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[[Image:Long S in US Bill of Rights.JPG|right|thumb|250px|An italicized long s used in the word Congress in the [[United States Bill of Rights]].]]
{{Redirect|hp|other uses|HP (disambiguation)}}
The '''long''', '''medial''' or '''descending''' '''s''' ('''ſ''') is a form of the [[Lower case|minuscule]] letter '[[s]]' formerly used where 's' occurred in the middle or at the beginning of a word, for example ſinfulneſs ("sinfulness"). The modern [[letterform]] was called the '''terminal''' or '''short s'''.
{{Redirect|HP|the computer company|Hewlett Packard]}}
{{Original research|date=September 2008}}


==History==
'''Horsepower''' ('''hp''' or '''HP'''<ref>Collins Concise Dictionary ISBN 0004722574</ref>) is the name of several non-metric [[units of measurement|units]] of [[Power (physics)|power]]. In scientific discourse, the term "horsepower" is rarely used because of its various definitions and the already existent [[SI]] unit for power, the [[watt]] (W). However, use of the term "horsepower" persists as a legacy in many languages and industries, particularly as a unit of measurement of the maximum power output of [[internal-combustion engine]]s of [[automobile]]s; and often of [[trucks]], [[buses]], and [[ship]]s. The use of 'HP' is being slowly replaced by [[kW]] (kilowatt) and [[Megawatt|MW]] (megawatt).
[[Image:Milton paradise.jpg|thumb|250px|right|[[Title page]] of [[John Milton]]'s [[Paradise Lost]]]]


The long 's' is derived from the old Roman cursive medial s, which was very similar to an elongated [[check mark]]. When the distinction between [[upper case]] (capital) and [[lower case]] (small) letter-forms became established, towards the end of the eighth century, it developed a more vertical form.<ref name = "A Ox">Lyn Davies. ''A Is for Ox'', London: 2006. Folio Society.</ref> At this period it was occasionally used at the end of a word, a practice which quickly died out but was occasionally revived in [[Italy|Italian]] [[printing]] between about 1465 and 1480.<!-- Note: thus the statement later in this article that the long 's' "''never'' occurred at the end of a word" is not strictly correct, although the exceptions are too rare and archaic to invalidate the point made there. --> The short 's' was also normally used in the combination 'sf', for example in 'ſatisfaction'. In German written in [[Fraktur (script)|fraktur]], the rules are more complicated: short 's' also appears at the end of distinct elements within a word.
There are two important factors to consider when evaluating the measurement of "horsepower":
* The inconsistent ''[[#Current definitions|definitions]]'' of the "horsepower" unit itself
* The various ''[[#Measurement|standards]]'' used in measuring the value of "horsepower"
These factors can be combined in unexpected ways &mdash; the power output for an engine rated at "100 horsepower" might not be what a reader expects. For this reason, various groups have attempted to standardize not only the definition of "horsepower" but the measurement of "horsepower". In the interim, more confusion may surface.


The long 's' is subject to confusion with the [[lower case]] or [[Lower case|minuscule]] '[[f]]', sometimes even having an 'f'-like nub at its middle, but on the left side only, in various kinds of [[Roman type|Roman]] [[typeface]] and in [[blackletter]]. There was no nub in its [[italics|italic]] typeform, which gave the stroke a [[descender]] curling to the left&mdash;not possible with the other typeforms mentioned without [[kerning]].
== History of the term "horsepower" ==
The development of the steam engine provided a reason to equate the output of horses with 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 term "horsepower" was coined later 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 engine]]s.<ref>{{cite web
|url=http://www.pballew.net/arithm17.html#hp
|title=Math Words &mdash; horsepower
|publisher=pballew.net/
|accessdate=2007-08-11}}</ref> 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, therefore the horse travelled 2.4 × 2π × 12 feet in one minute. Watt judged that the horse could pull with a [[force]] of 180 pounds (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 ft·lbf/min.<ref>{{Citation
|last=Tully
|first=Jim
|publisher=American Society of Mechanical Engineers
|title=Philadelphia Chapter Newsletter
|date=September 2002
|url=http://sections.asme.org/Philadelphia/sept02.htm
|accessdate=2007-08-11}} (see the AMSE puzzler answer)</ref>


The nub acquired its form in the [[blackletter]] style of writing. What looks like one stroke was actually a wedge pointing downward, whose widest part was at that height ([[x-height]]), and capped by a second stroke forming an [[ascender]] curling to the right. Those styles of writing and their derivatives in type design had a cross-bar at height of the nub for letters 'f' and 't', as well as 'k'. In Roman type, these disappeared except for the one on the medial 's'.
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 ft·lbf/min figure.


