac {D ^ {2} \ times N} {2 {,} 5}}}$

(D = diameter of the cylinder; N = number of cylinders)

The English engine construction was particularly influenced by the emphasis on the cylinder diameter squared as an important factor of the abstract performance determination. Engines with the largest possible stroke and small bore were taxed less and therefore preferred, ultimately until January 1947.

### Tax PS

The Motor Vehicle Tax Act of April 8, 1922 established a tax formula for the use of motor vehicles that was valid from July 1, 1922 to March 31, 1928.

VrTwo-stroke engines : 0.45 × number of cylinders × cylinder bore² (in cm²) × piston stroke (in m) Four-stroke engines : 0.30 × number of cylinders × cylinder bore² (in cm²) × piston stroke (in m).
Between

In § 3 the amount of the tax was determined, for example for motorcycles up to 1.5 horse power 10  Reichsmarks , over 4 HP 35 Reichsmarks were to be paid. For passenger cars, depending on the tax horsepower, between 20 and 80 Reichsmarks had to be paid. The tax for trucks and buses and coaches was calculated according to their own weight (over 500 to over 4000 kg); e.g. for trucks over 4000 kg 100 ℛℳ, for buses over 4000 kg 200 ℛℳ. The tax rate was redefined on January 4, 1924. The tax has now been increased significantly for large-displacement cars, for example for 20 taxable horsepower 1000 ℛℳ and for 40 taxable horsepower 2600 ℛℳ.

For foreign vehicles, the tax horsepower was calculated according to the structure and the number of seats:

seating
places
Open
summer hood
Closed
structure
1-2 07 hp 09 hp
3-4 12 hp 14 hp
5-6 16 hp 18 hp

With effect from April 1, 1928, only the cylinder capacity became the basis for taxation in the German Reich for motorcycles and motor vehicles. For each 100 cm³ displacement, 12 12 for cars and 8 ℛℳ for motorcycles were calculated. Motorcycles with a capacity of up to 200 cm³ were now tax exempt.

### French ch and CV

In French, cheval-vapeur ( ch , pl. Chevaux-vapeur ) means horsepower.

The unit ch is, however, often confused with the key figure cheval fiscal ( CV or cv , pl. Chevaux fiscaux ) used in France and Belgium . This is used to determine the vehicle tax or registration fees. The formula for the cv has been changed several times over the years; it is different in France and Belgium. Currently u. a. Engine power and CO 2 emissions are taken into account.

The term cheval-vapeur also denotes units of measurement for electricity and heating power in French.

## Related units

### Horsepower

The English or mechanical horsepower has the unit symbol hp (horsepower) or bhp (brake horsepower). It is based on the English units of pound-force ( lb f ) and foot ( ft ) and is also used in industrial plants in the United States . It is defined per minute:

1 hp = 33,000 lb f  × ft / min = 550 lb f  × ft / s

Conversion table
PS hp kW
1 PS = 1 0.98632 0.735499
1 hp = 1.01387 1 0.74570
1 kW = 1.35962 1.34102 1

### Poncelet

A poncelet is defined similarly to horse power, with a difference in the underlying mass: 1 p = 100 kp · m / s; (1 PS = 75 kp m / s)

## Horsepower information

To specify how a PS specification is to be understood, various suffixes or prefixes can be specified.

### PSi

PSi is occasionally used - but not in accordance with DIN standards - to indicate that a value is an indicated (i.e. indirectly determined) output of a compressor or a piston engine  - especially a steam engine or steam locomotive  .

### PSw or WPS

PSw or WPS is occasionally used, but not in accordance with DIN standards, to indicate that a value is a shaft output, especially in the case of turbines .

### PSe

Nameplate of a steam engine, power specified in PSe.

PSe or EPS is occasionally used, but not in accordance with the DIN standard, to indicate that a value is the effective power of a motor measured at the end of the shaft.

