Tax horsepower, puissance fiscale, cavalli fiscali, Steuer-PS...

Alright, let's try again

I'm collecting info about the various horsepower rating systems that were in effect mainly between the two World Wars. So far I have:

United Kingdom

"RAC Rating", developed around 1904/6, tax formula from 1910-01-01 to 1947-12-12:

HP = N * B * B / 2.5

where N is number of cylinders and B bore in inches.

United States of America

"SAE Rating" - the same as "RAC Rating"????

Germany

"Steuer-PS" formula from 1906-06-03 to 1928-04-01:

PS = 12 * C / p (4-stroke engines)

PS = 18 * C / p (2-stroke engines)

where C is engine capacity in litres and p the ratio of the circumference of a circle to its diameter (~ 3.1416).

France

"Puissance fiscale" formula - I have found several formulae for postwar years (1957-77, 1978-97 and 1998-?), but nothing definite for earlier periods. The best I can come up with so far is this, which appears to have been the formula for approx. 1926-56:

CV = 18 * C / 3.15

where C is, again, engine capacity in litres and 3.15, apparently, a rounded figure for p.

Also, it seems, the result was rounded up or down to the next full figure, unlike in Germany where the result of the formula was always rounded up ("You have 4.01 PS? Sorry chap, you pay for 5!")

Before 1926, I have found references to changes in the formula for January 1913, September 1923 and around 1925, but I haven't yet figured out what they were. There also seems to have been an extra formula for OHV engines, at least in some years.

Italy

"Cavalli fiscali" formula - not much here, either. I assume that in the mid-twenties the formula was something like:

CV = 24 * C / p

where C is engine capacity in litres and p the ratio of the circumference of a circle to its diameter (~ 3.1416).

Spain

????

Can anyone expand on this?

It's laughable how they wanted to put pi = 3.14159... into those formulas, not least because they would put an arbitrary factor of 12, 18, or 24 into the formulas for "fiscal" reasons. Even more hilarious is the approcimation 3.15. What were they thinking of? Surely, "for fiscal reasons" 12/pi, 18/pi and 24/pi could be approximated by 4, 6 and 8, respectively, and it would also have brought marginally greater tax revenues...

Although this is an interesting issue, I think there cannot be any doubt that we see stupidity at work here.

Hang on, here...

I have transformed these formulae for convenience here, since with today's electronic calculators it's not difficult to calculate engine capacity. By contrast, in the teens and twenties that was rather difficult, and these formulae were all based on bore and stroke alone!;)

E.g. the German formula was actually:

PS = 0.003 * N * B * B * S

where N is number of cylinders, B bore and S stroke in centimeters.

Furthermore, the approximation for Pi is everything but ridiculous - it is even used today, in most countries, for calculating engine capacity. In Germany, I believe, pi is approximated today as 3.12! Why? Because if you have the bore and want the piston area, you have to approximate Pi/4 which is roughly 0.785, and if you want one decimal point less you have to decide bewtween 3.16 and 3.12! So, 3.15 isn't that bad, really... But here I have to stress that this French formula (and the approximation) is just an educated guess I've made based on a number of samples.

So what's wrong with the Bible's approximation pi = 3? (1st Book of Kings, 7:23)

I mean, why bother about whether pi is approximately 3.12 or 3.16 or 3.15, when all of it are approximations within 1 (one) percent? After all, 12, 18 and 24 are factors that vary by 100%. Hence my remark on stupidity. You might just as well say that the formula is 23.76*B*S*C/pi or something like that, but nobody has yet come up with such a weird idea. Hence they should either stick to pi = 3 or its true value, pi = 3.1415926535.... but it goes withut saying that such precision has nothing to do with fiscal viewpoints. That's why it's laughable, but then again, most fiscal issues are laughable.

I'm afraid I don't understand what you are trying to say There's no Pi (approximation or not) involved in these formulae! A hundred years ago the concept of "engine capacity" was largely unknown, just as Formula One engines today don't have bore and stroke anymore ;) - hence my attempt to convert these formulae to a more comprehensible format (i.e. in today's language), but apparently I have only confused the issue

So, let's cut the crap and get back to the original intention of the thread: Anyone who knows anything about any tax formula of the past (or even present), please post away - regardless of format, Pi approximation or whatever - just post what you've found!

