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Difference between revisions of "Horsepower"
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==Definition== | ==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: | 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|Mechanical horsepower]] — 0.74569987158227022 | * [[#Mechanical horsepower|Mechanical horsepower]] — 0.74569987158227022 kW](33,000 ft·lbf per minute) | ||
* [[#Metric horsepower|Metric horsepower]] — 0.73549875 kW | * [[#Metric horsepower|Metric horsepower]] — 0.73549875 kW | ||
* [[#Electrical horsepower|Electrical horsepower]] — 0.746 kW | * [[#Electrical horsepower|Electrical horsepower]] — 0.746 kW | ||
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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: | 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 | : 1 hp = 33,000 ft·lbf·min<sup>−1</sup> = 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. | 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. | ||
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=== Boiler horsepower === | === Boiler horsepower === | ||
A '''boiler horsepower''' is used for boilers in power plants. It is equal to 33,475 | 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=== | === Electrical horsepower=== | ||
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=== Relationship with torque === | === Relationship with torque === | ||
For a given [[torque]], the equivalent power may be calculated. The standard equation relating torque in | 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: | ||
:<math>P / {\rm hp} = {[\tau / ({\rm ft \cdot lbf})] [\omega / ({\rm r/min})] \over 5252}</math>. | :<math>P / {\rm hp} = {[\tau / ({\rm ft \cdot lbf})] [\omega / ({\rm r/min})] \over 5252}</math>. | ||
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#Relationship between torque and power|torque]]. | 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#Relationship between torque and power|torque]]. | ||
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<math>P / {\rm hp} = {{2025 \times 5 } \over 375} = 27</math>. | <math>P / {\rm hp} = {{2025 \times 5 } \over 375} = 27</math>. | ||
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 | 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 <math>P = Fv</math>. | ||
=== RAC horsepower (taxable horsepower) === | === RAC horsepower (taxable horsepower) === | ||
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This is equal to the displacement in cubic inches divided by 10π then divided again by the stroke in inches. [http://www.designchambers.com/wolfhound/wolfhoundRACHP.htm] | This is equal to the displacement in cubic inches divided by 10π then divided again by the stroke in inches. [http://www.designchambers.com/wolfhound/wolfhoundRACHP.htm] | ||
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 ([[Revolutions per minute|rpm]]), hampering the true power output and efficiency of the engine. | 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 ([[Revolutions per minute|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. | 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== | ==Measurement== | ||
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In general: | In general: | ||
:[[#Indicated horsepower (ihp)|Indicated]] or gross horsepower (theoretical capability of the engine) | :[[#Indicated horsepower (ihp)|Indicated]] or gross horsepower (theoretical capability of the engine) | ||
::minus | ::minus [[friction]]al losses within the engine (bearings, rods, etc), equals | ||
:[[#Brake horsepower (bhp)|Brake]] or net horsepower (power delivered directly by the engine) | :[[#Brake horsepower (bhp)|Brake]] or net horsepower (power delivered directly by the engine) | ||
::minus | ::minus [[friction]]al losses in the transmission (bearings, gears, etc.), equals | ||
:[[#Shaft horsepower (shp)|Shaft]] horsepower (power delivered to the driveshaft) | :[[#Shaft horsepower (shp)|Shaft]] horsepower (power delivered to the driveshaft) | ||
::minus shaft losses (friction, slip, cavitation, etc), equals | ::minus shaft losses ([[friction]], slip, cavitation, etc), equals | ||
:[[#Effective horsepower (ehp)|Effective]] or wheel horsepower | :[[#Effective horsepower (ehp)|Effective]] or wheel horsepower | ||
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== History of the term "horsepower" == | == 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[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 | 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[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> | :<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 ft·lbf/min[http://sections.asme.org/Philadelphia/sept02.htm]. | This was rounded to an even 33,000 ft·lbf/min[http://sections.asme.org/Philadelphia/sept02.htm]. | ||
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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: | 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 ft = 0.3048m | ||
* 1 lbf = '' | * 1 lbf = ''g<sub>n</sub>'' × 1 lb = 9.80665 m/s<sup>2</sup> × 1 lb × 0.45359237 kg/lb = 4.44822 kg·m/s<sup>2</sup> = 4.44822 N | ||
*60 seconds = 1 minute | *60 seconds = 1 minute | ||