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#1 f1steveuk

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Posted 15 September 2012 - 14:42

I thought I'd researched the Land Speed Record in depth, but I found an anomaly I can't work out!

The Napier Railton of John Cobb had two Napier Lion broad arrow engines, these were, depending on whose archive you believe, either donated by, or brought from Betty Carstairs, and had, at one time, powered her 'Estelle' powerboats.

Now according to hand written notes of Reid Railton, the only mod's needed, or done to these engines for the records were, pre war, the fitting of an anti-stall device, and post war, the changing of the cork floats in the carb's and some jetting issues.

So, reading documents that have come into my hands I get the following,

Flying mile record,1939, John Cobb, Napier Railton, capacity 48,029 cc (makes sense for two 24 litre Lions!!). But for 1947 the capacity is officially listed as 47,886cc. It's only a small reduction, but so small as to rule out sleeving down the engines, and why would you anyway, you'd more likely bore them out!

Just curious as to how this has occurred, but they are pretty official documents!

Edited by f1steveuk, 15 September 2012 - 14:44.


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#2 Vitesse2

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Posted 15 September 2012 - 15:50

There do seem to be different capacities quoted for the Lion, according to which source you believe.

Wikipedia quotes 1,461.6 in³ (23.9 L), sourced to Alec Lumsden's "British Piston Engines and their Aircraft" (Airlife Publishing, 2003).

However, they also quote the same bore and stroke figures - 5.5 x 5.125 inches - as in this 1919 article from Flight:

http://www.flightglo.....20- 0397.html

Now, I make that 1461.72 in³ = 23953.299 cm³. This of course gives us yet another figure for two engines - 47906.598 cm³!

As with a lot of these things, my guess would be that it depends on either which ready reckoner was used or how many places whoever calculated it counted pi to! Maybe even something to do with converting fractions to decimals ...

Another handy article from Flight, although without any indications of engine capacities:

http://www.flightglo.....20- 0877.html

#3 f1steveuk

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Posted 15 September 2012 - 16:01

My first inclination would be to assume it's just a matter of interpretation, but the documents I have, come from the same source, and quote the same (and correct) engine numbers!!!

#4 Vitesse2

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Posted 15 September 2012 - 16:30

But presumably whoever wrote the second one didn't have the first one to hand to refer to? Otherwise surely they'd just have copied it, rather than go to all the trouble of recalculating?

Additionally, by my reckoning, 47,886 cm³ would be two engines of 1,461.1 in³ - what's half a cubic inch between friends? ;)

#5 f1steveuk

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Posted 15 September 2012 - 16:36

But presumably whoever wrote the second one didn't have the first one to hand to refer to? Otherwise surely they'd just have copied it, rather than go to all the trouble of recalculating?

Additionally, by my reckoning, 47,886 cm³ would be two engines of 1,461.1 in³ - what's half a cubic inch between friends?;)



I'd be tempted to say, it depends on if the friends were male and female.....................

Quite so, but both documents are signed by the same chap, from the same office!

#6 Allan Lupton

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Posted 15 September 2012 - 17:12

It probably revolves round the accuracy of the value of pi that was used.
Using Excel (which uses what I believe to be a reasonable 3.141592654) a bore and stroke of 5.5" × 5.125 gives the displacement per engine as 23943.71453 c.c. (i.e. 47887.42906 for two)

48029 implies a pi of 3.15 which wasn't a common simplification but 22/7 was and that gives 47906.7

In a book that is sometimes right I have seen the claim that the two engines in the LSR Railton were ex-Schneider Trophy - did Betty Carstairs get 'em from Gloster's in the first place?

Edited by Allan Lupton, 15 September 2012 - 17:13.


#7 f1steveuk

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Posted 15 September 2012 - 17:33

Well, the engines in the Napier Railton came from Estelle V, and from what I recall, these were new from the Napier factory.

I'd be surprised if they were Schneider Trophy engines, and even when Eyston used the R Type's (Rolls-Royce I know) in Thunderbolt (R25 and R27), they couldn't be used with the same supercharger ratios and fuel mixes so it may have been pointless.