What I'm saying is that it is silly to make formulas invloving bore, stroke, pi, number of cylinders etc. In racing, total engine capacity has been a good enough spec for a century or so. So why aren't the formulas of the type

tax = X * currency unit * engine capacity

with X a simple factor? Why did they make it more obscure than it really needs to be?

In Spain is something like this:

Formula Caballos Fiscales

0.08*(0.785*C2*D)0.6*F

Where:
C=Bore in centimetres
D=Stroke in centimetres
F=Number of cylinders


I have no idea where those numbers are coming from.

Some English definitions:
1 horsepower = 33,000 ft/lb per minute
1 RAC horsepower = bore squared x number of cylinders, divided by 2.5
- from the 1956 edition of The Observers Book of Automobiles
The same source notes that 1 French horsepower = 32,549 ft/lb per minute, without saying whether that is the fiscal CV. I suspect not
It also notes that GB and USA used different methods of calculating brake horsepower, making US figures slightly higher by comparison

As an aside, the 105E Anglia with its oversquare engine and the Bentley 4.5 with its 1930's long stroke engine were both about 18 RAC hp. This is from memory without checking.
I'll have to find my calculatoe and the relevant reference books.

Thanks so far for the input!

Originally posted by DOHC
What I'm saying is that it is silly to make formulas invloving bore, stroke, pi, number of cylinders etc. In racing, total engine capacity has been a good enough spec for a century or so. So why aren't the formulas of the type

tax = X * currency unit * engine capacity

with X a simple factor? Why did they make it more obscure than it really needs to be?

Although really OT, I'm beginning to like this little deviation...

DOHC, try to understand that engine capacity was an "unknown quantity" in the early days of motoring - for the simple reason alone that it was difficult to calculate! I don't think it was used at all a hundred years ago except for the most elitist technical discussions. The "man on the street" wouldn't know the significance of it until much later, when readymade tables allowed quick calculations to be made, and these were finally used in advertising.

Before that, the "size" of an engine used to be refered to by its "horsepower" - a convenient term in the very early days, for people needed the analogy to the horsedrawn cart to get a grasp of what an engine would be capable of (even if HP was never very accurate). Very soon, engine (& car) manufacturers discovered that by embellishing the HP output they could sell considerably more cars to an unsuspecting clientel. What was needed was a more clearcut indicator of engine power than the self-imposed HP rating of the manufacturers.

Engineers used all sorts of data to determine an engine's power output, such as piston area, piston speed etc. - all too confusing for the simple customer who wanted to buy a car. Hence, a formula was needed that related all this data into a known quantity, i.e. horsepower! And so, the engineers deviced formulae that incorporated some of the most important engine features, such as number of cylinders, bore, sometimes also stroke, and created a "horsepower rating" that was based on facts, not commercial considerations.

That's why formulae such as the "Formula Caballos Fiscales" were invented - relatively easy to calculate, and based on easily obtainable facts of the engine design:

0.08*(0.785*C2*D)0.6*F

And if you look closely, you can see that the engine's capacity is hidden in this formula, calculated with an approximation of Pi.;)

Originally posted by DOHC
What I'm saying is that it is silly to make formulas invloving bore, stroke, pi, number of cylinders etc. In racing, total engine capacity has been a good enough spec for a century or so. [/B]

Oh and by the way, have you realised that "total engine capacity" is a "formula invloving bore, stroke, pi, number of cylinders"?

Originally posted by D-Type
As an aside, the 105E Anglia with its oversquare engine and the Bentley 4.5 with its 1930's long stroke engine were both about 18 RAC hp. This is from memory without checking.
I'll have to find my calculatoe and the relevant reference books.

