The tax horsepower or taxable horsepower was an early system by which taxation rates for automobiles were reckoned in some European countries, such as Britain, Belgium, Germany, France, and Italy; some US states like Illinois charged license plate purchase and renewal fees for passenger automobiles based on taxable horsepower. The tax horsepower rating was computed not from actual engine power but by a simple mathematical formula based on cylinder dimensions. At the beginning of the twentieth century, tax power was reasonably close to real power; as the internal combustion engine developed, real power became larger than nominal taxable power by a factor of ten or more.
- where D is the diameter (or bore) of the cylinder in inches and n is the number of cylinders 
The formula was calculated from total piston surface area (i.e. "bore" only). The factor of 2/5 accounts for characteristics that were widely seen in engines at the time, such as a Mean effective pressure in the cylinder of 90psi (6.2 bar) and a maximum piston speed of 1000 feet per minute (5 metres per second).
The system introduced a somewhat progressive way of taxing higher-value cars more than low-cost ones but was also introduced to protect the domestic British motor industry from foreign imports, especially the Ford Model T. Henry Ford's mass production methods meant that the Model T was competitively priced with British-built cars despite being a much larger, more durable and more powerful car than any similarly-priced model. In 1912 Ford opened a factory to build Model Ts in Manchester, to circumvent the import tariffs that, up to that point, had increased the effective price of foreign cars. Under the RAC's formula the Model T was now a 22 'tax horsepower' car, making it much more expensive to run than its British-built rivals on sale for the same price.
At first the RAC rating was usually representative of the car's actual (brake) horsepower, but as engine design and technology progressed in the 1920s and 1930s these two figures began to drift apart, with an engine making much more power than its RAC rating (and the car's model name) suggested: by 1924 the Austin Seven's 747cc engine produced 10.5 brake horsepower, 50% more than its official rating.
It was common for the name of a model to include both its RAC tax horsepower and its actual power output, such as the Wolseley 14/60 and the Alvis 12/70 of 1938 - note that the Alvis's engine makes more brake horsepower than the Wolseley but makes less power under the RAC system and thus would be taxed less. By 1948 the Standard Flying Twelve, a typical mid-size saloon, produced 44 bhp from a 1.6-litre engine or nearly four times as much horsepower as the RAC system suggested, even though manufacturers were still restricted to making slow-revving engines with narrow bores and long strokes to keep abreast of the tax structure.
To minimise tax ratings British designers developed engines of a given swept volume (capacity) with very long stroke and low piston surface area. Another effect was the multiplicity of models: Sevens, Eights, Nines, Tens, Elevens, Twelves, Fourteens, Sixteens etc. each to fit with a taxation class. Larger more lightly stressed engines may have been equally economical to run and, in less variety, produced much more economically.
The system discouraged manufacturers from switching to more fuel-efficient overhead valve engines as these generally required larger bores, while the established sidevalve layout could easily use very narrow bores. Despite OHV engines having significant benefits in economy, refinement and performance the RAC system often made these engines more expensive to run because it placed them in a higher tax class than sidevalve engines of identical power output.
British cars and cars in other countries applying the same approach to automobile taxation continued to feature long thin cylinders even in the 1950s and 1960s, after taxation had ceased to be based on piston diameters, partly because limited funds meant that investment in new models often involved new bodies while under the hood/bonnet engines lurked from earlier decades with only minor upgrades such as (typically) higher compression ratios as higher octane fuels slowly returned to European service stations.
The emphasis on long strokes, combined with the nature of British roads in the pre-motorway era, meant that British engines tended to deliver strong low- and mid-range torque for their size but have low maximum speeds. The long stroke also meant that piston speeds and the load on the big end bearings became excessive at higher cruising speeds. Many smaller British cars did not cope well with sustained cruising at 60 mph or more, which led to reliability problems when the vehicles were exported to other markets, especially the United States. Cars such as the Austin A40, the Morris Minor and the Hillman Minx all achieved notable sales in the USA in the late 1940s (after the RAC Horsepower formula had been withdrawn but when car designs were still influenced by it) until the short service life of the engines when asked to routinely drive long distances at freeway speeds became clear. Other imports, notably the Volkswagen Beetle, which originated in countries with different fiscal horsepower rules and existing high speed road networks, proved more reliable and achieved much greater success.