The long 's' was used in [[ligature (typography)|ligatures]] in various languages. Three examples were for 'si', 'ss', and 'st', besides the [[German language|German]] 'double s' '[[ß]]'.
''Engineering in History'' recounts that John Smeaton initially estimated that a horse could produce 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.<ref>{{cite book
|url=http://print.google.com/print?id=AVn_Sm56OCoC&pg=171&lpg=171&dq=smeaton&sig=6N_TJXrLqwQI-Fm7mU9ebKS1djA
|title=Engineering in History
|author=Richard Shelton Kirby
|publisher=Dover Publications
|pages=171
|date=[[August 1]], [[1990]]
|isbn=0486264122
|accessdate=2007-08-11}}</ref>


Long 's' fell out of use in Roman and italic typography well before the middle of the 19th century; in French the change occurred from about 1780 onwards, in English in the decades before and after 1800, and in the United States around 1820. This may have been spurred by the fact that long 's' looks somewhat like 'f' (in both its Roman and italic forms), whereas short 's' did not have the disadvantage of looking like another letter, making it easier to read correctly, especially for people with vision problems.
Put into perspective, a healthy human can produce about 1.2 hp briefly (see [[Orders of magnitude (power)]]) and sustain about 0.1 hp indefinitely, and trained athletes can manage up to about 0.3 horsepower for a period of several hours.


Long 's' survives in German [[blackletter]] typefaces. The present-day German 'double s' '[[ß]]' (das Eszett "''the ess-zed''" or scharfes-ess, the sharp S) is an atrophied [[ligature (typography)|ligature]] form representing either 'ſz' or 'ſs' (see [[ß]] for more). Greek also features a normal [[Sigma (letter)|sigma]] 'σ' and a special terminal form 'ς', which may have supported the idea of specialized 's' forms. In Renaissance Europe a significant fraction of the literate class was familiar with Greek.
Most observers familiar with horses and their capabilities estimate that Watt was either a bit optimistic or intended to under promise and over deliver; few horses can maintain that effort for long. Regardless, comparison to a horse proved to be an enduring marketing tool.


==Modern usage==
===Horsepower from a horse===
[[Image:CycleDesign Kopie.jpg|thumb|right|250px|Long s in [[Berlin]] 2002]]
R. D. Stevenson and R. J. Wasserzug published an article in Nature 364, 195-195 ([[15 July]] [[1993]]) calculating the upper limit to an animal's power output. The peak power over a few seconds has been measured to be as high as 14.9 hp. However, for longer periods an average horse produces less than one horsepower.


The long 's' is represented in [[Unicode]] by the sign U+017F in the Latin Extended-A range, and may be represented in [[HTML]] as <code>&amp;#x17F;</code> or <code>&amp;#383;</code>.
==Current definitions==
The following definitions have been widely used:
{|class=wikitable
|-
|valign=top|[[#Mechanical horsepower|Mechanical&nbsp;horsepower]]
|≡ 33,000&nbsp;ft·[[pound-force|lb<sub>f</sub>]]/min
= 550&nbsp;ft·lb<sub>f</sub>/s<br>
= 745.6999&nbsp;[[Watt|W]]
|-
|valign=top|[[#Metric horsepower|Metric&nbsp;horsepower]]
|≡ 75&nbsp;[[kilogram-force|kg<sub>f</sub>]]·m/s<br>
= 735.49875&nbsp;W (exactly)
|-
|[[#Electrical horsepower|Electrical&nbsp;horsepower]]
|≡746&nbsp;W
|-
|valign=top|[[#Boiler horsepower|Boiler&nbsp;horsepower]]
|≡ 33,475 [[Btu]]/h
=9809.5 W
|-
|valign=top|[[#Hydraulic horsepower|Hydraulic&nbsp;horsepower]]
|colspan=2|=Flow Rate([[US gal]]/[[minute|min]]) * Pressure([[lbf/in²|psi]]) / 1714
|}
Hydraulic horsepower is equivalent to mechanical horsepower. The formula given above is for conversion to mechanical horsepower from the factors acting on a hydraulic system.

Additionally, the term "horsepower" has been applied to calculated (estimated rather than measured) metrics:
* [[Tax horsepower|RAC horsepower]] is based solely on the dimensions of a piston engine (1 litre of engine displacement is equal to 10 RAC horsepower)

===Mechanical horsepower===
:''See [[#History of the term "horsepower"|History of the term "horsepower"]]''
The term <nowiki>"horsepower"</nowiki> was coined by the engineer [[James Watt]] in 1782 while working in the performance of steam engines. This occurred while using a [[pit pony|mine pony]] to lift coal out of a coal mine. He conceived the idea of defining the power exerted by these animals to accomplish this work. He found that, on the average, a mine pony could pull (lift by means of a pulley) 22,000 foot-pounds per minute. Rather than call this "pony" power, he increased these test results by 50 percent, and called it horsepower i.e. 33,000 foot-pounds of work per minute.

