# The Ford Cosworth DFV. Why a 2993cc V8?

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### #1 Henk Vasmel

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Posted 30 September 2012 - 11:58

For some time I have been wondering why the displacement of DFV engines is usually given as 2993 cc. We are talking here about the design values for the original DFV, not actually measured values, rebores or later versions with different bore and stroke values. They will come later.

Because for a lot of engines slightly different values are published, I wanted to know what the correct values were, so after finding published bore and stroke dimensions and sometimes using conversions from inches into millimeters (25.4 exact) and using an Excel worksheet using the function Pi(), not a rounded value, I usually get close to one of the published capacity values. Sometimes I had to be creative with inch to millimeter conversion because the value published is usually given with decimals, where the correct value in inches had been using fractions. It is also known that before the advent of electronic calculators different values for pi have been used, like 3.14 or even 3.12 (in Germany).

Indeed for most engines I found a good correlation, but the most important one that stands out is the DFV.

I have just rechecked some of my sources, and they come up with a bore of 3.373 inches and a stroke of 2.55 inches (down from the FVA’s 2.72). Now none of these numbers convert easily into fractions, so we must use them as is.

Using the values given above, we arrive at a displacement of 2987, 6cc short of the published value of 2993. The values in mm for bore and stroke are now: 85.6742 and 64.77. This seems far too precise, but rounding these numbers does not really help. By playing a little bit, I have been able to reach 2992 but then I know the corresponding bore and stroke are no longer as published. Playing with the value of Pi doesn’t help either, you need almost 3.15 to get there, which I cannot accept. The number of cylinders is exactly 8, and not a fraction more, so we can rule out that one as well.

Is there anybody out there who can help me solve this conundrum?

### #2 Tim Murray

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Posted 30 September 2012 - 12:49

This site contains a vast amount of data on the DFV:

http://www.historice.../dfv/specs.html

They quote 3.373" bore and 2.555" stroke. Using these measurements the displacement works out at 182.64 cu in/2992.99 cc.

However, using the metric dimensions they quote, displacement works out at 2988.5 cc. I'm assuming that Cosworth worked in inches, not millimetres, as many of the other quoted dimensions seem to be exact measurements in inches, and that the discrepancies are due to inaccurate conversion to metric (as that site demonstrates).

### #3 Geoff E

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Posted 30 September 2012 - 12:55

Although Wiki is not always reliable, the stroke is given there as 2.555 inches - this increase in stroke by 0.2% would seem to produce the 6cc that you are looking for. http://en.wikipedia....ki/Cosworth_DFV

### #4 Henk Vasmel

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Posted 30 September 2012 - 15:59

So I should really stop referring to books and start using the internet as a first source ;-) I really thought that "Such Sweet Thunder" should be the most accurate reference, but it turns out not to be.

2.555 is indeed a value which produces the correct displacement. Until now I had only found 2.55. Actually 2.555 should be presented as 2.56 (rounding up instead of cutting off). And this also shows that thousands of inches have been used and not fractions which I saw as a possibility.

Thank you very much for your quick help.

### #5 Charles E Taylor

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Posted 30 September 2012 - 17:57

So I should really stop referring to books and start using the internet as a first source ;-) I really thought that "Such Sweet Thunder" should be the most accurate reference, but it turns out not to be.

2.555 is indeed a value which produces the correct displacement. Until now I had only found 2.55. Actually 2.555 should be presented as 2.56 (rounding up instead of cutting off). And this also shows that thousands of inches have been used and not fractions which I saw as a possibility.

Thank you very much for your quick help.

Take a look Here

I hope that helps.

Charlie

### #6 AAGR

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Posted 01 October 2012 - 09:26

Did any of you know Keith Duckworth ? I did - and rather well, too.

I can tell you, for sure, that the last thing he would have worried about was the minutae of dimensions - just so long as the overall capacity was sub-3-litres !

AAGR

### #7 Allen Brown

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Posted 01 October 2012 - 11:15

It is also known that before the advent of electronic calculators different values for pi have been used, like 3.14 or even 3.12 (in Germany).

As I'm old enought to remember how we did calculations before electronic calculators were invented - and have a daughter whose school encourages mental arithmetic - I find it hard to believe that anyone did long hand calcs using 3.14 or 3.12. I was taught to use 22/7 which is 3.1428, close enough to the true value of 3.1415926...

VAT was 47/40 iirc. We pre-electronic people were surpringly capable.

### #8 Roger Clark

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Posted 01 October 2012 - 11:45

As I'm old enought to remember how we did calculations before electronic calculators were invented - and have a daughter whose school encourages mental arithmetic - I find it hard to believe that anyone did long hand calcs using 3.14 or 3.12. I was taught to use 22/7 which is 3.1428, close enough to the true value of 3.1415926...

VAT was 47/40 iirc. We pre-electronic people were surpringly capable.

Isn't 22/7 3.1429 to four places of decimals or 3.142857 recurring if you need it.

Not that it matters. The important thing is to understand the accuracy of the original measurements and the effect that has on the precision of the result. AAGR says it all.