The distortive effects on engine design were seen to reduce the saleability of British vehicles in export markets. While the system had protected the home market from the import of large-engined low-priced (because produced in such high volumes) American vehicles the need for roomy generously proportioned cars for export was now paramount and the British government abandoned the tax horsepower system with effect from 1 January 1947 replacing it at first with a tax on cubic capacity, which was in turn replaced by a flat tax applying from 1 January 1948.
During the early twentieth century, automobiles in the United States were specified with a figure identical to RAC horsepower and computed using the same formula; this was known either as "NACC horsepower" (named for the National Automobile Chamber of Commerce), "ALAM horsepower" (for NACC's predecessor, the Association of Licensed Automobile Manufacturers), or "SAE horsepower" (for the Society of Automotive Engineers). (This last term should not be confused with later horsepower ratings by the SAE.) This value was sometimes used for taxation and license fee purposes.
Although tax horsepower was computed on a similar basis in several other European countries during the two or three decades before the Second World War, continental cylinder dimensions were already quoted in millimeters, reflecting the metric measurement system. As a result of roundings when converting the formula between the two measurement systems, a British tax horse-power unit ended up being worth 1.014 continental (i.e. French) tax horse-power units.
Before World War II, France was the leading European producer of powerful luxury automobiles. Brands such as Bugatti, Delage, Delahaye, and Talbot-Lago made vehicles that are highly collectible today.
After World War II, the government of France decided to end this situation. Since that time, the dirigiste approach of the French government uses puissance fiscale tax regulations to encourage manufacturers to build cars with small engines, and French motorists to buy them.
French-made vehicles had very small engines relative to vehicle size by international standards. The 1948-1990 Citroën 2CV model for example was launched with a 375 cc two-cylinder engine that weighs only 100 pounds (45 kg), considered a Quadricyle in some regions. Since many export markets did not have this same constraint, the French automobile industry became less relevant as an export power.
In France, fiscal horsepower survives. It was first redefined in 1956; the formula became more complicated but now it took account of cylinder stroke as well as bore and number of cylinders (which together make Engine Displacement) along with rpm to take into account the total volume the engine takes in per minute, rather than one dimension. These new rules meant there was no longer any fiscal advantage in producing engines with narrow cylinders, and as noted above, a number of reasons not to. The French government modified the fiscal horsepower formula again in 1978 and in 1998. Since 1998 the taxable power is calculated from the sum of a CO2 emission figure (over 45), and the maximum power output of the engine in kilowatts (over 40) to the power of 1.6.
Diesel engines have long been favoured by French fiscal horsepower calculations. First, since 1956, diesel engines have had a .7 coefficient applied to the calculated value, thus lowering the fiscal horsepower. Secondly, diesel powered vehicles generally produce less CO2 than equivalent gasoline powered models, which in turn reduces the calculated fiscal horsepower using the post 1998 formulas. In 2016, Paris considered banning diesel vehicles because of serious smog incidents attributed to diesel. A French air quality researcher notes “The decades-long support for diesel by EU governments [is] a self-inflicted public health crisis of historic proportions." 
Tax horse-power (Steuer-PS) was introduced in Germany on 3 June 1906 however in contrast to many regions, i.e. British and French tax horsepower formulae above, it was calculated based on the overall engine displacement from its implementation.
The German formula applied a higher tax horse-power factor to two stroke engine cars than to four stroke engined cars based on the fact each cylinder in a two stroke engine fires (has a power stroke) every revolution where an otto cycle or 4 stroke cylinder only fires every second revolution .
The formula for tax horsepower was as follows:
- Units of tax horse-power (Steuer-PS) for four-stroke engined cars = 0.30·i·d2·s
- Units of tax horse-power (Steuer-PS) for two-stroke engined cars = 0.45·i·d2·s
In these formulae:
- i = the number of cylinders
- d = the diameter (or bore) of each cylinder
- s = the stroke length of each cylinder
Incomplete fractions were rounded up to the nearest whole number so a four stroke engined car of 1,000cc would end up designated as a 4PS (or four horsepower) car for car tax purposes.
After April 1928, recognizing the logic of the linear relationship between tax horsepower and engine capacity, the authorities simply set car tax rates according to engine size for passenger cars. (For commercial vehicles vehicle tax became a function of vehicle weight.) Attempts to correlate new tax horsepower values with old ones result in small differences due to roundings used in the new formula which are, for most purposes, unimportant.