Assuming the third [[General Conference on Weights and Measures|CGPM]] (1901, CR 70) definition of [[standard gravity]], ''g'', and the [[Pound (mass)#International pound|international avoirdupois pound]] (1958), one mechanical horsepower is:


{| align="right"
:{|
| <math>\int_a^b </math>
|-
|1 hp
|≡ 33,000&nbsp;ft·lb<sub>f</sub>/min
|colspan=3|by definition
|-
|
|= 550&nbsp;ft·lb<sub>f</sub>/s
|since
|align=right|1&nbsp;min&nbsp;
|= 60&nbsp;s
|-
|
|= 550 × 0.3048 × 0.45359237&nbsp;m·[[kilogram-force|kg<sub>f</sub>]]/s&nbsp;
|since
|align=right|1&nbsp;ft
|= 0.3048&nbsp;m and
|-
|
|= 76.0402249068&nbsp;kg<sub>f</sub>·m/s
|
|align=right|1&nbsp;lb
|= 0.45359237&nbsp;kg
|-
|
|= 76.0402249068 × 9.80665&nbsp;kg·m²/s³
|
|align=right|''g''
|= 9.80665&nbsp;m/s²
|-
|
|= 745.69987158227022&nbsp;W
|since
|align=right|1&nbsp;W
|≡ 1&nbsp;[[joule|J]]/s = 1&nbsp;[[Newton|N]]·m/s = 1&nbsp;(kg·m/s²)·(m/s)
|}
|}


The long 's' survives in elongated form, and with an italic-style curled descender, as the [[integral]] symbol {{unicode|∫}} used in [[calculus]]; [[Gottfried Wilhelm von Leibniz]] based the character on the Latin word ''summa'' (sum), which he wrote ''ſumma''. This use first appeared publicly in his paper ''De Geometria'', published in ''[[Acta Eruditorum]]'' of June, 1686,<ref>''Mathematics and its History'', John Stillwell, Springer 1989, p. 110</ref> but he had been using it in private manuscripts since at least 1675.<ref>''Early Mathematical Manuscripts of Leibniz'', J. M. Child, Open Court Publishing Co., 1920, pp. 73–74, 80.</ref>
Or given that 1 hp = 550 ft·lbf/s, 1 ft = 0.3048 m, 1 lb = 4.448 N, 1 J = 1 N·m, 1 W = 1 J/s: 1 hp = 746 W


In linguistics a similar glyph ({{IPA|ʃ}}) (called "[[Esh (letter)|esh]]") is used in the [[International Phonetic Alphabet]], in which it represents the [[voiceless postalveolar fricative]], the first sound in the English word ''shun''.
cross multiply and cancel out:
{| class="wikitable"
|-
| 550 <s>ft</s>-<s>lb</s>/<s>s</s>
| 0.3048 <s>m</s>
| 4.448 <s>N</s>
| 1 <s>J</s>
| 1 W
|-
| 1 hp
| 1 <s>ft</s>
| 1 <s>lb</s>
|1 <s>N</s>-<s>m</s>
|1 <s>J</s>/<s>s</s>
|} = 745.66272 W or 746 W


In Scandinavian and German-speaking countries, relics of the long ſ continue to be seen in signs and logos that use various forms of [[fraktur]] typefaces. Examples include the logos of the Norwegian newspapers [[Aftenposten|Aftenpoſten]] and [[Adresseavisen|Adresſeaviſen]], and the packaging logo for Finnish 'Siſu' pastilles.
=== Metric horsepower ===
Metric horsepower began in [[Germany]] in the 19th century and became popular across Europe and Asia. The various units used to indicate this definition ("PS", "CV", "pk", and "ch") all translate to "horse power" in English, so it is common to see these values referred to as "horsepower" or "hp" in the press releases or media coverage of the German, French, Italian, and Japanese automobile companies. British manufacturers often intermix metric horsepower and mechanical horsepower depending on the origin of the engine in question.


The similarity between the printed long 'ſ' and 'f', and modern-day unfamiliarity with the former letter has been the subject of much humour based on the intentional misreading of s as f, e.g. pronouncing ''[[Greensleeves]]'' as ''Greenfleeves'' and ''song'' as ''fong'' in a [[Flanders and Swann]] monologue<ref>{{cite web|url=http://www.beachmedia.com/gorbuduc.html|title=The Greensleeves Monologue Annotated}}</ref>.
Metric horsepower, as a rule, is defined as 0.73549875&nbsp;kW, or roughly 98.6% of mechanical horsepower. This was a minor issue in the days when measurement systems varied widely and engines produced less power, but has become a major sticking point today. Exotic cars from Europe like the [[McLaren F1]] and [[Bugatti Veyron]] are often quoted using the wrong definition, and their power output is sometimes even converted twice because of confusion over whether the original "horsepower" number was metric or mechanical.{{Fact|date=May 2008}}

