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=== Compound engines === {{Main|Compound steam engine}} A method to lessen the magnitude of energy loss to a very long cylinder was invented in 1804 by British engineer [[Arthur Woolf]], who patented his ''Woolf high-pressure '''compound engine''''' in 1805. In the compound engine, high-pressure steam from the boiler expands in a '''high-pressure (HP) cylinder''' and then enters one or more subsequent '''lower-pressure (LP) cylinders'''. The complete expansion of the steam now occurs across multiple cylinders, with the overall temperature drop within each cylinder reduced considerably. By expanding the steam in steps with smaller temperature range (within each cylinder) the condensation and re-evaporation efficiency issue (described above) is reduced. This reduces the magnitude of cylinder heating and cooling, increasing the efficiency of the engine. By staging the expansion in multiple cylinders, variations of torque can be reduced.{{sfn|Hunter|1985|p=}} To derive equal work from lower-pressure cylinder requires a larger cylinder volume as this steam occupies a greater volume. Therefore, the bore, and in rare cases the stroke, are increased in low-pressure cylinders, resulting in larger cylinders.{{sfn|Hunter|1985|p=}} Double-expansion (usually known as '''compound''') engines expanded the steam in two stages. The pairs may be duplicated or the work of the large low-pressure cylinder can be split with one high-pressure cylinder exhausting into two low pressure cylinders, giving a three-cylinder layout where cylinder and piston diameter are about the same, making the reciprocating masses easier to balance.{{sfn|Hunter|1985|p=}} Two-cylinder compounds can be arranged as: * '''Cross compounds''': Also known as 'receiver' compounds. Cylinders out of phase (< 180°), requiring the use of an exhaust 'receiver', which is usually no more than the valve chest or casing itself. * '''Woolf compounds''': The cylinders are in phase or 180° phase shifted. * '''Tandem compounds''': A form of Woolf compound. The cylinders are end to end, driving a common [[connecting rod]] * '''Angle compounds''': A form of Cross compound. The cylinders are arranged in a V (usually at a 90° angle) and drive a common crank. With two-cylinder compounds used in railway work, the pistons are connected to the cranks as with a two-cylinder simple at 90° out of phase with each other (''quartered''). When the double-expansion group is duplicated, producing a four-cylinder compound, the individual pistons within the group are usually balanced at 180°, the groups being set at 90° to each other. In one case (the first type of [[Vauclain compound]]), the pistons worked in the same phase driving a common crosshead and crank, again set at 90° as for a two-cylinder engine. With the three-cylinder compound arrangement, the LP cranks were either set at 90° with the HP one at 135° to the other two, or in some cases, all three cranks were set at 120°.<ref>{{Cite journal |date=1889-05-11 |title=Triple Expansion Engine |url=https://doi.org/10.1038/scientificamerican05111889-294 |journal=Scientific American |volume=60 |issue=19 |pages=294–295 |doi=10.1038/scientificamerican05111889-294 |issn=0036-8733}}</ref> The adoption of compounding was common for industrial units, for road engines and almost universal for marine engines after 1880; it was not universally popular in railway locomotives where it was often perceived as complicated. This is partly due to the harsh railway operating environment and limited space afforded by the [[loading gauge]] (particularly in Britain, where compounding was never common and not employed after 1930). However, although never in the majority, it was popular in many other countries.<ref name="van Riemsdijk, Compound Locomotives" />
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