### #9 D-Type

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Posted 01 October 2012 - 14:33

Regarding the value of π : The FIA used to specify (and as far as I know they still do) that when calculating an engines capacity the value of π shoiuld be taken as 3.1416. This is more accurate than 22/7 but less accurate than the value used by Excel. But this does not explain discrepancies as large as Hank is asking about.

Whether the dimensions were originally specified in inches and 64ths, inches and thou, or mm and microns, the first conversion might have occurred when setting up the machine tools to make the engine (if the machine was calibrated in different units from the drawings).

Next would be the published figures: this would depend on the units the readership was comfortable with. Once published, these figures could well have been converted back and forth several times between publications. Published figures includes those on homologation documents, entry forms, manuals, technical articles, the technical press and the popular press. It would also depend on whether the conversion was rounded up at the bore and stroke stage or at the calculated capacity. At some stage the effect of tolerances has to be included in the calculations. Likewise, deliberate boring of cylinders (desaxé) can marginally lengthen the effective stroke (no, I don't understand why either). All these contribute to the small discrepancies we often see.

The other factor is simply the possibility for human error - whether deliberate or accidental. Deliberate is the man who can't recall the exact capacity and writes "3000cc" as the capacity or guesses a number fairly close to the limit. Then there's the genuine error such as writing "2998" when "2989" is intended.`

Then if you physically measure an engine, the errors inherent in any measurement come in.

As AAGR said, all that really mattered to Cosworth was that the engine was legal, ie less than 3 litres, and as close to that figure as they could get.

### #10 Henk Vasmel

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Posted 01 October 2012 - 17:07

As I'm old enought to remember how we did calculations before electronic calculators were invented - and have a daughter whose school encourages mental arithmetic - I find it hard to believe that anyone did long hand calcs using 3.14 or 3.12. I was taught to use 22/7 which is 3.1428, close enough to the true value of 3.1415926...

VAT was 47/40 iirc. We pre-electronic people were surpringly capable.

The value of 3.12 is not all there is to it. in the original formula for the surface of a circle, there is a factor of pi/4. For 3.14 that gives 0.785. However, for German tax regulations, they officially defined pi/4 as 0.78, which gives a value of pi=3.12. I remember when starting to be interested in cars in a serious way in the late sixties, in German publications engine capacities for cars were given as two values, the real capacity and the Tax capacity which was a bit less. the difference was indeed pi/3.12.

### #11 Henk Vasmel

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Posted 01 October 2012 - 17:34

Regarding the value of π : The FIA used to specify (and as far as I know they still do) that when calculating an engines capacity the value of π shoiuld be taken as 3.1416. This is more accurate than 22/7 but less accurate than the value used by Excel. But this does not explain discrepancies as large as Hank is asking about.

Whether the dimensions were originally specified in inches and 64ths, inches and thou, or mm and microns, the first conversion might have occurred when setting up the machine tools to make the engine (if the machine was calibrated in different units from the drawings).

Next would be the published figures: this would depend on the units the readership was comfortable with. Once published, these figures could well have been converted back and forth several times between publications. Published figures includes those on homologation documents, entry forms, manuals, technical articles, the technical press and the popular press. It would also depend on whether the conversion was rounded up at the bore and stroke stage or at the calculated capacity. At some stage the effect of tolerances has to be included in the calculations. Likewise, deliberate boring of cylinders (desaxé) can marginally lengthen the effective stroke (no, I don't understand why either). All these contribute to the small discrepancies we often see.

The other factor is simply the possibility for human error - whether deliberate or accidental. Deliberate is the man who can't recall the exact capacity and writes "3000cc" as the capacity or guesses a number fairly close to the limit. Then there's the genuine error such as writing "2998" when "2989" is intended.`

Then if you physically measure an engine, the errors inherent in any measurement come in.

As AAGR said, all that really mattered to Cosworth was that the engine was legal, ie less than 3 litres, and as close to that figure as they could get.

The value of Pi in five significant digits would be enough to get a correct displacement, which is usually only given in four digits. At most it would be 1cc off.
We are talking here about design values for displacement, so they are dependent only of the numbers on the original drawing, chosen for whatever reason. Converting a drawing into a real engine is difficult enough so measuring in real life is more than likely to give a different value, even if you can measure 100% exactly, which of course is impossible.
Desaxé boring can indeed increase the actual stroke by a little bit. I understand how it works, but don't know how to explain to a person who is not present. certainly not through text only, I need a drawing.
Human error comes in next, but usually that is easy to detect. rounding up to 3000 is indeed very common, so usually I am wary of numbers that end in a 0. But the Ferrari 750 Monza is a real 3000 and more examples are available.

The idea "who cares" can only be answered by "I care". even if it didn't matter to Cosworth, for the design bore and stroke dimensions up to a thousandth of an inch were chosen and quite possibly verified to be under 3 litre. End of story for them, but I want to present the conforming design displacement, knowing full well what factors can influence that value.