==== PS ====
This unit ({{lang-de|Pferdestärke}} = horse strength) is no longer a statutory 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 "horsepower", but mathematically different from the British unit. It is defined by the ''Physikalisch-Technische Bundesanstalt'' (PTB)<ref>[http://www.ptb.de/de/publikationen/download/pdf/einheiten.pdf Die gesetzlichen Einheiten in Deutschland (in German)] on [http://www.ptb.de/ PTB.de]</ref> in [[Braunschweig (city)|Braunschweig]] as exactly:

: 1 PS = 75 [[kilopond]]·[[Meter|metre]]/[[second]] ~= 735.5 [[newton]]·m/s ~= 735.5 W ~= 0.7355 kW ~= 0.98632 hp (SAE)

The PS was adopted by the [[DIN|Deutsches Institut für Normung (DIN)]] and then by the automotive industry throughout most of Europe, under varying names. In 1992, the PS was rendered obsolete by EEC directives, when it was replaced by the kilowatt as the official power measuring unit. It is still in use for commercial and advertising purposes, as many customers are not familiar with the use of kilowatts for engines.

====pk, hk, and hv====
The Dutch ''paardenkracht'' (pk), the Swedish ''hästkraft'' (hk), the Finnish ''hevosvoima'' (hv), the Norwegian and Danish ''hestekraft'' (hk), and the Hungarian ''lóerő'' (LE) all equal the German ''Pferdestärke'' (PS).

==== CV and cv ====

In Italian ("Cavalli"), Spanish ("Caballos"), and Portuguese ("Cavalos"), 'CV' is the equivalent to the German 'PS'. It is also used as the French term for the Pferdestärke, but in French, this should be written in lowercase letters as 'cv'.

In addition, the capital form 'CV' is a French unit for [[tax horsepower]], short for ''chevaux vapeur'' ("steam horses") or ''cheval-vapeur''. CV is a non-linear rating of a motor vehicle for tax purposes.<ref>[http://home.att.net/~numericana/answer/units.htm Measurements, Units of Measurement, Weights and Measures - numericana.com]</ref> The CV rating, or fiscal power, is <math>\left(\tfrac{P}{40}\right)^{1.6} + \tfrac{U}{45}</math>, where ''P'' is the maximum power in kilowatts and ''U'' is the amount of CO<sub>2</sub> emitted in grams per kilometre. The fiscal power has found its way into naming of automobile models, such as the popular [[Citroën 2CV|Citroën deux-chevaux]]. The cheval-vapeur (ch) unit should not be confused with the French cheval fiscal (CV).

In the 19th century the French had their own unit, which they used instead of the CV or horsepower. It was called the [[poncelet]] and was abbreviated 'p'.

==== ch ====

This is a French unit for automobile power. The symbol ch is short for ''chevaux'' ("horses"). Some sources give it as 0.7355 kW, but it is generally used interchangeably with the German 'PS'.

=== Boiler horsepower ===

A '''boiler horsepower''' is used for boilers in [[power station|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 [[degree Fahrenheit|°F]] (100 [[degree Celsius|°C]]) in one hour.

=== Electrical horsepower===

The '''electrical horsepower''' is used by the electrical industry for electrical machines and is defined to be exactly 746 W at 100% efficiency. Electric motors can never run at 100% efficiency. The nameplates on electrical motors show their power output, not their power input.

=== Relationship with torque ===
For a given [[torque]], the equivalent power may be calculated. The standard equation relating torque in [[foot-pound]]s, rotational speed in [[RPM]] and horsepower is:
:<math>P [ {\rm hp}] = {[\Tau / ({\rm ft \cdot lbf})] [\omega / ({\rm r/min})] \over 5252}</math>

Where <math>P</math> is power, <math>\tau</math> is torque, and <math>\omega</math> is rotations per minute.
Outside the United States, most countries use the [[newton meter]] as the unit of torque. Most [[automobile]] specifications worldwide have torque listed in newton meters. The standard equation relating torque in newton meters, rotational speed in [[RPM]] and power in kilowatts is:
:<math>P [ {\rm kW}] = {[\Tau / ({\rm N \cdot m })] [\omega / ({\rm r/min})] \over 9549}</math>

These are based on Watt's definition of the mechanical horsepower. The constants 5252 and 9549 are rounded.

5252 comes from 33,000 (ft.lbf/min) / 2π (radians/revolution),

and 9549 comes from 60 (s/min) x 1000 (W/kW) / 2π (radians/revolution).

See [[torque#Relationship between torque and power|torque]].

=== Drawbar horsepower ===
:''See [[Power at rail]]''
Drawbar horsepower (dbhp) 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 the locomotive keeps a continuous record of the [[Drawbar (haulage)|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; is normally a second locomotive with its brakes applied, in addition to a static load.