I think I'll put this down to bad math's!

#8 arttidesco

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Posted 15 September 2012 - 19:37

I think I'll put this down to bad math's!


Unfortunately, like infinity, pi is merely a concept ;)


#9 Geoff E

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Posted 15 September 2012 - 19:51

Unfortunately, like infinity, pi is merely a concept ;)


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#10 arttidesco

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Posted 15 September 2012 - 20:02

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:rotfl:


#11 Vitesse2

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Posted 15 September 2012 - 20:11

Unfortunately, like infinity, pi is merely a concept ;)

Mmmm ... Π ...

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#12 Geoff E

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Posted 15 September 2012 - 20:32

Mmmm ... Π ...

Posted Image


A bit of a problem with the 4th decimal place ... perhaps that explains the anomaly. :)

#13 arttidesco

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Posted 15 September 2012 - 20:32

Mmmm ... Π ...

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Shall I bring the cloted cream ?

#14 Robin Fairservice

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Posted 15 September 2012 - 22:35

I decided to look in David Venable's book "Napier". On page 132, giving a description of the Lion engine in about 1916, the Lion's dimensions were given as 138.7 mm bore, and stroke 130.2 mm giving a swept volume of 23,970 c.c. Using my TI calculator, and Pi as 3.1415926, I make this 23606.686 cc. This calculation is using far to many decimal places, and I wonder what the actual measurement accuracy of the quoted dimensions was.

Also according to his book, the VIIID engines that Cobb used were sold to him from the "Estelle" which had been laying around the Acton factory for some years.

Edited by Robin Fairservice, 15 September 2012 - 22:36.


#15 Vitesse2

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Posted 15 September 2012 - 23:01

I decided to look in David Venable's book "Napier". On page 132, giving a description of the Lion engine in about 1916, the Lion's dimensions were given as 138.7 mm bore, and stroke 130.2 mm giving a swept volume of 23,970 c.c. Using my TI calculator, and Pi as 3.1415926, I make this 23606.686 cc. This calculation is using far to many decimal places, and I wonder what the actual measurement accuracy of the quoted dimensions was.

Also according to his book, the VIIID engines that Cobb used were sold to him from the "Estelle" which had been laying around the Acton factory for some years.

The 1958 Flight article I linked does suggest that the production engines were possibly of a slightly larger bore than the prototypes. However, it is perhaps worth pointing out that 5.5 inches is exactly 139.7 mm, not 138.7. And when working to one decimal place, 130.2 mm is as close as you can get to 5.125 inches. 130.1 is nearly 3 thou below, 130.2 a smidgin under 1 thou above.

But it looks to me like the Napier designers were working in Imperial not metric. After all, they were British, dammit! None of that blasted Continental rubbish! I mean, why work in tenths when you can use nice uncomplicated fractions like eighths? :drunk:

#16 Tim Murray

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Posted 15 September 2012 - 23:10

Every reference I can find lists the bore as 5.5 inches and the stroke as 5.125 inches. It's when people start converting these dimensions to metric that the errors seem to creep in - there are a variety of different metric bore measurements to be found. My calculator tells me that the correct metric dimensions are 139.7 mm bore (as Richard says) and 130.175 mm stroke, which gives the capacity of 23,943.71453 cc quoted above by Allan.

However, remember that in those days there were no calculators. This sort of calculation was done either by long multiplication or using a slide rule, with the possibility of errors and inaccuracy creeping in. If I could remember where I put my old slide rule I could check how accurate an answer it gives. The difference between the two capacities originally quoted by Steve is around 0.3%. I suspect that any slide rule inaccuracy would be greater than this.

Edited by Tim Murray, 15 September 2012 - 23:21.