Surely not the 105E, D?
The RAC rating system was long dead by then
But it could have been 18 ornery HP (of the 33,000 variety)

as i recall..bugatti data plates always had a space for a "chassis" number, rated power and weight.....pre-great war [molsheim was part of germany] power was called out as "Motor P.S."...immediate post-war "hp" was used[??]...finally the then normal french "cv" was used...

i know it's an aside but how was the horsepower rated for steamship or large steam generators [pre-turbine] rated? was there an international rating for steam? ..just wondering..

i do vaguely remember some formula that regarded bore as a controlled dimension but left stroke free....hence the lion-peugeots with a pair of small diameter cylinders that are so tall the driver had to look around them!!!!

Originally posted by fines

Oh and by the way, have you realised that "total engine capacity" is a "formula invloving bore, stroke, pi, number of cylinders"?

Yes, Michael, , I most certainly have. And as capacity C=N*b*b*s*pi/4, it is of course totally absurd that the German, French and Italian rules divide C by pi to remove that factor. Perhaps the idea is to get a "tax capacity" which any damn fool can calculate, even if one doesn't know the value of pi, , a sort of amusing little trick. Of course, one needs to know the capacity C and the local legal approximation of pi.

That's madness. And I don't think we can get away by saying that it at least has method...

If the purpose of these formulae was to calculate the amount of duty payable then the constants used in the calculation are irrelevant. What matters is how many pounds, francs or marks you had to pay; what's interesting is the variable used in the calculations. The continental European countries seem to have based their calculation on cubic capacity, while the British (and the Americans?) were only interested in piston area. The same principle applied to a number of early racing formulae, based on the theory that piston speed was a limiting factor and that, as a result, rotational speed and stoke were interchangeable.

What it led to, of course, was long stroke engines, which hampered the development of engines in Britain for many years.

Originally posted by Roger Clark:
What it led to, of course, was long stroke engines, which hampered the development of engines in Britain for many years.

The madness in a nutshell...It also tended to segregate British and continental racing developments based on road cars, post-war trade and fiscal restrictions or not - where else but Britain would 4 cyl. side-valve engines (of c. 750 ccm and 1172 ccm) prevail for so long in racing? And yet, with one hand tied behind their backs, the grass roots of British motor sports fostered so much ingeniouity and talent that would help pave the way for British dominance - which was then given a further prod by the intoduction of the modern 105E, which was the engine to match the already established British chassis superiority in Formul Junior. There was no looking back after the 105E started receiving the attention of tuners...


Limiting piston area was, of course, also used in racing formulae early on - one famous result being the Lion-Peugeots, with the stroke of the engine so long that it towered above the drivers, who had to look around it rather than over it...

Originally posted by David McKinney

Surely not the 105E, D?
The RAC rating system was long dead by then
But it could have been 18 ornery HP (of the 33,000 variety)

Somebody asked the question in a magazine (maybe even M*** Sp***) what the hp of the new Anglia was. The answer was that with a bore of 80.9mm, the RAC hp for the Anglia was 16.2 hp and for comparison the Bentley 4.4 was 24.8 hp. I think the writer (WB?) was making a point.

Originally posted by DOHC
Yes, Michael, , I most certainly have. And as capacity C=N*b*b*s*pi/4, it is of course totally absurd that the German, French and Italian rules divide C by pi to remove that factor. Perhaps the idea is to get a "tax capacity" which any damn fool can calculate, even if one doesn't know the value of pi, , a sort of amusing little trick. Of course, one needs to know the capacity C and the local legal approximation of pi.

That's madness. And I don't think we can get away by saying that it at least has method...

Sigh! Apparently, my explanation capabilities are not of the first order today (were they ever?) - my point was that these formulae did originally not include engine capacity nor Pi, since these parameters were not generally known at the time. It's only my transformation of these formulae that use C and p because, today, these are better known than bore and stroke.

Originally posted by DOHC
Of course, one needs to know the capacity C and the local legal approximation of pi.

That's exactly the point: capacity (and pi) were, if not unknown, not easily determined those days - hence the formulae were based on number of cylinders, bore and sometimes stroke...