If the drawbar force (<math>F</math>) is measured in (lbf) and speed (<math>v</math>) is measured in miles per hour (mph), then the drawbar power (<math>P</math>) in horsepower (hp) is:

<!-- prev, confusing :<math>P / {\rm hp} = {(F / {\rm lbf}) (v / {\rm mph}) \over 375}</math> -->
:<math>P = {Fv\over 375}</math>

Example: How much power is needed to pull a drawbar load of 2025 pounds-force at 5 miles per hour?

<math>P = {{2025 \times 5 } \over 375} = 27</math>

The constant "375" is because 1 hp = 375 lbf·mph. 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) ===
{{seealso|Tax horsepower}}
This measure was instituted by the [[Royal Automobile Club]] in [[United Kingdom|Britain]] and was used to denote the power of early 20th century British [[automobile|cars]]. Many cars took their names from this figure (hence the [[Austin Motor Company|Austin]] Seven and [[Riley (automobile)|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 horsepower|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.<ref>{{cite web
|url=http://www.designchambers.com/wolfhound/wolfhoundRACHP.htm
|title=The RAC HP (horsepower) Rating - Was there any technical basis?
|author=Richard Hodgson
|publisher=wolfhound.org.uk
|accessdate=2007-08-11}}</ref> {{Failed verification|date=August 2007}}<!-- Has this Ref been placed at the wrong point? The cited source does support a lot of this stuff, but I don't see where it supports the assertion that "This is equal to the displacement in cubic inches divided by 10π then divided again by the stroke in inches." -->

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 potential power output and efficiency of the engine.

The situation persisted for several generations of four- and six-cylinder British engines: for example, [[Jaguar (car)|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-8]]s]

==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 the case of an engine dynamometer, power is measured at the engine's [[flywheel]] (i.e., at the crankshaft output). With a chassis dynamometer or "rolling road", power output is measured at the driving wheels. This accounts for the significant power loss through the drive train. As an example, an early-production [[British Leyland|BL]] [[Mini]] {{auto cm3in3|850}} engine produced about {{auto bhp|34|1}} at the flywheel, of which only {{auto bhp|18.2|}} reached the driving wheels.{{Fact|date=September 2008}}

In general:
:[[#Nominal horsepower (nhp)|Nominal]] is derived from the size of the engine and the piston speed and is only accurate at a pressure of 7 lbf/in².<ref name=Brown>Brown, DK ''Before the ironclad'', pub Conway, 1990, p188.</ref>

:[[#Indicated horsepower (ihp)|Indicated]] or gross horsepower (theoretical capability of the engine)
::minus frictional losses within the engine (bearing drag, rod and crankshaft windage losses, oil film drag, etc.), equals
:[[#Brake horsepower (bhp)|Brake]] / net / crankshaft horsepower (power delivered directly to and measured at the engine's crankshaft)
::minus frictional losses in the transmission (bearings, gears, oil drag, windage, etc.), equals
:[[#Shaft horsepower (shp)|Shaft]] horsepower (power delivered to and measured at the output shaft of the transmission, when present in the system)
::minus frictional losses in the universal joint/s, differential, wheel bearings, tire and chain, (if present), equals
:[[#Effective horsepower (ehp)|Effective]], True (thp) or commonly referred to as wheel horsepower (whp)

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 BMEP (Brake Mean Effective pressure). This is a coefficient of theoretical brake horsepower and cylinder pressures during combustion.

=== Nominal horsepower ===
Nominal horsepower (nhp) is an early Nineteenth Century [[rule of thumb]] used to estimate the power of steam engines.

nhp = 7 x area of piston x equivalent piston speed/33,000

For paddle ships the piston speed was estimated as 129.7 x (stroke)<sup>1/3.35</sup>

For the nominal horsepower to equal the actual power it would be necessary for the mean steam pressure in the cylinder during the stroke to be 7 psi and for the piston speed to be of the order of 180-248 ft/s.<ref name="Brown" />

=== Indicated horsepower ===
Indicated horsepower (ihp) is the theoretical power of a reciprocating engine if 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 engine]]s in the 19th century but is misleading because the mechanical efficiency of an engine means that the actual power output may only be 70% to 90% of the indicated horsepower.

=== Brake horsepower ===
Brake horsepower (abbreviated ''bhp'') is the measure of an engine's horsepower without the loss in power caused by the gearbox, generator, differential, water pump, and other auxiliary components such as alternator, power steering pump, muffled exhaust system, etc. "Brake" refers to how horsepower was originally measured and calculated, by means of a [[De Prony brake]] connected to the engine's output shaft. More recently, an engine [[dynamometer]] is used instead of a De Prony brake. The output delivered to the driving wheels is less than that obtainable at the engine's crankshaft.

=== British horsepower ===
The acronym ''bhp'' may also be used for ''British horsepower'', which has the same definition as the American SAE gross brake horsepower: 33,000 lb·ft/minute. More information on American SAE horsepower measurements is below.

