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 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.

Britain

The so-called RAC horsepower rating was devised in 1910 by the RAC at the invitation of the British government.^[1] The formula is:

${\displaystyle {\frac {D\times D\times n}{2.5}}}$

where:

${\displaystyle D}$ is the diameter (or bore) of the cylinder in inches,

${\displaystyle n}$ is the number of cylinders^[2]

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 90 psi (6.2 bar) and a maximum piston speed of 1,000 feet per minute (5.1 m/s).

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 other available similarly-priced models. 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 a 22 'tax horsepower' car, making it 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 diverge, with engines making much more power than their RAC ratings suggested: by 1924 the 747 cc (45.6 cu in) engine of the Austin Seven (named for its 7 hp rating) produced 10.5 brake horsepower, 50 percent more than its official rating.

1912 Wolseley 16-20 see also 1913 Vauxhall 30-98 and many others

It became 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.

To minimise tax ratings British designers developed engines 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.^[3] 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 made these engines more expensive to own because it placed them in a higher tax class than sidevalve engines of identical power output.^[3] Despite this, by 1948 the Standard Flying Twelve, a typical mid-size saloon, produced 44 bhp (45 PS; 33 kW) from a 1.6-litre (98 cu in) engine, nearly four times as much horsepower as the RAC system suggested.

While the RAC system had protected the home market from the import of large-engined low-priced mass-produced American cars, the need for roomy generously proportioned cars for export was now paramount and the British government abandoned the tax horsepower system^[1] with effect from 1 January 1947^[4] replacing it at first with a tax on cubic capacity, which was in turn replaced by a flat tax applying from 1 January 1948.^[5] However British cars and cars in other countries applying the same approach to automobile taxation continued to feature long, relatively narrow cylinders even in the 1950s and 1960s, partly because limited investment meant that new car models often had new bodies but their engines were carried over from earlier generations.

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 low maximum speeds. The long stroke also meant that piston speeds and the load on the big end bearings became potentially damaging at high power outputs. Many smaller British cars did not cope well with sustained cruising at 60 mph (97 km/h) 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 initial sales success in the US in the late 1940s, until the short service life of the engines when asked to routinely drive long distances at freeway speeds became clear. Other imports originating in countries with different tax rules and existent high speed road networks, in particular the Volkswagen Beetle, proved more reliable, and achieved greater sales success.^[3]

Australia

In Australia, the various states had their own automobile taxation system. Several depended on the RAC formula, but the flaws of this system were well known as early as 1909.^[6] Another formula was the Dendy-Marshall formula, which included an engine's stroke. Several Australian states used Dendy-Marshall, although Western Australia reverted to RAC hp in 1957.^[7] The Union of South Africa also depended on Dendy-Marshall, at least in the 1920s.^[8] The Automobile Club of Australia's "A.C.A. formula" used the same calculations as did Dendy-Marshall formula.^[9] The Australian Bureau of Statistics used RAC hp in their Registration of New Motor Vehicles, Make of Vehicles, Australia statistics until this publication was discontinued in June 1976.^[10]

Several Australian states also added vehicle weight to the power rating, to get a power-weight unit which determined taxation.

The Dendy-Marshall / A.C.A. formula is as follows:

${\displaystyle HP={\frac {D\times D\times L\times n}{12}}}$

where:

${\displaystyle HP}$ = nominal horsepower

${\displaystyle D}$ = the diameter (or bore) of the cylinder in inches

${\displaystyle L}$ = the length (or stroke) of the cylinder in inches

${\displaystyle n}$ = the number of cylinders

United States

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 is still used for taxation and license fee purposes in the State of Missouri for passenger vehicles, with electric vehicles assigned to the 12-23 Horsepower bracket by statute.^[11][12]

Continental Europe

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 quoted in millimeters. 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.^[1]

France

The Cheval Fiscal, often abbreviated to CV from "chevaux-vapeur" (literally "steam horses") in tax law, is used for the issuing of French registration certificates known as "cartes grises" ("grey cards"). It is an administrative unit originally calculated partly from the power of the engine and used to calculate the amount of tax that may be due at the time of registration.

The Citroën 2CV (two tax horsepower) was the car that kept such a name for the longest time.

Its use in France dates from 1 January 1913. It was updated in 1956, with further revisions in 1978 and a new emission-based system introduced in 1998.