#17 Marticelli

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Posted 15 September 2012 - 23:49

I think there may be a simpler answer. I was always puzzled by an anomaly with the Sunbeam Matabele V 12 engine used in the famous 1000HP Sunbeam land speed record car. Bill Boddy mentioned in an erudite article that one bank of cylinders was lower capacity than the other and this was because although both banks of cylinders had the same bores and nominal stroke, the conrods were masters to one bank and slaves to the other, thus marginally reducing the effective stroke on that bank.

I think the Lion uses a similar arrangement, with the centre bank with master rods and slave rods on each of the side banks. The difference in capacities is probably the result of the first calculation being based on the bore and stroke of the centre cylinders multiplied by three, while the lower capacity results from the reduced effective stoke of the side banks running slave rods. I think you will find that explains the change in capacity. Interestingly I have Edwardian Humberettes which employ a similar arrangement of a master rod and a slave rod, which presumably makes a similar difference to the two cylinders making the swept volume marginally lower on the slave rod side.

Incidentally I have always preferred the term 'swept volume' to 'capacity' as it seems a more accurate way of describing what is happening inside an engine, as it takes combustion chamber volume out of the equation.

Marticelli

#18 Robin Fairservice

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Posted 16 September 2012 - 00:34

I am sure that English car engine sizes were always expressed in c.c. and litres. It seemed to be only the USA that used cubic inches. I have a 1933 book by George Eyston and he used litres and c.c.

#19 Vitesse2

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Posted 16 September 2012 - 07:50

I am sure that English car engine sizes were always expressed in c.c. and litres. It seemed to be only the USA that used cubic inches. I have a 1933 book by George Eyston and he used litres and c.c.

No argument with that. But these are aero engines. Just taking a few at random from a Wiki list, Napier, Alvis and Bristol seem to have built everything in inches and eighths, Rolls-Royce in inches and tenths. The only British companies I can find building to exact metric measurements are Siddeley-Deasy and Sunbeam. The Sunbeams were of course designed by Louis Coatalen - who was French  ;) Wolseley's earliest efforts are Imperial, then switch to metric.

http://en.wikipedia....ircraft_engines

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#20 f1steveuk

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Posted 16 September 2012 - 08:12

The Napier Lion did have con rods with wrist pins and slave con rods. On a broad arrow engine, the crank is so short that there isn't enough space for all 12 big ends. I'm puzzled why the 1000HP "Slug" Matabeles would have this system as they were V12s!

The documents I am querying are dated 1959, so reasonably within historic striking distance to have access the the other documents, (that I have copies of) from the governing body of the time.

Railton's paperwork suggests that the engines were owned by Carstairs, but were kept at the factory, and that they were standard production engines.

#21 RCH

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Posted 16 September 2012 - 08:14

No argument with that. But these are aero engines. Just taking a few at random from a Wiki list, Napier, Alvis and Bristol seem to have built everything in inches and eighths, Rolls-Royce in inches and tenths. The only British companies I can find building to exact metric measurements are Siddeley-Deasy and Sunbeam. The Sunbeams were of course designed by Louis Coatalen - who was French ;) Wolseley's earliest efforts are Imperial, then switch to metric.

http://en.wikipedia....ircraft_engines


But surely with the superb logic of us British, engine sizes were always quoted in metric but the engineers always worked in Imperial?



#22 arttidesco

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Posted 16 September 2012 - 08:17

I am sure that English car engine sizes were always expressed in c.c. and litres. It seemed to be only the USA that used cubic inches. I have a 1933 book by George Eyston and he used litres and c.c.


Going a tad off topic, did anyone apart from the British mix vulgar or common fractions and metric units in the same way as the Bentley 4 1/2 Litre or MG "One and a Quarter Litre" YB ?

#23 Vitesse2

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Posted 16 September 2012 - 08:35

But surely with the superb logic of us British, engine sizes were always quoted in metric but the engineers always worked in Imperial?

Looking at contemporary pieces in Flight, the critical figures tended to be horsepower and weight - but of course aircraft designers were more concerned with power to weight ratios: as in "will this engine pull my airframe off the gound?"

And car adverts were all about RAC HP: as in "how much will it cost me to tax this thing?"

