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Horsepower

From Academic Kids

The horsepower (hp) is the name of several non-metric units of power. In scientific discourse the 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 power of internal-combustion engines.

The various types of horsepower are:

Contents

Horsepower (hp)

According to the most common definition of horsepower, one horsepower is defined as exactly:

1 hp = 745.69987158227022 W

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-bitch by two
And that's how many watts there are in a horsepower.

The horsepower was first used by James Watt during a business venture where his steam engines substituted horses. It was defined that a horse can lift 33,000 pounds force with a speed of 1 foot per minute: 33,000 ftlbfmin-1. This is sometimes called a mechanical horsepower to distinguish it from the other definitions of horsepower below.

Engine horsepower

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:

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 an engine means that the actual power output may be only 70-90% of the indicated horsepower.

Brake horsepower (bhp)

Brake horsepower was a term commonly used before the 1970s in the United States, and is still common in the United Kingdom. It indicates the brake, the device for measuring the true power of the engine. Stating power in 'bhp' gives some indication this is a true reading, rather than a calculated or predicted one. However, several manufacturers started to strip their engines of essential ancillaries for the purposes of getting a high horsepower figure to use in marketing the car.

hp (SAE)

In the United States the term fell into disuse after the American Society of Automotive Engineers (SAE) recommended manufacturers use "hp (SAE)" to indicate the power of the engine, given that particular car's complete engine installation. This may also be stated as "SAE net hp" or simply "net hp". The British market seemed not to need the correction.

Drawbar horsepower (dbhp)

Drawbar horsepower is the power a railroad locomotive has available to haul a train. 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.

Shaft horsepower (shp)

Shaft horsepower is the power delivered to the propellor shaft of a ship. 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%).

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.

Summary for a ship

Indicated horsepower (theoretical capability of the engine)

minus frictional losses within the engine (bearings, rods, etc), equals

Brake horsepower (power delivered directly by the engine)

minus frictional losses in the transmission (bearings, gears, etc.), equals

Shaft horsepower (power delivered to the shaft)

minus shaft losses (slip, cavitation, etc), equals

Effective horsepower

RAC 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 hence had names such as "40/50hp", which indicated the RAC figure followed by the true measured power.

RAC horsepower cannot be given as a proportion to metric power. Instead, it is derived from dimensions of the engine and certain assumptions about engine efficiency. When invented, it gave a rough guide to its true power rating; 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.

<math>RAC h.p. = {D^2 * n}/2.5 \,<math>
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. [1] (http://www.designchambers.com/wolfhound/wolfhoundRACHP.htm)

Metric horsepower

PS

This unit (German: Pferdestrke = 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)[2] (http://www.ptb.de/) in Braunschweig as exactly:

1 PS = 75 kpm/s = 735.49875 W = 1.013869665424 hp (SAE)

The PS was adopted by the Deutsches Institut fr Normung (DIN), and subsequently, by the automotive industry throughout most of Europe. (In the nineteenth century, however, the French did not use this German unit, but had one of their own, the Poncelet.) In 1992, the PS was rendered obsolete by EEC derictives, where it was replaced by the kW as the official power measuring unit, but in situations where hp was used for commercial and advertising purposes, it continued to be used, as customers are not familiar with the usage of kW for combustion engines.

pk

A Dutch paardekracht equals the German Pferdestrke hence

1 pk = 735.49875 W

CV

Often the French name for the Pferdestrke. Also a French unit for tax horsepower, short for chevaux vapeur ("steam horses"), hence Citron 2CV.

In Italy, Spain and Portugal, 'CV' is the equivalent to the German 'PS'.

ch

This is a French unit for automobile power. The symbol ch is short for chevaux ("horses"). Some sources give it as 735.5 W, 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).

Electrical horsepower

The electrical horsepower is used by the electrical industry for electric motors and is defined to be exactly 746 watts.

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[3] (http://www.pballew.net/arithm17.html). 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:

<math> 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}}<math>

This was rounded to an even 33,000 ftlbf/min[4] (http://sections.asme.org/Philadelphia/sept02.htm).

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 ftlbf/min figure[5] (http://www.i5ive.com/article.cfm/history_bizarre_mysterious/114862).

Engineering in History recounts that John Smeaton initially estimated that a horse could product 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[6] (http://print.google.com/print?id=AVn_Sm56OCoC&pg=171&lpg=171&dq=smeaton&sig=6N_TJXrLqwQI-Fm7mU9ebKS1djA).

Regardless, comparison to a horse proved to be an enduring marketing tool.

Conversion of historical definition to watts

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

  • 1 ft = 0.3048 m
  • 1 lbf = gn(1 lb) = (9.80665 m/s2)(1 lb)(0.45359237 kg/lb) = 4.44822 kgm/s2 = 4.44822 N
  • 60 seconds = 1 minute
<math>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}}<math>

And the watt is defined as <math>1\ \mbox{W} = 1 \frac{\mbox{N} \cdot \mbox{m}}{\mbox{s}} <math> so the historical figure of 33,000 ftlbf/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 0486264122da:Hestekraft

de:Pferdestrke et:Hobujud es:Caballo de vapor fi:Hevosvoima fr:Cheval-vapeur he:כוח סוס it:Cavallo vapore ja:馬力 lt:Arklio galia nl:Paardenkracht no:Hestekrefter pl:Koń parowy ru:Лошадиная сила sl:Konjska moč sv:Hstkraft zh:馬力 (功率)

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