===SAE horsepower===
==== SAE gross horsepower ====
Prior to the 1972 model year, American automakers rated and advertised their engines in brake horsepower (bhp), frequently referred to as '''SAE gross horsepower''' because it was measured in accord with the protocols defined in [[Society of Automotive Engineers|SAE]] standards J245 and J1995. As with other brake horsepower test protocols, SAE gross hp was measured using a blueprinted test engine running on a stand with no belt-driven accessories, air cleaner, mufflers, or emission control devices and sometimes fitted with long tube "test headers" in lieu of the OEM exhaust manifolds.{{Fact|date=September 2008}} The atmospheric correction standards for barometric pressure, humidity and temperature were relatively idealistic. The resulting gross power and torque figures therefore reflected a maximum, theoretical value and not the power of an installed engine in a street car. Gross horsepower figures were also subject to considerable adjustment by the manufacturer's advertising and marketing staff under the direction of product managers.{{Fact|date=September 2008}} The power ratings of mass-market engines were often exaggerated beyond their actual gross output, while those of the highest-performance [[muscle car]] engines often tended to be closer in actual output to their advertised, gross ratings.{{Fact|date=September 2008}}

No pre-1972 engine in its unaltered, production line stock form, as installed in the vehicle, has ever yielded documented, qualified third party validated power figures that equal or exceed its original gross rating.{{Fact|date=September 2008}} Claims that such engines were "under-rated" are therefore dubious; for example, the 1969 427 ZL1 Chevrolet, rated at {{Auto bhp|430|1}}, is frequently cited{{Who|date=September 2008}} as an "under-rated" high performance engine, yet it produced only {{Convert|376|hp|kW}}.<ref>...[http://www.camaros.org/copo.shtml "ZL1 DYNO TEST - COPO CAMARO WEBSITE"]...</ref>

====SAE net horsepower====
In the United States the term "bhp" fell into disuse in 1971-72, as automakers began to quote power in terms of '''SAE net horsepower''' in accord with SAE standard J1349. Like SAE gross and other brake horsepower protocols, SAE Net hp is measured at the engine's crankshaft, and so does not account for transmission losses. However, the SAE net hp testing protocol calls for standard production-type belt-driven accessories, air cleaner, emission controls, exhaust system, and other power-consuming accessories. This produces ratings in closer alignment with the power produced by the engine as it is actually configured and sold. The change to net hp effectively deflated power ratings to assuage the [[auto insurance]] industry and environmental and safety lobbies.

Because SAE gross ratings were applied liberally, there is no precise conversion from gross to net. Comparison of gross and net ratings for unchanged engines shows a variance of anywhere from 40 to 150 horsepower. The [[Chrysler Hemi engine|Chrysler 426 Hemi]], for example, in 1971 carried a 425 hp gross rating and a net rating of 350 hp, while the same company's [[Chrysler Slant-6 engine|225 Slant 6]] carried a rating of 145 bhp but 110 net hp.{{Facts|date=September 2008}}

==== SAE certified horsepower ====
In 2005, the SAE introduced a new test protocol for engine horsepower and torque.<ref>[http://www.sae.org/certifiedpower/ SAE J2723 Certified Power]</ref> The new protocol eliminates some of the flexibility in power measurement, and requires an independent observer present when engines are measured. The test is voluntary, but engines completing it can be advertised as "SAE-certified".

Many manufacturers began switching to the new rating immediately, with multi-directional results; the rated output of [[Cadillac|Cadillac's]] [[supercharger|supercharged]] [[GM Premium V engine#Supercharged|Northstar]] V8 jumped from {{convert|440|hp|kW}} to {{convert|469|hp|kW}} under the new tests, while the rating for [[Toyota Motor Corporation|Toyota's]] [[Toyota Camry|Camry]] 3.0&nbsp;L ''[[Toyota MZ engine#1MZ-FE|1MZ-FE]]'' V6 fell from {{convert|210|hp|kW}} to {{convert|190|hp|kW}}. The first engine certified under the new program was the 7.0&nbsp;L [[GM LS engine#LS7|LS7]] used in the 2006 [[Chevrolet Corvette]] Z06. Certified power rose slightly from {{convert|500|hp|kW}} to {{convert|505|hp|kW}}.

=== DIN hp ===
'''DIN horsepower''' is the power measurement protocol in the [[Germany|German]] [[DIN]] standard 70020. It is sometimes abbreviated as "PS", which stands for ''Pferdestärke'', which is the [[German language|German]] word for horsepower. DIN hp is measured at the engine's output shaft, and is usually expressed in [[#Metric horsepower|metric (Pferdestärke)]] rather than [[#Mechanical horsepower|mechanical]] horsepower.