#24 Catalina Park

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Posted 16 September 2012 - 09:27

The Napier Lion did have con rods with wrist pins and slave con rods. On a broad arrow engine, the crank is so short that there isn't enough space for all 12 big ends. I'm puzzled why the 1000HP "Slug" Matabeles would have this system as they were V12s!

Why does a Harley Davidson use that system? (Why did Indian use a fork and blade and a HRD Vincent use side by side?)


#25 275 GTB-4

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Posted 16 September 2012 - 09:49

No argument with that. But these are aero engines. Just taking a few at random from a Wiki list, Napier, Alvis and Bristol seem to have built everything in inches and eighths, Rolls-Royce in inches and tenths. The only British companies I can find building to exact metric measurements are Siddeley-Deasy and Sunbeam. The Sunbeams were of course designed by Louis Coatalen - who was French ;) Wolseley's earliest efforts are Imperial, then switch to metric.

http://en.wikipedia....ircraft_engines


Aero engines, so may have been designed for droning along at constant speed and built for reliability....maybe compression was raised in the interests of output thus reducing capacity??? :cat:


#26 Tim Murray

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Posted 16 September 2012 - 09:59

As Marticelli pointed out above, we are talking about swept volume here, not total cylinder capacity, so the compression ratio is irrelevant.

#27 Allan Lupton

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Posted 16 September 2012 - 10:10

I think the Lion uses a similar arrangement, with the centre bank with master rods and slave rods on each of the side banks. The difference in capacities is probably the result of the first calculation being based on the bore and stroke of the centre cylinders multiplied by three, while the lower capacity results from the reduced effective stoke of the side banks running slave rods. I think you will find that explains the change in capacity.

Incidentally I have always preferred the term 'swept volume' to 'capacity' as it seems a more accurate way of describing what is happening inside an engine, as it takes combustion chamber volume out of the equation.

Whilst I agree with this reasoning, it isn't the answer as the lowest displacement quoted it the one that assumes all three banks have the 5½" stroke.

Oh and "displacement" is the term I prefer to the misused "capacity", but "swept volume" is as good. Capacity as such is never quoted (or known outside the design office).

As stated our engine makers on the whole worked in inches and fractions (usually eighths) but never ever quoted displacement in cubic inches. Also as has been noted we (and our continental neighbours to an extent) were inclined to refer to approximate fractions of litres rather than c.c. as in MG 1½ litre (1548 c.c. V type) 1½ litre Jaguar (actually 1776 c.c.), 4½ litre Bentley (4398 c.c.!) and 2½ litre Riley (2443 c.c.)

Edited by Allan Lupton, 16 September 2012 - 10:12.


#28 f1steveuk

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Posted 16 September 2012 - 13:46

Why does a Harley Davidson use that system? (Why did Indian use a fork and blade and a HRD Vincent use side by side?)



I thought both Harley and Vincent were fork and blade, which do use a common big end as there is an inner and outer big end o the crankshaft? This means con rods of similar length.


On the Napier, although it is a common big end, the "slave" con rod attaches to a "wrist pin" on and main con rods big end , meaning the slave con rods are shorter, though the trow is the same because of the length of the attachment casting.


#29 Marticelli

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Posted 16 September 2012 - 14:01

The Napier Lion did have con rods with wrist pins and slave con rods. On a broad arrow engine, the crank is so short that there isn't enough space for all 12 big ends. I'm puzzled why the 1000HP "Slug" Matabeles would have this system as they were V12s!

V configuration engines use three different arrangements for big ends, side by side, 'knife and fork' and master and slave rods. I am not sure when the first example of the latter was used on a V twin (possibly the aforementioned Humberette) but the idea was essential to the success of the seven cylinder 50HP 'Monosoupape' Gnome rotary, as it would have been impossible to fit seven narrow big ends side by side on one crankpin.

The same motive clearly drove designers to use master and slave rods on V configuration engines, and V12s would surely have been most likely to benefit as they are the longest of all until V16s arrived... Bear in mind that aeroengines are built for aircraft where weight is the biggest enemy, and anything to keep them light and compact would be worth considering.