There is an interesting article about the RAC rating here:

http://www.designcha...fhoundRACHP.htm



As an aside, steamrollers and traction engines were rated according to the following fomula

HP = N * D * D /10 where N = No of cylinders, D = Cylinder diameter (inches)

thus a machine with one 9" cylinder was 8HP, one with two 7" cylinders was 10HP.

the infamous tax system in the UK that gave us the morgan three wheeler still lingers in japan...i think the break is at 900cc and thus the difference between a white number plate and a yellow one..[yellow is the [relative] tiddler]..i believe japan has strict limits on overall width of the small displacement cars[and vans!!] but seems to have no height restrictions[JDM only]..makes car watching rather interesting in tokyo i'll tell you!....
seems japan also requires a funny green/yellow magnetic badge to be displayed on cars driven by "learners".

also can someone explain the "HP" numbers given to pre-wwI american cars.. they seem to fall into 30 40 50 60 and other evenly rounded numbers..[i don't recall # of cylinders being a factor...but a "60 HP lozier" was a formidable device indeed.]

interesting subject.

i seem to remember that Italy has long held u rule in which you had to pay considerably more tax if your engine capacity was above 2 litre. Hence a special version of the Alfa V6 of just under 2 litre, for the italian market only.
And I believe the computation of fiscal HP had an element discriminating against engines with more than 4 cylinders. And as a matter of fact, there was not a normal engine in France with more than 4 cyl. between approx. 1960 and the introduction of the Douvrin V6 in the 70s.

Concerning those little cars in Japan (and Korea): I have read the rule is as follows; you are not allowed to park on the street in the cities if your car is above a certain width and length. Makes sense, I think.

mat1

ITALY

I don't know how to calculate Cavalli Fiscali, but I found on assicurarsi.net a conversion table:

CV	CILINDRATA (engine capacity - cm³)

 1	from 19.8 to 57.1

 2	from 57.2 to 106.1

 3	from 106.2 to 164.8

 4	from 164.9 to 231.8

 5	from 231.9 to 306.4

 6	from 306.5 to 387.8

 7	from 387.9 to 475.6

 8	from 475.7 to 569.5

 9	from 569.6 to 669.0

10	from 669.1 to 774.0

11	from 774.1 to 884.1

12	from 884.2 to 999.2

13	from 999.3 to 1119.1

14	from 1119.2 to 1243.6

15	from 1243.7 to 1372.5

16	from 1372.6 to 1505.8

17	from 1505.9 to 1643.3

18	from 1643.4 to 1784.9

19	from 1785.0 to 1930.5

20	from 1930.6 to 2080.1

21	from 2080.2 to 2233.4

22	from 2233.5 to 2390.4

23	from 2390.5 to 2551.1

24	from 2551.2 to 2715.4

25	from 2715.5 to 2883.2

26	from 2883.3 to 3054.5

27	from 3054.6 to 3229.1

28	from 3229.2 to 3407.1

29	from 3407.2 to 3588.4

30	from 3588.5 to 3772.8

31	from 3772.9 to 3960.5

32	from 3690.6 to 4151.2

33	from 4151.3 to 4345.1

34	from 4345.2 to 4542.0

35	from 4542.1 to 4741.9

36	from 4742.0 to 4944.7

37	from 4944.8 to 5150.5

38	from 5150.6 to 5359.2

39	from 5359.3 to 5570.7

40	from 5570.8 to 5785.5

41	from 5785.6 to 6002.1

42	from 6002.2 to 6221.9

43	from 6222.0 to 6444.5

44	from 6444.6 to 6669.8

45	from 6669.9 to 6897.7

46	from 6897.8 to 7128.2

47	from 7128.3 to 7361.4

48	from 7361.5 to 7597.2

49	from 7597.3 to 7835.5

50	more than 7835.6

I don't know when this table was first used, but I don't recall any modification. We simply don't use it anymore for taxes (now we pay according to Max Power, in kW), but it's still in use by insurance companies.

I don't think that number of cylinders was never considered.