It was originally defined using the following formula:

${\displaystyle CV=n\times D^{2}\times L\times \omega \times K}$

where:

${\displaystyle n}$ is the number of cylinders,

${\displaystyle D}$ is the cylinder bore in centimeters,

${\displaystyle L}$ is the stroke in centimeters,

${\displaystyle \omega }$ is the engine speed in revolutions per second,

${\displaystyle K}$ is a coefficient depending on the number of cylinders (single-cylinder engine : 0.00020; two-cylinder engine : 0.00017; four-cylinder engine: 0.00015; six-or-more-cylinder engine: 0.00013)

1956 formula

In a circular issued on 28 December 1956, the chevaux fiscaux was defined as:

${\displaystyle P={K\times n\times D^{2}\times L\times w}}$

where:

${\displaystyle P}$ = puissance administrative,

${\displaystyle K}$ = constant of 0.00015,

${\displaystyle n}$ = number of cylinders,

${\displaystyle D}$ = bore in centimeters,

${\displaystyle L}$ = stroke in centimeters,

${\displaystyle w}$ = speed of rotation in revolutions per second

The result is multiplied by 0.7 for a diesel engine.

1978 formula

1978 Engine Speed Parameter Formulas

For calculating ${\displaystyle K}$, k1, k2... kn represent the theoretical speed in km/h of the vehicle with the engine running at 1000 rpm in 1st, 2nd... nth forward gears. ${\displaystyle K}$ is a representation of the average speed across the forward gears, with various adjustments added for various transmission types.
Forward speeds	Manual transmissions	Forward speeds	Automatic transmissions[lower-alpha 1]
3 speeds (or fewer)	${\displaystyle K={\frac {k1+k2+k3}{3}}}$	2-speed	${\displaystyle K={\frac {k1+k2}{2.7}}}$
4 speeds	${\displaystyle K={\frac {k1+k2+k3+k4}{4}}}$	3-speed	${\displaystyle K={\frac {k1+k2+k3}{3.48}}}$
5 speeds	k5 ≤ 1.25*k4: ${\displaystyle K={\frac {k1+k2+k3+k5}{4}}}$	4-speed[lower-alpha 2][13]	k4 ≤ 1.4*k3: ${\displaystyle K={\frac {k1+k2+k4}{3.48}}}$
	k5 > 1.25*k4: ${\displaystyle K={\frac {k1+k2+k3+1.25\ k4}{4}}}$		k4 > 1.4*k3: ${\displaystyle K={\frac {k1+k2+1.4\ k3}{3.48}}}$
Manual w/ Overdrive	For transmissions with one or more overdrive speeds, the over- drive ratio is only applied to the fourth (top) gear. The calculations are administered as for a five-speed transmission.	CVT	${\displaystyle K={\frac {km+kM}{2.3}}}$ km and kM represent the velocity at 1000 rpm reached in the lowest and highest available ratios
↑ "Automatics" include semi-automatic transmissions. ↑ The provision for four-speed automatics was added on 15 May 1983.

A new system was announced on 23 December 1977^[13] to come into force on 1 January 1978 calculated by the following formula:

${\displaystyle P=m\left(0.0458\ {\frac {C}{K}}\right)^{1.48}}$

where:

${\displaystyle P}$ = puissance administrative,

${\displaystyle m}$ = coefficient of 1 for petrol or 0.7 for diesel,

${\displaystyle C}$ = engine capacity in cubic centimeters,

${\displaystyle K}$ = parameter calculated from a weighted arithmetic average speed in kilometers per hour theoretically reached by the vehicle at an engine speed of 1000 revolutions per minute in each gearbox ratio (see dropdown table to the right for more details).

1998 formula

From 1998 until January 2020,^[14] the fiscal tax depended on a standardised value of carbon dioxide CO₂ emissions in grams per kilometer (g/km) and the maximum engine power in kilowatts (kW). If C is the amount of CO₂ released and P the engine power, then:

${\displaystyle P_{A}={\frac {C}{45}}+\left({\frac {P}{40}}\right)^{1.6}}$

${\displaystyle P_{A}}$ is expressed in horsepower, rounded to the nearest integer. The official emission rate of CO₂ included in the calculation is taken from the European certificate of conformity.

Japan

In pre-war Japan, different prefectures had different automobile tax structures. Tokyo Prefecture was naturally the strictest, due to the population and vehicle density there, and used a tax horsepower system of their own devising:^[25]

${\displaystyle {\text{tax HP}}={\frac {D\times S\times n}{3}}}$

where

${\displaystyle D}$ = the diameter (or bore) of the cylinder in inches,

${\displaystyle S}$ = the piston stroke in inches,

${\displaystyle n}$ = the number of cylinders

Unlike the British system, the Tokyo system favored short-stroked engines, but since the tax categories were rather wide and only represented a portion of vehicle taxes it had less impact on sales. In 1950 new legislation was passed that taxed engine displacement in 500 cc increments. The automobile tax is paid every year during the road tax obligation.^[26]

Impact on engine design and on auto-industry development

The fiscal benefits of reduced cylinder diameters (bore) in favor of longer cylinders (stroke) in Britain and Ireland 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.^[1] 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 US 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 US, where license plate fees, even adjusted for horsepower ratings, were comparatively much lower than European car taxes.

References

• This entry incorporates information from the equivalent entry in the French Wikipedia at 31 December 2009
• This entry incorporates information from the equivalent entry in the Spanish Wikipedia at 31 December 2009