Horsepower

, U.S. The development of the steam engine provided a reason to compare the output of horses with that of the engines that could replace them. In 1702, Thomas Savery wrote in ''The Miner's Friend'': :So that an engine which will raise as much water as two horses, working together at one time in such a work, can do, and for which there must be constantly kept ten or twelve horses for doing the same. Then I say, such an engine may be made large enough to do the work required in employing eight, ten, fifteen, or twenty horses to be constantly maintained and kept for doing such a work... The idea was later used by James Watt to help market the Watt steam engine, an improved Newcomen steam engine. He had previously agreed to take royalties of one-third of the savings in coal from the older Newcomen steam engines. 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 in radius; therefore, the horse travelled feet in one minute. Watt judged that the horse could pull with a force of . So: : P = \frac{W}{t} = \frac{Fd}{t} = \frac{180~\text{lbf} \times 2.4 \times 2\,\pi \times 12~\text{ft}}{1~\text{min}} = 32{,}572~\frac{\text{ft} \cdot \text{lbf}}{\text{min}}. Engineering in History recounts that John Smeaton initially estimated that a horse could produce per minute. A common legend states that the unit was created when one of Watt's first customers, a brewer, specifically demanded an engine that would match a horse, and chose the strongest horse he had and driving it to the limit. In that legend, Watt accepted the challenge and built a machine that was actually even stronger than the figure achieved by the brewer, and the output of that machine became the horsepower. In 1993, R. D. Stevenson and R. J. Wassersug published correspondence in Nature summarizing measurements and calculations of peak and sustained work rates of a horse. Citing measurements made at the 1925 Iowa State Fair, they reported that the peak power over a few seconds has been measured to be as high as and also observed that for sustained activity, a work rate of about per horse is consistent with agricultural advice from both the 19th and 20th centuries and also consistent with a work rate of about four times the basal rate expended by other vertebrates for sustained activity. and for a period of several hours. The Jamaican sprinter Usain Bolt produced a maximum of 0.89 seconds into his 9.58 second sprint world record in 2009. In 2023 a group of engineers modified a dynamometer to be able to measure how much power a horse can produce. This horse was measured to . ==Calculating power==

When torque is in pound-foot units, rotational speed is in rpm, the resulting power in horsepower is : \{P\}_\mathrm{hp} = \frac{\{T\}_\mathrm{ft {\cdot} lbf} \{N\}_\mathrm{rpm}}{5252}. The constant 5252 is the rounded value of (33,000 ft⋅lbf/min)/(2π rad/rev). When torque is in inch-pounds, : \{P\}_\mathrm{hp} = \frac{\{T\}_\mathrm{in {\cdot} lbf} \{N\}_\mathrm{rpm}}{63{,}025}. The constant 63,025 is the approximation of : 33{,}000~\frac{\text{ft} {\cdot} \text{lbf}}{\text{min}} \times \frac{12~\frac{\text{in}}{\text{ft}}}{2\pi~\text{rad}} \approx 63{,}025 \frac{\text{in} {\cdot} \text{lbf}}{\text{min}}. ==Definitions==

