Mathematical improbabilities

"Cé hé sin" (michael-m-mouse) 05/21/2020 at 16:55 • Filed to: Citroën, Traction Avant, RAC, CV fiscal

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3 = 6.

Yes, really, at least according to Auto Union’s advertising agency.

The DKW of that unusual name had, like other Auto Union models up to the 1960s, a three cylinder two stroke engine. The somewhat implausible claim was that this was equivalent in terms of power to a six cylinder four stroke of twice the size on the grounds that each of those three pistons was producing power each time it descended rather than every other time.

In addition to three equalling six, it has been found that eleven equals fifteen.

Meet the Citroen Traction Avant 11.

It derived its name from its 11 CV, or horse power, engine.

Meet, on the other hand, the UK built (because of import tariffs) Citroen Fifteen, which was sold in Light or Big versions. The Big was, well, bigger, with a longer wheelbase and wider track.

So the 15 had a more powerful engine, with a hefty 15 bhp to shift a car weighing just over a tonne at a very leisurely pace? Mais non. Both had 1.9 engines with 55 bhp. So what’s going on, and how can 11, 15 and 55 all be correct?

It’s all down to tax. France at the time, and for many years after, taxed cars according to their power, except they didn’t. Cars were taxed according to an arcane formula which in the case of the 1.9 Traction Avant worked out at 11 fiscal hp or CV. The UK did the same but they used their own but equally arcane formula which produced what was called RAC hp. So the Citroen had 15 RAC hp and at the same time 11 CV and 55 bhp.

RAC hp, incidentally was derived from:

hp = ( D 2 x n ) / 2.5 where D was the bore in inches and n the number of cylinders. Undersquare engines with few cylinders were therefore favoured.

French fiscal HP at the time of the Traction Avant (there were several changes over the years) was derived by:

CV = D 2 x N x L x w x K, where D and N are as above, w is engine speed in revs per second and K a coefficient depending on the number of cylinders.

So there we have it. Three equals six, and 55 equals both 11 and 15.

Snuze: Needs another Swede > Cé hé sin 05/21/2020 at 17:00

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I always liked these tax schemes based on power output. Clearly dreamed up by politicians and not engineers.  

dogisbadob > Cé hé sin 05/21/2020 at 17:02

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toilet paper math :p

TheRealBicycleBuck > Cé hé sin 05/21/2020 at 17:05

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Same logic with Yamaha RD350. But you missed the most important point - the sound! Just listen to this thing!

ranwhenparked > Snuze: Needs another Swede 05/21/2020 at 17:10

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What, you mean the Hellcat doesn’t make 55hp?

HFV has no HFV. But somehow has 2 motorcycles > Snuze: Needs another Swede 05/21/2020 at 17:16

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It just means engineers have to make other aspects of the car better. Or make the engine better overall instead of focusing on peak HP. 

Cé hé sin > Snuze: Needs another Swede 05/21/2020 at 17:31

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Not entirely, to be fair. At the beginning of the last century the RAC and F rench systems gave some kind of approximation to the actual power without having to go to the trouble of measuring it. The idea was that cars were a luxury and the rich could afford mor e powerful ones and could pay mor e tax.

Jb boin > Snuze: Needs another Swede 05/21/2020 at 17:34

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The actual French chevaux fiscaux calculation is now only based on CO2 and peak horsepower, previously there was more complex calculations benefiti ng diesel and turbo engines.

In France, its only used/paid once for the calculation of the price of the registration certificate (carte grise/grey card) which varies between the regions , for example on mine in 2020 its 43€/CV ; it is half the price per CV to register a car that is at 10 years old or more.

My manual A3 1.8T 150hp of 1999 without Quattro is a 9cv while a 1998 model year (the way its calculated changed in 1999) would have been 7cv while at the same time the 1.8 NA 125hp would have been 9cv in 1998 and 8cv in 1999.

You can find some CV values here .

Cé hé sin > TheRealBicycleBuck 05/21/2020 at 18:00

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Strokers are all about the exhaust aren’t they? Not just the noise but as a means of extracting power.

Honda NSR500

TheRealBicycleBuck > Cé hé sin 05/21/2020 at 18:06

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I was surprised to learn about the importance of a tuned exhaust to the performance of a two-stroke engine. My introduction to the concept was with model airplane engines. A friend of mine bought a tunable pipe to go on his Extra 300. Seeing how the rpm changed with the pipe position was a revelation. 

Cé hé sin > TheRealBicycleBuck 05/21/2020 at 18:16

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Yes, it’s everything! It was somebody in MZ in E ast Germany who figured this out. Took a while and the defection of a rider to Suzuki but eventually strokers became unbeatable.

Chan - Mid-engine with cabin fever > Cé hé sin 05/21/2020 at 18:18

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Damn.gif

Cé hé sin > Jb boin 05/21/2020 at 18:26

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M ais oui, le systeme est bizarre !

ranwhenparked > Jb boin 05/21/2020 at 18:36

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For the sake of fun, about what would 323hp and 675 g/km cost - over or under $40?