And just to contradict F1steveuk above, if you do the kinematics, you discover that although the effective length of the conrods is the same, the throw (ie the actual stroke achieved) differs, hence the difference in swept volume. This was my original point of course!

Marticelli

Edited by Marticelli, 16 September 2012 - 14:05.


#30 f1steveuk

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Posted 16 September 2012 - 14:31

if you do the kinematics, you discover that although the effective length of the conrods is the same, the throw (ie the actual stroke achieved) differs, hence the difference in swept volume. This was my original point of course!

Marticelli



I'm having trouble getting my head around that, but I'll take your word for it! ;)

#31 Ray Bell

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Posted 16 September 2012 - 19:39

They must have been a nightmare to balance...

However, in answer to the Goulburn enquiry, I'd suggest 'designer preference' and 'production cost' being the principal deciders.

To respond to the Canberra notation, I would suggest that you think again, Mick. Changing the compression ratio doesn't change the 'capacity', which, as was noted previously, is really the swept volume.

This whole subject is one of great fascination, you wouldn't reckon it was possible to get it wrong yet you know that the most insignificant short cut in calculations can make a significant different to the result.

#32 D-Type

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Posted 16 September 2012 - 21:44

To throw another pebble into the water: the conversion from inches to millimetres was fractionally different in the USA, Britain and Canada.

I think these different swept volumes are most likely down to different values of pi.

Regardless of which vlue for pi is used, converting the inches to mm and rounding then calculating the volumes in cc could produce a different answer to calculating the swept volume in cubic inches, converting to cc and rounding.

Multiplying using log tables, whether 4-figure like we used at school, 7-figure or 10-figure which I used in an engineering office pre-computer and pre-calculator, will give a different answer again.

Any volunteers to investigate all the variables and calculate the differences accurately?

#33 Ray Bell

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Posted 16 September 2012 - 21:57

Originally posted by f1steveuk
I'm having trouble getting my head around that, but I'll take your word for it!


It's because the conrod is not parallel to the bore centreline when at bottom dead centre...

#34 Robin Fairservice

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Posted 17 September 2012 - 05:16

I cannot find my 5 figure or 4 figure log tables, but I found my 7 figure tables. Using those, and my calculator, I arrived at 23,944.65 c.c for the capacity of one engine, working from the inch dimensions, and converting the volume to metric at the end. I referenced the Canadian Metric Practice Guide to obtain a conversion factor from cubic feet to c.c's of 1 cubic foot = 28.316 85 dm cubed.

I tried my slide rule, but the accuracy of reading wasn't high enough and I have forgotten how to get answers to three decimal places.

Regarding old methods of caluculating, in the 1950's we had some hand calculators in our office that would do arithmetical calculations to a reasonable accuracy. The makers name began with "F" and I think that they were either german or Swiss made.

#35 David McKinney

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Posted 17 September 2012 - 05:50

Facit?
(Though they were actually Swedish)

#36 275 GTB-4

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Posted 17 September 2012 - 07:25

As Marticelli pointed out above, we are talking about swept volume here, not total cylinder capacity, so the compression ratio is irrelevant.


Ohhh, I see, so if I deck a block to raise compression ratio rather than skim a head...I am not changing swept volume, but could I be considered as altering the capacity under LSR rules? :)

That's what I was suggesting may have happened and may have accounted for the small changes noted...

#37 Allan Lupton

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Posted 17 September 2012 - 08:02

To throw another pebble into the water: the conversion from inches to millimetres was fractionally different in the USA, Britain and Canada.

First I've heard of that.
25.4 mm = one imperial inch has to be pretty universal.
Go back to the 19th century when French and German inches existed and you have a point because they were significantly differnet.

Ohhh, I see, so if I deck a block to raise compression ratio rather than skim a head...I am not changing swept volume, but could I be considered as altering the capacity under LSR rules? :)

Engine size rules have always been based on displacement, no matter if the description was the slipshod use of "capacity". As I wrote before, capacity as such is never quoted (or known outside the design office).