=== ECE hp ===
'''ECE R24''' is the [[ECE Regulations|European standard]] for measuring engine output.<ref>[http://www.unece.org/trans/main/wp29/wp29regs/r024r2e.pdf ECE Regulation 24, Revision 2, Annex 10]</ref> It is quite similar to the DIN 70020 standard, but with different requirements for connecting an engine's fan during testing. ECE is seen{{Who|date=September 2008}} as slightly more liberal than DIN, and ECE figures tend to be slightly higher than DIN.{{Fact|date=September 2008}}

=== 9768-EC ===
'''9768-EC''' is a [[European Union]] standard, generally very similar to ISO-14396.

=== ISO 14396 ===
'''ISO 14396''' is a new standard from the ISO for all engines not intended for on-road use.

=== Shaft horsepower ===
Shaft horsepower (shp) is the power delivered to the [[propeller]] shaft of a [[ship]] or an airplane powered by a piston engine or a turbine engine (the combination of turbine engine and propeller commonly called a [[turboprop]]). 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%). This metric is uncommon in the automobile industry, though drivetrain losses can be significant.

===Effective (true, wheel) hp===
Effective horsepower (ehp), True horsepower (thp) or wheel horsepower (whp) is the power converted to useful work. In the case of a road vehicle this is the power actually turned into forward motion as measured on a [[Dynamometer#Chassis dynamometer|chassis dynamometer]]. Thp is generally 10% to 20% less than the engine's bhp rating due to drivetrain losses.{{Dubious|date=September 2008}}{{Fact|date=September 2008}}


==See also==
==See also==
{{Commons|Langes s}}
*[[Brake specific fuel consumption]] - how much propellant is needed to generate horsepower
* [[ß]] (Eszett)
* [[Esh (letter)]]
* [[Integral sign]]
* [[R rotunda]]


==References==
==Notes==
<!--See [[Wikipedia:Footnotes]] for an explanation of how to generate footnotes using the <ref(erences/)> tags-->
{{reflist}}
{{reflist}}


==External links==
==External links==
*[http://typefoundry.blogspot.com/2008/01/long-s.html James Mosley on long ''s'']
*[http://www.epi-eng.com/ET-PwrTrq.htm Power and Torque Explained] A clear explanation of the relationship between Power and Torque, and how they relate to engine performance.
*[http://auto.howstuffworks.com/horsepower.htm How Stuff Works - Horsepower]
*[http://www.straightdope.com/classics/a1_110.html The Straight Dope on long ''s'']
*[http://tiger.towson.edu/~apeak1/ow/doi.html The American Declaration of Independence with long s's]
*[http://craig.backfire.ca/pages/autos/horsepower "Horsepower and Torque"] An article showing how power, torque, and gearing affect a vehicle's performance.
*[http://babelstone.blogspot.com/2006/06/rules-for-long-s.html The Rules for Long S]
*[http://www.imperialtometric.com/conversion_en.htm Online Horsepower Converter]
*[http://babelstone.blogspot.com/2006/07/long-and-short-of-letter-s.html The Long and the Short of the Letter S]
*[http://www.nitrod.com/articles/HorsepowerTA.pdf "Horsepower and power losses"] Explains Horsepower and the power losses in the engine and powertrain.

*[http://www.web-cars.com/math/horsepower.html "What is Horsepower?"] (picture)
{{Latin alphabet}}
*[http://www.straightdope.com/mailbag/mhorsepower.html "What's the difference between horsepower and torque?"] at the [[Straight Dope]]


{{DEFAULTSORT:S - Long}}
[[Category:Imperial units]]
[[Category:Units of power]]
[[Category:History of the English language]]
[[Category:Customary units in the United States]]
[[Category:Typography]]
[[Category:Palaeographic letter variants]]


[[bg:Конска сила]]
[[als:Langes s]]
[[ca:Cavall de vapor]]
[[br:S hir]]
[[cs:Koňská síla]]
[[de:Langes s]]
[[da:Hestekraft]]
[[et:Pikk s]]
[[de:Pferdestärke]]
[[es:S larga]]
[[et:Hobujõud]]
[[fr:S long]]
[[es:Caballo de vapor]]
[[it:S lunga]]
[[eo:Ĉevalpovo]]
[[he:S ארוכה]]
[[eu:Zaldi Potentzia]]
[[la:Littera s longa]]
[[fr:Cheval-vapeur]]
[[nl:Lange s]]
[[gl:Cabalo de vapor]]
[[ja:長いs]]
[[ko:마력]]
[[pl:Długie s]]
[[hr:Konjska snaga]]
[[pt:S longo]]
[[it:Cavallo vapore]]
[[fi:Pitkä s]]
[[he:כוח סוס]]
[[sv:Långt s]]
[[kk:Ат күші]]
[[zh:长s]]
[[ku:Hespxurtanî]]
[[lt:Arklio galia]]
[[hu:Lóerő]]
[[ms:Kuasa kuda]]
[[nl:Paardenkracht]]
[[ja:馬力]]
[[no:Hestekraft]]
[[nn:Hestekraft]]
[[pl:Koń parowy]]
[[pt:Cavalo-vapor]]
[[ru:Лошадиная сила]]
[[sk:Konská sila]]
[[sl:Konjska moč]]
[[sh:Konjska snaga]]
[[fi:Hevosvoima]]
[[sv:Hästkraft]]
[[vi:Mã lực]]
[[tr:Beygir gücü]]
[[uk:Кінська сила]]
[[zh:馬力]]

Revision as of 03:05, 13 October 2008

File:Long S in US Bill of Rights.JPG
An italicized long s used in the word Congress in the United States Bill of Rights.