Manwich - now Keto-Friendly > Jb boin 05/21/2020 at 18:42

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And what I find really interesting is a 2020 Nissan Leaf is rated at 3-6cv

https://www.largus.fr/fiche-technique/Nissan/Leaf/2020.html

While the 2020 Tesla Model 3 is rated at 0 CV even for the highest performance versions

https://www.largus.fr/fiche-technique/Tesla/Model+3/2020.html

And the Renault Zoe is rated from 1-4 CV

https://www.largus.fr/fiche-technique/Renault/Zoe/2020.html

And what’s really surprising is the Peugeot e208 is rated at 4cv while some diesel models are rated at 3cv

https://www.largus.fr/fiche-technique/Peugeot/208/2020.html  

I would have guessed that all electric cars might have had a 0 or 1 cv rating.

Jb boin > ranwhenparked 05/21/2020 at 18:55

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I am bit too lazy to do the calculation but 675g/km seems way too much for that little power, a Chiron does 516g/km for 1500hp.

The 2020 Supra with the 4 cylinders has 15cv while the 6 cylinders has 23cv which would be around 650€ and 1000€ for the carte grise but more importantly, the bonus/malus écologique (calculated on the CO2 rejection on the WLTP cycle and only paid when buying a new car that in 2020 starts at 138g/km and tops at 213g/km at 20000€) will cost around an additional ~2200€ for the 4 cylinders and ~6750€ for the 6 cylinders so the total would be 2850€ for the 4 cylinders and 7750€ for the 6 cylinders.

Not to mention that there is an additional luxury car tax of 500€ for each cv over 36cv but it should be removed for 2021 as its not effective (not many of those cars at all and rich buyers have no issue buying them abroad).

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Forgot to mention but the hybrids have extremely low CO2 values making them having very low malus ecologique and relatively low chevaux fiscaux v al ues, for example the new Peugeot 3008 H ybrid 4 (4 wheel drive “SUV” w ith 300hp) hav 9cv and 29 g/km while the non-hybrid FWD 180hp version has 10 cv and 128g/km.  

Jb boin > Manwich - now Keto-Friendly 05/21/2020 at 19:09

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Just found out that previous informations were not totally correct, it seems that since 2020 the calculation for the chevaux fiscaux doesnt use the CO2 anymore but in most case it doesnt make a great difference according to this page .

PA being (i believe ) for Puissance Administrative (Fiscal Power) and PM for Puissance Moteur.

ranwhenparked > Jb boin 05/21/2020 at 19:32

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Well, it's rated at 422 g/mile, I'm pretty sure I did the conversion right

Jb boin > ranwhenparked 05/21/2020 at 19:47

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Yes but under which test protocol, the values in France starting this year are being based on the average of the WLTP protocol (previously based on the NEDC protocol), it wont be the same values with other test protocols and cant be compared directly but you can compare two cars that are using the same test protocol.

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And its important to note that with WLTP the base car is tested then each option gets tested independently so taking bigger wheels or a sunroof will result in a higher CO2 value and possibly in a higher tax bracket while before only the engine and transmission was distinctive (manufacturers were doing the tests on the lightest possible version to lower the values).

ranwhenparked > Jb boin 05/21/2020 at 19:55

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OK then -   I am  just going to go back to not caring about emissions.

Snuze: Needs another Swede > Cé hé sin 05/21/2020 at 20:35

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I should have clarified in my post that I specifically meant the calculation part of it. I was still groggy from pain meds following my surgery.

In particular I was thinking of t he RAC system because it  has very limited relevance to actual power, at least if an engineer is clever.

The CV system would be harder to cheat.  

Distraxi's idea of perfection is a Jagroen > Cé hé sin 05/21/2020 at 21:17

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And to add insult to injury, 99% of 2CVs were not in fact tax rated at 2CV, even in France. 

duurtlang > ranwhenparked 05/22/2020 at 05:27

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422 g/mile = 262 g/km.

Manwich - now Keto-Friendly > Jb boin 05/22/2020 at 10:33

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But I still don’t understand why all Tesla Model 3 vehicles are rated at 0 CV while something like the far less powerful Leaf has a much higher rating.

Jb boin > Manwich - now Keto-Friendly 05/22/2020 at 11:09

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It must be incomplete/invalid information on the website, on another one it shows 9cv for the latest models .

But according to this electric vehicle forum topic , the peak power used for the calculation would be the peak power after 30 minutes of full throttle which makes the retained maximum power on electric vehicles sensibly lower than their real peak power and it seems that the hybrid peak power is only based on the combustion engine.

And i forgot that it was still a thing but it seems that the carte grise is still free for electric vehicle and even for hybrids/PHEV on some regions .

ranwhenparked > duurtlang 05/22/2020 at 15:19

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Me fail math? That’s unpossible!