To clarify the background a bit more, my real hobby is to create a database of results for all important races in motor racing history. (define important!). Details for the cars include most importantly the chassis number (=identity), the license plate (if available) and the engine displacement. It was in trying to get exact values for the latter that I found that I had to do my calculations myself. Many published numbers are a bit off and that suggested different engines where they actually are the same. So finding bore and stroke came higher on my list and I learned about the conversion between inches and millimeters. and the use of 1/64 of an inch. This taught me that some engines are often misrepresented. Is a Fiat 1100 a 4-1090 or a 4-1089. Actually it is almost exactly 4-1089.5. And the Ford GT40 (and other cars that use these engines) are they V8-4727 or V8-4736. The former value is used very often, yet I believe the latter to be correct. I could go on for a long time, but then it would get boring. Maybe I have to come back to this and I will be reboring.

### #12 Magoo

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Posted 01 October 2012 - 17:55

When you study engines for a while you may find these discrepancies are not terribly unusual. I think we are trying to wring a degree of accuracy from these stats that was never intended. They were presented as general information.

### #13 byrkus

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Posted 01 October 2012 - 19:25

The value of 3.12 is not all there is to it. in the original formula for the surface of a circle, there is a factor of pi/4. For 3.14 that gives 0.785. However, for German tax regulations, they officially defined pi/4 as 0.78, which gives a value of pi=3.12. I remember when starting to be interested in cars in a serious way in the late sixties, in German publications engine capacities for cars were given as two values, the real capacity and the Tax capacity which was a bit less. the difference was indeed pi/3.12.

Is that why in certain publication Citroën 2CV engine is noted as having 597 cc, instead of 602?

### #14 Tony Matthews

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Posted 01 October 2012 - 20:25

Maybe I have to come back to this and I will be reboring.

### #15 Henk Vasmel

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Posted 02 October 2012 - 18:23

Is that why in certain publication Citroën 2CV engine is noted as having 597 cc, instead of 602?

The numbers fit, so this could well be the case. Indeed I remember things like that from (too) long ago. I need to dig up some German publications from the late 60s to be really sure. But my guess is: Yes, indeed.

### #16 Glengavel

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Posted 03 October 2012 - 09:24

If you believe some of the nasty rumours, the value of pi could be as large as 3.68...

### #17 Pat Clarke

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Posted 04 October 2012 - 06:26

If you believe some of the nasty rumours, the value of pi could be as large as 3.68...

I thougyt it had been shown that pi = 4!

http://www.funnyjunk...res/1251260/Pi/

Pat

### #18 Glengavel

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Posted 04 October 2012 - 10:10

I thougyt it had been shown that pi = 4!

http://www.funnyjunk...res/1251260/Pi/

Pat

I got that apex for elbow, what I should have worked out is that if you set pi = 2.69, your 3500cc engine suddenly becomes a 3000cc engine. But as I say these were nasty, scurrilous and totally unfounded rumours (m'lud).

### #19 Michael Ferner

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Posted 04 October 2012 - 17:21

The value of 3.12 is not all there is to it. in the original formula for the surface of a circle, there is a factor of pi/4. For 3.14 that gives 0.785. However, for German tax regulations, they officially defined pi/4 as 0.78, which gives a value of pi=3.12. I remember when starting to be interested in cars in a serious way in the late sixties, in German publications engine capacities for cars were given as two values, the real capacity and the Tax capacity which was a bit less. the difference was indeed pi/3.12.

Yes, I remember that, too! The "Steuer-Formel Hubraum" against the real "Hubraum".

I thougyt it had been shown that pi = 4!

http://www.funnyjunk...res/1251260/Pi/

Pat

That's actually very clever!

### #20 arttidesco

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Posted 04 October 2012 - 18:19

Yes, I remember that, too! The "Steuer-Formel Hubraum" against the real "Hubraum".

Seems Tax officials the world over love to appear generous while robbing tax payers blind

### #21 Michael Ferner

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Posted 04 October 2012 - 19:57

"Robbing"?

### #22 arttidesco

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Posted 04 October 2012 - 21:27

"Robbing"?

Auf Deutsch "rauben" zb: Die Zöllner rauben Steuerzahler Blind. Bin lange nicht mehr in Deutschland hat so ein spruch ein sinn auf Deutsch ?

### #23 Michael Ferner

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Posted 05 October 2012 - 16:15

No more sense than it has in English. If you think that Public Service shouldn't be shouldered by those who enjoy it, then you'll like the future, because that is precisely what you'll get: no more Public Service. At a time when every nation in the so-called first world has accrued debts beyond imagination, to say that tax payers are being robbed is... well, "naive" is the least offending word that I can think of. If NOW isn't the time to wake up, then when????

### #24 arttidesco

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Posted 05 October 2012 - 16:57

No more sense than it has in English. If you think that Public Service shouldn't be shouldered by those who enjoy it, then you'll like the future, because that is precisely what you'll get: no more Public Service. At a time when every nation in the so-called first world has accrued debts beyond imagination, to say that tax payers are being robbed is... well, "naive" is the least offending word that I can think of. If NOW isn't the time to wake up, then when????

Call me naive