The long, medial or descending s (ſ) is a form of the minuscule letter 's' formerly used where 's' occurred in the middle or at the beginning of a word, for example ſinfulneſs ("sinfulness"). The modern letterform was called the terminal or short s.

History

Title page of John Milton's Paradise Lost

The long 's' is derived from the old Roman cursive medial s, which was very similar to an elongated check mark. When the distinction between upper case (capital) and lower case (small) letter-forms became established, towards the end of the eighth century, it developed a more vertical form.[1] At this period it was occasionally used at the end of a word, a practice which quickly died out but was occasionally revived in Italian printing between about 1465 and 1480. The short 's' was also normally used in the combination 'sf', for example in 'ſatisfaction'. In German written in fraktur, the rules are more complicated: short 's' also appears at the end of distinct elements within a word.

The long 's' is subject to confusion with the lower case or minuscule 'f', sometimes even having an 'f'-like nub at its middle, but on the left side only, in various kinds of Roman typeface and in blackletter. There was no nub in its italic typeform, which gave the stroke a descender curling to the left—not possible with the other typeforms mentioned without kerning.

The nub acquired its form in the blackletter style of writing. What looks like one stroke was actually a wedge pointing downward, whose widest part was at that height (x-height), and capped by a second stroke forming an ascender curling to the right. Those styles of writing and their derivatives in type design had a cross-bar at height of the nub for letters 'f' and 't', as well as 'k'. In Roman type, these disappeared except for the one on the medial 's'.

The long 's' was used in ligatures in various languages. Three examples were for 'si', 'ss', and 'st', besides the German 'double s' 'ß'.

Long 's' fell out of use in Roman and italic typography well before the middle of the 19th century; in French the change occurred from about 1780 onwards, in English in the decades before and after 1800, and in the United States around 1820. This may have been spurred by the fact that long 's' looks somewhat like 'f' (in both its Roman and italic forms), whereas short 's' did not have the disadvantage of looking like another letter, making it easier to read correctly, especially for people with vision problems.

Long 's' survives in German blackletter typefaces. The present-day German 'double s' 'ß' (das Eszett "the ess-zed" or scharfes-ess, the sharp S) is an atrophied ligature form representing either 'ſz' or 'ſs' (see ß for more). Greek also features a normal sigma 'σ' and a special terminal form 'ς', which may have supported the idea of specialized 's' forms. In Renaissance Europe a significant fraction of the literate class was familiar with Greek.

Modern usage

Long s in Berlin 2002

The long 's' is represented in Unicode by the sign U+017F in the Latin Extended-A range, and may be represented in HTML as &#x17F; or &#383;.

The long 's' survives in elongated form, and with an italic-style curled descender, as the integral symbol ∫ used in calculus; Gottfried Wilhelm von Leibniz based the character on the Latin word summa (sum), which he wrote ſumma. This use first appeared publicly in his paper De Geometria, published in Acta Eruditorum of June, 1686,[2] but he had been using it in private manuscripts since at least 1675.[3]

In linguistics a similar glyph (ʃ) (called "esh") is used in the International Phonetic Alphabet, in which it represents the voiceless postalveolar fricative, the first sound in the English word shun.

In Scandinavian and German-speaking countries, relics of the long ſ continue to be seen in signs and logos that use various forms of fraktur typefaces. Examples include the logos of the Norwegian newspapers Aftenpoſten and Adresſeaviſen, and the packaging logo for Finnish 'Siſu' pastilles.

The similarity between the printed long 'ſ' and 'f', and modern-day unfamiliarity with the former letter has been the subject of much humour based on the intentional misreading of s as f, e.g. pronouncing Greensleeves as Greenfleeves and song as fong in a Flanders and Swann monologue[4].

See also

Wikimedia Commons has media related to Langes s.

Notes

  1. ^ Lyn Davies. A Is for Ox, London: 2006. Folio Society.
  2. ^ Mathematics and its History, John Stillwell, Springer 1989, p. 110
  3. ^ Early Mathematical Manuscripts of Leibniz, J. M. Child, Open Court Publishing Co., 1920, pp. 73–74, 80.
  4. ^ "The Greensleeves Monologue Annotated".

External links

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