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The 'tax horsepower' or taxable horsepower was an early system by which taxation rates for automobiles were reckoned in some European countries, like Britain, Germany, France, Italy and certain US states, (such as Illinois), where license plate purchase and renewal fees for passenger automobiles were based on taxable horsepower.
The tax horsepower rating was based on a pure mathematical formula based on cylinder dimensions.
The British system was based on the RAC horsepower rating which only included total piston area. To optimise engine size and lower the tax rating, typical British cars developed engines of very long stroke and low cylinder area for a given swept volume. That tradition continued long after the tax horsepower was abolished.
The tax horsepower rating was often used as the car model name. The Citroën 2CV (French ''deux chevaux'', two horses) was the car that kept such a name for the longest time.
At a very early stage the tax power was reasonably close to real power. As the development of the internal combustion engine continued, real power overtook the tax rating by a factor of ten or more.
Taxation can modify incentives and tax horsepower is no exception. Large engines are penalized, so engineers working under this regime are encouraged to make unusual efforts to minimize engine size. This had very little effect in the USA, where license plate fees, even adjusted for horsepower ratings, were comparatively much lower than European auto taxes.
French-made vehicles after World War II in particular have had very small engines relative to vehicle size. The very small Citroën 2CV for example has a 425 cm³ two cylinder engine that weighs only 100 pounds, and at the opposite extreme, the large Citroën SM has a still modest 2,700 cm³ six cylinder engine that weighs only 300 pounds.
Cars with small displacement engines often have improved fuel economy over comparable cars with larger engines for several reasons. First, the lower weight of a small engine reduces the amount of fuel needed to accelerate the car. Second, small displacement engines tend to be designed with fewer cylinders and correspondingly fewer parts, which helps to reduce internal friction. Third, to produce the same amount of power, a smaller engine runs at higher throttle openings and manifold pressures compared to a larger engine operating at the same RPM. This reduces pumping losses; in a nutshell, this is the energy the engine must expend to pull in air past the throttle into the cylinders, akin to sucking a milkshake through a thin straw (part throttle) or a thick straw (open throttle). Fourth, smaller engines allow for creating smaller and more aerodynamically efficient body designs, further improving fuel economy. While it is possible for larger engines to achieve good fuel economy, it is usually easier and cheaper to achieve this goal with a smaller engine.

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