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## Individual evidence

1. US Government Printing Office (Ed.): The Relation of the Horsepower to the Kilowatt , No. 34 and 35, 1915, p. 9
2. Directive 2009/3 / EC
3. Calendar sheet January 19, 2011: James Watt was born 275 years ago. In: Wissenschaft Aktuell. Retrieved August 20, 2013 .
4. Formulas. Retrieved August 20, 2013 .
5. How much horsepower does a horse have? In: Science Online. Retrieved August 20, 2013 .
6. US Government Printing Office (Ed.): The Relation of the Horsepower to the Kilowatt , No. 34 and 35, 1915, p. 11
7. a b The legal units in Germany. (PDF; 1600 kB) Physikalisch-Technische Bundesanstalt, National Metrology Institute, June 2015, archived from the original on September 24, 2015 ; Retrieved on January 1, 2020 (page 7 of the PDF marked with page numbers 12/13).
8. ^ Basics of sports medicine. (PDF; 156 kB)
9. Human power output during repeated sprint cycle exercise: the influence of thermal stress . PMID 10090637
10. How much horsepower does a horse have?
11. ^ Curt Hanfland: The modern mechanical engineering. Verlag der Literaturwerke "Minerva", Volume 1, Leipzig 1928, p. 87.
12. Expertise in automotive engineering. Holland and Josenhans Verlag, Stuttgart 1982, ISBN 3-7782-3520-6 , p. 17.
13. ^ Automotive paperback. 19th edition. Robert Bosch GmbH, 1984, ISBN 3-18-418005-0 , p. 331.
14. The engine of the Camaro ZL-1 COPO, which was built in 1969 for drag racing in small numbers, was given as 430 bhp, without soundproofing it achieved over 500 bhp. In the delivery condition, the output was a realistic 376 bhp. (see Camaro Research Group: COPO 427: The Relentless Pursuit of Acceleration )
15. Special notes on buying a used car in the USA. TÜV Süd - "Performance data: The horsepower output of American vehicles has been given in net SAE.PS since 1972. Since then, it has been more or less exactly the same as our DIN PS. Before that, the so-called gross SAE PS, which are considerably higher than our DIN specifications, applied. "
16. ^ Reichsstempelgesetz
17. ^ Tariff for the Reichsstempelgesetz
18. ^ Werner Oswald : Mercedes-Benz Passenger Cars 1886–1945. Volume 1, Motorbuch Verlag, Stuttgart 2001, ISBN 3-613-02167-6 , p. 107.
19. Carl Theodor Wiscott: The taxation of motor vehicles and fuels. To create a modern road network. VDI, Berlin 1928, (dissertation TH Braunschweig)
20. Kurt Mair: The motorcycle. Heel Verlag, reprint of the 2nd edition 1937, ISBN 978-3-86852-307-2 , p. 97.
21. ^ Curt Hanfland: The modern mechanical engineering. Volume 2, Verlag der Literaturwerke "Minerva", Leipzig 1928, p. 313.
22. ^ Victor W. Page: Early Motorcycles. Dover Publications, New York 1914. (Reprint: 2004, ISBN 0-486-43671-3 , p. 99) (English)
23. Olaf von Fersen (ed.): A century of automobile technology. Passenger cars. VDI Verlag, 1986, ISBN 3-18-400620-4 , p. 695.
24. Implementing provisions of the Motor Vehicle Tax Act: § 3. In: Stilke's Rechtsbibiliothek. No. 44, Berlin 1926, p. 730.
25. Motor Vehicle Tax Act of April 8, 1922 (Reichsgesetzblatt p. 396). In: Stilke's legal library. No. 44, Berlin 1926, p. 723.
26. Implementing provisions of the Motor Vehicle Tax Act. Section 10, auxiliary table. In: Stilke's legal library. No. 44, Berlin 1926, p. 757.
27. Implementing provisions of the Motor Vehicle Tax Act. § 6. In: Stilke's legal library. No. 44, Berlin 1926, p. 732.
28. Werner Oswald: German Cars 1920–1945. Motorbuch Verlag, Stuttgart 1983, ISBN 3-87943-519-7 .
29. ^ Curt Hanfland: The modern mechanical engineering. Volume 2, Verlag der Literaturwerke "Minerva", Leipzig 1928, p. 313.
30. ^ Automotive paperback. 19th edition. Robert Bosch GmbH, 1984, ISBN 3-18-418005-0 , p. 28.