Imperial horsepower Assuming the third CGPM (1901, CR 70) definition of standard gravity, , is used to define the pound-force as well as the kilogram force, and the international avoirdupois pound (1959), one imperial horsepower is: : Or given that 1 hp = 550 ft⋅lbf/s, 1 ft = 0.3048 m, 1 lbf ≈ 4.448 N, 1 J = 1 N⋅m, 1 W = 1 J/s: 1 hp ≈ 745.7 W Metric horsepower (PS, KM, cv, hk, pk, k, ks, ch) s by 1 metre in 1 second. The various units used to indicate this definition (PS, KM, cv, hk, pk, k, ks and ch) all translate to horsepower in English. British manufacturers often intermix metric horsepower and mechanical horsepower depending on the origin of the engine in question. DIN 66036 defines one metric horsepower (Pferdestärke, or PS) as the power to raise a mass of 75 kilograms against the Earth's gravitational force over a distance of one metre in one second: = 75 Kilogram-force|⋅m/s = 1 PS. This is equivalent to 735.49875 W, or 98.6% of an imperial horsepower. In 1972, the PS was replaced by the kilowatt as the official power-measuring unit in EEC directives. Tax-horsepower ratings were originally more or less directly related to engine displacements, but, , many countries have changed over to systems based on emissions so the current systems are not directly comparable to old tax horsepower. The Citroën 2CV is named for its French fiscal horsepower rating, (2CV). Electrical horsepower Nameplates on electrical motors show their available shaft power output, not the electrical power input. This power output is ordinarily stated in watts or kilowatts. In the United States, the power output is stated in horsepower. Hydraulic horsepower Hydraulic horsepower can be the power available within hydraulic machinery or power through the down-hole nozzle of a drilling rig, or it can be used as an estimate of the mechanical power needed to generate a given hydraulic flow rate. It may be calculated as The term boiler horsepower was originally developed at the Philadelphia Centennial Exhibition in 1876, where the best steam engines of that period were tested. The average steam consumption of those engines (per output horsepower) was determined to be the evaporation of of water per hour, based on feed water at , and saturated steam generated at . This original definition is equivalent to a boiler heat output of . A few years later in 1884, the ASME redefined the boiler horsepower as the thermal output equal to the evaporation of 34.5 pounds per hour of water "from and at" . This considerably simplified boiler testing, and provided more accurate comparisons of the boilers at that time. This revised definition is equivalent to a boiler heat output of . Present industrial practice is to define boiler horsepower as a boiler thermal output equal to , which is very close to the original and revised definitions. Boiler horsepower is still used to measure boiler output in industrial boiler engineering in the US. Boiler horsepower is abbreviated BHP, which is also used in many places to symbolize brake horsepower. Drawbar power Drawbar power (dbp) is the power a railway 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 railway car called a dynamometer car coupled behind a locomotive keeps a continuous record of drawbar tension and speed. From these, the power generated can be calculated. To determine the maximum power available, a controllable load is required; it is normally a second locomotive with its brakes applied, in addition to a static load. If the drawbar force () is measured in pounds-force (lbf) and speed () is measured in miles per hour (mph), then the drawbar power () in horsepower (hp) is \{P\}_\mathrm{hp} = \frac{\{F\}_\mathrm{lbf} \{v\}_\mathrm{mph}}{375}. Example: How much power is needed to pull a drawbar load of 2,025 pounds-force at 5 miles per hour? \{P\}_\mathrm{hp} = \frac{2025 \times 5}{375} = 27. The constant 375 is because 1 hp = 375 lbf⋅mph. If other units are used, the constant is different. When using coherent SI units (watts, newtons, and metres per second), no constant is needed, and the formula becomes . This formula may also be used to calculate the power of a jet engine, using the speed of the jet and the thrust required to maintain that speed. Example: how much power is generated with a thrust of 4000 pounds at 400 miles per hour? \{P\}_\mathrm{hp} = \frac{4000 \times 400}{375} = 4266.7. RAC horsepower (taxable horsepower) This measure was instituted by the Royal Automobile Club and was used to denote the power of early 20th-century British cars. Many cars took their names from this figure (hence the Austin Seven and Riley Nine), while others had names such as "40/50 hp", which indicated the RAC figure followed by the true measured power. Taxable horsepower does not reflect developed horsepower; rather, it is a calculated figure based on the engine's bore size, number of cylinders, and a (now archaic) presumption of engine efficiency. 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. The United Kingdom was not the only country that used the RAC rating; many states in Australia used RAC hp to determine taxation. The RAC formula was sometimes applied in British colonies as well, such as Kenya (British East Africa). : \text{RAC h.p.} = \frac{D \times D \times n}{2.5} where : D is the diameter (or bore) of the cylinder in inches, : n is the number of cylinders. 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 (bore smaller than stroke), which tended to impose an artificially low limit on rotational speed, hampering the potential power output and efficiency of the engine. The situation persisted for several generations of four- and six-cylinder British engines: For example, Jaguar's 3.4-litre XK engine of the 1950s had six cylinders with a bore of and a stroke of , where most American automakers had long since moved to oversquare (large bore, short stroke) V8 engines. See, for example, the early Chrysler Hemi engine. ==Measurement==