In 1933 the Hitler government came into power and identified promotion of the auto-industry as key to economic recovery: new cars purchased after April 1933 were no longer burdened by an annual car tax charge and German passenger car production surged from 41,727 in 1932 to 276,804 in 1938. Thereafter war and military defeat led to a change in car tax policy and after 1945 tax horse-power returned in West Germany, applying the 1928 formula, as a determinant of annual car tax on new cars purchased in or after 1945. However, the introduction of tax on road fuel in 1951 and progressive increases in fuel tax thereafter reduced the importance of annual car tax so that today far more of the tax on car ownership is collected via fuel taxes than via annual car tax.
The 26 cantons of Switzerland used (and use) a variety of different taxation methods. Originally, all of Switzerland used the tax horsepower, calculated as follows:
- i is the number of cylinders,
- d is the diameter (or bore) of the cylinder in cm
- S is the piston stroke in cm
or 0.4 times engine displacement in cc
The limits between the horsepower denominations were drawn at either 0.49, 0.50, or 0.51 in different cantons. Thus, the eight horsepower category would cover cars of about 7.5 - 8.5 CV. In 1973 Berne switched to a taxation system based on vehicle weight, and a few other cantons followed. In 1986 Ticino switched to a system based on a calculation including engine size and weight. Nonetheless, the tax horsepower system remains in effect for seven cantons as of 2007[update]. The plethora of different taxation systems has contributed to there always being an uncommonly wide variety of different cars marketed in Switzerland.
Fiscal horsepower also lives on in Spain, but is defined simply in terms of overall engine capacity. It therefore encourages small engines, but does not influence the ratio of cylinder bore to stroke. The current Spanish definition does, however, add a factor that varies in order to favour four-stroke engines over two-stroke engines.
Impact on engine design and on auto-industry development
The fiscal benefits of reduced cylinder diameters (bore) in favor of longer cylinders (stroke) may have been a factor in encouraging the proliferation of relatively small six-cylinder-engined models appearing in Europe in the 1930s, as the market began to open up for faster middle-weight models. The system clearly perpetuated side-valve engines in countries where the taxation system encouraged these engine designs, and delayed the adoption of overhead valve engines because the small cylinder diameter reduced the space available for overhead valves and the lengthy combustion chamber in any case reduced their potential for improving combustion efficiency.
Another effect was to make it very expensive to run cars imported from countries where there was no fiscal incentive to minimise cylinder diameters: this may have limited car imports from the USA to Europe during a period when western governments were employing naked protectionist policies in response to economic depression, and thereby encouraged US auto-makers wishing to exploit the European auto-markets to set up their own dedicated subsidiary plants in the larger European markets.
Taxation can modify incentives and tax horsepower is no exception. Large capacity (displacement) engines are penalized, so engineers working where engine capacity is taxed are encouraged to minimize capacity. This rarely happened in the USA, where license plate fees, even adjusted for horsepower ratings, were comparatively much lower than European car taxes.
Naming and classification of individual car models
The tax horsepower rating was often used as the car model name. For example, the Morris Eight got its name from its horsepower rating of eight; not from the number of cylinders of the engine. British cars of the 1920s and 1930s were frequently named using a combination of tax horsepower and actual horsepower - for example, the Talbot 14-45 had an actual power of 45 hp and a tax horsepower of only 14 hp. The Citroën 2CV (French deux chevaux vapeur [fiscaux], two tax horsepowers) was the car that kept such a name for the longest time.
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- Richard Hodgson. "The RAC HP (horsepower) Rating - Was there any technical basis?". wolfhound.org.uk. Retrieved 2007-08-11.
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- Claus Jacobi (managing editor), Rudolf Augstein (proprietor & former managing editor) (8 May 1967). "AUTOMOBILE / ABSATZKRISE ... Durch Reichsgesetz befreite Adolf Hitler im Frühjahr 1933 alle Volksgenossen, die ein Automobil kauften, von der Kraftfahrzeugsteuer. Binnen zwei Jahren stieg der Auto-Absatz auf das Doppelte.". SPIEGEL-ONLINE. p. 27. Retrieved 2013-05-18.
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