#38 f1steveuk

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Posted 17 September 2012 - 15:26

It's because the conrod is not parallel to the bore centreline when at bottom dead centre...



Yep, see what you mean, at BDC, the con rod would be going off to one side. Makes more sense now!

I have had a chance to dig out my Napier papers (copied during a long long day at the Science Museum, which tells me,

Napier Lion VIID type E91, 1,350 bhp at 3,600 rpm (racing use only) higher geared supercharger, production run 7.

No special fuels listed.

Not that any of that helps!!

This is from Lion II, but clearly shows how the wrist pins mounted the slave con rods, allowing 12 cylinders in the length of not much more than a straight four.

Posted Image

The Lion was originally known as the Triple Four, and when complete the plugs was numbered from the front of the port bank, back down the centre bank toward the front, and then from the front to the rear of the starboard bank, making the firing order for the complete engine, 1,5,9,3,7,11,4,8,12,2,6,10. Don't think I'd commit that to memory!!

Edited by f1steveuk, 17 September 2012 - 15:52.


#39 Robin Fairservice

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Posted 17 September 2012 - 16:16

[quote name='Allan Lupton' date='Sep 17 2012, 01:02' post='5922560']
First I've heard of that.
25.4 mm = one imperial inch has to be pretty universal.
Go back to the 19th century when French and German inches existed and you have a point because they were significantly differnet.

Referring to the 1973 Canadian Standard for Metric Practice, the only Canadian linear measurement that was different were some land units such as the "French measure" or "Paris Foot" used in Quebec. This was equivalent to 12.789 inches. They also used Perch which was 18 feet in French measure and the Argent which was 180 feet, also in Fench measure. Newfoundland also had its own volume measures relating to the fishing industry. The US survey foot was 0.304 800 6 metres.

It is a fascinating document listing units for measuring countless things.


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#40 kayemod

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Posted 17 September 2012 - 16:45

It is a fascinating document listing units for measuring countless things.


Anyone else remember the printed back covers of those exercise books we had at school years ago? They listed lots of measurements that are barely known today, rods poles and perches and the like. I can't be the only one here who used to memorise avoirdupois and troy weights etc during boring lessons, but I couldn't quote any of them today.


#41 f1steveuk

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Posted 17 September 2012 - 17:13

Anyone else remember the printed back covers of those exercise books we had at school years ago? They listed lots of measurements that are barely known today, rods poles and perches and the like. I can't be the only one here who used to memorise avoirdupois and troy weights etc during boring lessons, but I couldn't quote any of them today.


I bet a grout your right.................

#42 Robin Fairservice

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Posted 17 September 2012 - 21:12

Anyone else remember the printed back covers of those exercise books we had at school years ago? They listed lots of measurements that are barely known today, rods poles and perches and the like. I can't be the only one here who used to memorise avoirdupois and troy weights etc during boring lessons, but I couldn't quote any of them today.


From 1969 to 1971 I worked in Colombo, Ceylon and I had a shock when some drawings were given to us with areas measured in Rods, Poles and Perches. A common plan scale was 8 chains to one inch. Ceylon changed to the Metric system before we left!

#43 Peter Morley

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Posted 17 September 2012 - 22:13

Anyone else remember the printed back covers of those exercise books we had at school years ago? They listed lots of measurements that are barely known today, rods poles and perches and the like. I can't be the only one here who used to memorise avoirdupois and troy weights etc during boring lessons, but I couldn't quote any of them today.


At university we were once given a question that had slugs as a unit of mass!

With the capacity issue it seems to me that it is a question of scale, given we are talking about such a large capacity the number of decimal places used in the calculation becomes far more significant e.g. it is a rounding error?

#44 Allan Lupton

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Posted 17 September 2012 - 22:34

The US survey foot was 0.304 800 6 metres.

That seems perverse when we consider, as I wrote before, that 25.4 mm = 1 inch is pretty well accepted - and that gives exactly .3048 m. = 1 ft.