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, but none is a clear indicator of either the measurement system or definition used. In general: :nominal horsepower is derived from the size of the engine and the piston speed and is only accurate at a steam pressure of ; :indicated or gross horsepower is the theoretical capability of the engine [PLAN/ 33000]; :brake/net/crankshaft horsepower (power delivered directly to and measured at the engine's crankshaft) equals ::indicated horsepower minus frictional losses within the engine (bearing drag, rod and crankshaft windage losses, oil film drag, etc.); :shaft horsepower (power delivered to and measured at the output shaft of the transmission, when present in the system) equals ::crankshaft horsepower minus frictional losses in the transmission (bearings, gears, oil drag, windage, etc.); :effective or true (thp), commonly referred to as wheel horsepower (whp), equals ::shaft horsepower minus frictional losses in the universal joint/s, differential, wheel bearings, tire and chain, (if present). All the above assumes that no power inflation factors have been applied to any of the readings. Engine designers use expressions other than horsepower to denote objective targets or performance, such as brake mean effective pressure (BMEP). This is a coefficient of theoretical brake horsepower and cylinder pressures during combustion. Nominal horsepower Nominal horsepower (nhp) is an early 19th-century rule of thumb used to estimate the power of steam engines. In Europe, the DIN 70020 standard tests the engine fitted with all ancillaries and the exhaust system as used in the car. The older American standard (SAE gross horsepower, referred to as bhp) used an engine without alternator, water pump, and other auxiliary components such as power steering pump, muffled exhaust system, etc., so the figures were higher than the European figures for the same engine. The newer American standard (referred to as SAE net horsepower) tests an engine with all the auxiliary components (detailed in Engine power test standards). Brake refers to the device which is used to provide an equal braking force, load to balance, or equal an engine's output force and hold it at a desired rotational speed. During testing, the output torque and rotational speed are measured to determine the brake horsepower. Horsepower was originally measured and calculated by use of the "indicator diagram" (a James Watt invention of the late 18th century), and later by means of a Prony brake connected to the engine's output shaft. Modern dynamometers use any of several braking methods to measure the engine's brake horsepower, the actual output of the engine itself, before losses to the drivetrain. Shaft horsepower Shaft horsepower (shp) is the power delivered to a propeller or turbine shaft. Shaft horsepower is a common rating for turboshaft and turboprop engines, industrial turbines, and some marine applications. Equivalent shaft horsepower (eshp) is sometimes used to rate turboprop engines. It includes the equivalent power derived from residual jet thrust from the turbine exhaust. of residual jet thrust is estimated to be produced from one unit of horsepower. == Engine power test standards==

There exist a number of different standards determining how the power and torque of an automobile engine is measured and corrected. Correction factors are used to adjust power and torque measurements to standard atmospheric conditions, to provide a more accurate comparison between engines as they are affected by the pressure, humidity, and temperature of ambient air. Some standards are described below. Society of Automotive Engineers/SAE International Early "SAE horsepower" In the early twentieth century, a so-called "SAE horsepower" was sometimes quoted for U.S. automobiles. This long predates the Society of Automotive Engineers (SAE) horsepower measurement standards and was another name for the industry standard ALAM or NACC horsepower figure and the same as the British RAC horsepower also used for tax purposes. Alliance for Automotive Innovation is the current successor of ALAM and NACC. SAE gross power Prior to the 1972 model year, American automakers rated and advertised their engines in brake horsepower, bhp, which was a version of brake horsepower called SAE gross horsepower because it was measured according to Society of Automotive Engineers (SAE) standards (J245 and J1995) that call for a stock test engine without accessories (such as dynamo/alternator, radiator fan, water pump), To attain certification the test must follow the SAE standard in question, take place in an ISO 9000/9002 certified facility and be witnessed by an SAE approved third party. A few manufacturers such as Honda and Toyota switched to the new ratings immediately. The rating for the Toyota Camry 3.0 L 1MZ-FE V6 fell from . All calibration and accessories had to be as on production engines. It is similar to DIN 70020 standard, but with different requirements for connecting an engine's fan during testing causing it to absorb less power from the engine. Economic Commission for Europe R85 ECE R85 is a UN standard for the approval of internal combustion engines with regard to the measurement of the net power. 80/1269/EEC 80/1269/EEC of 16 December 1980 is a European Union standard for road vehicle engine power. International Organization for Standardization The International Organization for Standardization (ISO) publishes several standards for measuring engine horsepower. • ISO 14396 specifies the additional and method requirement for determining the power of reciprocating internal combustion engines when presented for an ISO 8178 exhaust emission test. It applies to reciprocating internal combustion engines for land, rail and marine use excluding engines of motor vehicles primarily designed for road use. • ISO 1585 is an engine net power test code intended for road vehicles. • ISO 2534 is an engine gross power test code intended for road vehicles. • ISO 4164 is an engine net power test code intended for mopeds. • ISO 4106 is an engine net power test code intended for motorcycles. • ISO 9249 is an engine net power test code intended for earth moving machines. Japanese Industrial Standard (JIS) D 1001 JIS D 1001 is a Japanese net, and gross, engine power test code for automobiles or trucks having a spark ignition, diesel engine, or fuel injection engine. ==See also==