As regards large capacity engines (2000 cc or Diesel 2500 cc) used the same table; the difference was in VAT: it was 38% rather than 18% or 19% as usual. I don't recall when "IVA pesante" (= heavvy VAT) was canceled, I think it early 1990s but still now we like small engines.

Ciao,
Guido

Originally posted by dbw
the infamous tax system in the UK that gave us the morgan three wheeler still lingers in japan...i think the break is at 900cc and thus the difference between a white number plate and a yellow one..[yellow is the [relative] tiddler]..i believe japan has strict limits on overall width of the small displacement cars[and vans!!] but seems to have no height restrictions[JDM only]..makes car watching rather interesting in tokyo i'll tell you!....
seems japan also requires a funny green/yellow magnetic badge to be displayed on cars driven by "learners".

also can someone explain the "HP" numbers given to pre-wwI american cars.. they seem to fall into 30 40 50 60 and other evenly rounded numbers..[i don't recall # of cylinders being a factor...but a "60 HP lozier" was a formidable device indeed.]

I think that quite a lot of these early giant racers produced less than 10 HP/litre (mostly due to simple lack of revs) so the figures were probably roughly representative of the power produced. The famous Panhard "70" was a good example, although Scott-Moncrieff wrote that it eventually probably made nearer 90HP - sandbagging perhaps?

PdeRL

Originally posted by fines
United States of America

"SAE Rating" - the same as "RAC Rating"????

I have recently found a cars listing from a hill climb event in the USofA in 1908, where the quoted HP figures exactly matched the RAC rating.

Originally posted by fines
That's exactly the point: capacity (and pi) were, if not unknown, not easily determined those days

Pi unknown? It was perfectly known to and determined even by Euclid (a couple of thousand years ago)! Capacity could be determined by any competent engineer. Even in the era of reciprocating steam engines this was done on a routine basis.

Maybe your point is that the engineering wasn't particularly competent? :

Personally I think that Pi was considered "too exotic" for engineers to know about.

How silly.

Regarding posts on this thread about early racing fomulae which limited bore size, i note that the 2006 Grand Prix rules also have such a provision. I mentioned it at this week's TNF northern gathering but everybody seemed more interested in the colour of the McLaren. I think it is rather splendid that the AIACR, or whatever they call themselves nowadays, recognises tradition in this way.

Originally posted by dbw
the infamous tax system in the UK that gave us the morgan three wheeler still lingers in japan...i think the break is at 900cc and thus the difference between a white number plate and a yellow one..[yellow is the [relative] tiddler]..i believe japan has strict limits on overall width of the small displacement cars[and vans!!] but seems to have no height restrictions[JDM only]..makes car watching rather interesting in tokyo i'll tell you!....
seems japan also requires a funny green/yellow magnetic badge to be displayed on cars driven by "learners".

also can someone explain the "HP" numbers given to pre-wwI american cars.. they seem to fall into 30 40 50 60 and other evenly rounded numbers..[i don't recall # of cylinders being a factor...but a "60 HP lozier" was a formidable device indeed.]

That would be the 'kei' class of cars, sometimes called the 'K' cars (not to be confused with Chrysler products of the eighties). I believe the engine capacity limit is under 660cc, and maximum length is 3600mm (going on memory and info gleaned from playing too much Gran Turismo, in which there's a special race for this class of car). I seem to recall first reading about these cars in the early 90's, and going out and measuring my MG Midget out of curiosity. I think the MG was a tad too long, but not too wide! Too right that many cars in the kei class look absurdly tall, but some really neat cars have been built as well. The Suzuki Cappucino, Mazda AZ-1, and Honda Beat all come to mind.

As for American ratings, I tend to agree with VAR1016 in that they were approximations of the engine's output. Not to be confused with the horsepower ratings of many American cars in the sixties, as the power figures were usually taken on the dyno with as few power sapping ancilliaries as possible hooked up to the engine. That's why big block Chevys that are fundamentally identical lost a ton of power from one season to the next when the SAE changed their testing procedures.

And, haven't there been several 2-litre Ferraris made as well (206 Dino, 208GTB, etc.)?

-William