At university we were once given a question that had slugs as a unit of mass!

Only once?
Until one has to go metric the slug is as normal a unit of mass as the pound is a unit of force - or did you use pounds mass and poundals for force?

Edited by Allan Lupton, 17 September 2012 - 22:34.


#45 D-Type

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Posted 17 September 2012 - 22:57

1 in = 25.4mm was only agreed in 1959. Prior to that he US inch was officially 25.40005 mm or 1/39.37m which gave rise to the US Survey foot. Because of the huge number of legal documents and survey points using it, the use continued after 1959. There is also an Indian survey foot for similar reasons. The British inch was 25.399956 mm based onthe Imperial yard of 0.9144 mm. Check out "Inch" "Foot" etc on Wikipedia for more detail,

But these different conversions are too small to give different engine capacities (swept volumes) which we are supposed to bediscussing


#46 twotempi

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Posted 17 September 2012 - 22:58

Try the calculations using Cambridge 4 figure log tables, and also Pi - 22/7 ( or a value of 3.1416 - four decimal places would have been as far as they would have gone ).

Isn't there a statement in the rules on the value of Pi for calculating capacity ??

Log tables using 7 figure table were used more by surveyors rather than for a "simple" capacity calculation

These are probably their maths tools that were used at the time.

Can dig out my copy and see what the result is.

#47 twotempi

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Posted 17 September 2012 - 23:01

To further confuse the issue 1 litre is NOT 1000cc as they are measured at different temperatures. From memory 14deg C versus 16deg C !!

1 litre is 1000 mls


#48 Vitesse2

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Posted 17 September 2012 - 23:15

It should also be borne in mind that the reason Charles Babbage formulated the idea of his Difference Engine (the ancestor of the thing you're reading this on!) was that he had identified errors in published log tables and was seeking to produce really accurate ones ...

In the 1821 vignette of Babbage and his friend, the astronomer, John Herschel, checking manually calculated tables, Babbage, finding error after error, was driven to exclaim 'I wish to God these calculations had been executed by steam'. The grindingly tedious labor of manually checking tables was one thing. Worse was their unreliability.

http://www.computerh...abbage/history/

Since Babbage never completed his Difference Engine and there were many different books of tables on the market - probably all with errors (and each with different ones!) that must surely add yet more uncertainty as to the accuracy of calculations. Theoretically, two people doing the same calculation could come up with different results because one was using Cambridge tables and the other Macmillan.

I don't see any reason why a manually calculated set of logarithms from 1921 would be any more accurate than a set from 1821.

#49 D-Type

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Posted 17 September 2012 - 23:18

Try the calculations using Cambridge 4 figure log tables, and also Pi - 22/7 ( or a value of 3.1416 - four decimal places would have been as far as they would have gone ).

Isn't there a statement in the rules on the value of Pi for calculating capacity ?? I don't know when it came in to the rules or whether it's still there, but the 1972 FIA Yellow Book defines pi as 3.146 in Chapter I Clause 14

Log tables using 7 figure table were used more by surveyors rather than for a "simple" capacity calculation

These are probably their maths tools that were used at the time.

Can dig out my copy and see what the result is.



#50 seldo

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Posted 18 September 2012 - 01:54

QUOTE (twotempi @ Sep 17 2012, 23:58)
Try the calculations using Cambridge 4 figure log tables, and also Pi - 22/7 ( or a value of 3.1416 - four decimal places would have been as far as they would have gone ).

Isn't there a statement in the rules on the value of Pi for calculating capacity ?? I don't know when it came in to the rules or whether it's still there, but the 1972 FIA Yellow Book defines pi as 3.146 in Chapter I Clause 14

Log tables using 7 figure table were used more by surveyors rather than for a "simple" capacity calculation

These are probably their maths tools that were used at the time.

Can dig out my copy and see what the result is.

...Ooops - I hope not Duncan. That could be the whole cause of the problem. Maybe 3.1416 might be better....