I admit I simplified matters - but with Germany and tax nothing is simple.... ;-)
Ok, the long way:
EFFECTIVE displacement in ccm is calculated by Pi * bore * bore : 4 * stroke * cylinders : 1000 (* = multiply, : = divide)
With the cars you mention the results are (calculated with MS Excel 2002, Pi as an Excel function):
240D W115 2404 ccm (3,141592654 * 91 *91 :4 * 92,9 *4 : 1000 = 2403,834857828440 = 2404) 240D W123 2399 ccm (3,141592654 * 90,9 *90,9 :4 * 92,9 *4 : 1000 = 2398,554607126370 = 2399)However, the TAX displacement is calculated much different and that is what the model designations on the trunk lid are coming from, rounded-up to the next full 100 ccm and then divided by ten.
The calculation for the TAX displacement is: For Pi : 4 exactly 0.78 is assumed and bore and stroke are rounded down to the nearest 0,5 mm or full mm and then from the result everything behind the comma is _cut_ (no rounding here). Sounds complicated but comes from the 1950s when there were no computers used for calculation but printed charts and that way it was much easier.
240D W115 2376 ccm (0,78 * bore tax * bore tax * stroke tax * cylinders : 1000 = 0,78 * 91 * 91 * 92 * 4 : 1000 = 2376,97824 = 2376) 2376 rounded-up is 2400 divided by ten is 240 240D W123 2350 ccm (0,78 * bore tax * bore tax * stroke tax * cylinders : 1000 = 0,78 * 90,5 * 90,5 * 92 * 4 : 1000 = 2350,92936 = 2350) 2350 rounded-up is 2400 divided by ten is 240Yes.
With the designations MB sticks to the TAX displacement - and displacement tax was 2376 ccm with the 240D W115; rounded-up to the next full hundred ccm is 2400 divided by ten is 240.
(300D)
Right, displacement effective for that is 3005 ccm (3,141592654 * 91 * 91 :4 * 92,4 *5 : 1000 =
3004,793572285550 = 3005) but displacement tax is 2971 ccm (0,78 * 91 * 91 * 92 * 5 : 1000 = 2971,2228 = 2971) 2971 rounded-up is 3000 divided by ten is 300With the newer version the figures are (3,141592654 * 90,9 * 90,9 : 4 * 92,4 * 5 : 1000 =
2998,193258907960 = 2998) but displacement tax is 2938 ccm (0,78 * 90,5 * 90,5 * 92 * 5 : 1000 = 2938,6617 = 2938) 2938 rounded-up is 3000 divided by ten is 300Displacement effective is 4520 ccm (3,141592654 * 92 * 92 : 4 * 85 * 8 : 1000 = 4520,374837397280 = 4520) but displacement tax is 4489 ccm (0,78 * 92 * 92 * 85 * 8 : 1000 = 4489,3056 = 4489)
4489 rounded-up is 4500 divided by ten is 450 380 models (3818 cc, and later 3839 cc), Old effective 3818, (3,141592654 * 92 * 92 : 4 * 71,8 * 8 : 1000 = 3818,387215589700 = 3818) new effective 3839 (3,141592654 * 88 * 88 : 4 * 78,9 * 8 : 1000 = 3839,036275783220 = 3839)old tax is 3776 (0,78 * 92 * 92 * 71,5 * 8 : 1000 = 3776,29824 = 3776)
3776 rounded-up is 3800 divided by ten is 380new tax is 3793 (0,78 * 88 * 88 * 78,5 * 8 : 1000 = 3793,32096 = 3793)
3793 rounded-up is 3800 divided by ten is 380 6-cyl. 230 models (including 230 SL, 2306 cc), M127 II has 2307 effective (3,141592654 * 82 * 82 : 4 * 72,8 * 6 : 1000 = 2306,748335098960 = 2307) and tax is 2281 ccm (0,78 * 82 * 82 * 72,5 * 6 : 1000 = 2281,4532 = 2281) 2281 rounded-up is 2300 divided by ten is 230See above.
Yes, effective is 5025 (3,141592654 * 97 * 97 : 4 * 85 * 8 : 1000 = 5025,071697196480 = 5025) but tax is 4990 (0,78 * 97 * 97 * 85 * 8 : 1000 = 4990,5336 = 4990)
4990 rounded-up is 5000 divided by ten is 500 = 5.0
Effective is 2525 ccm (3,141592654 * 86 * 86 : 4 * 72,45 * 6 : 1000 = 2525,087453727130 = 2525) but tax is 2492 ccm (0,78 * 86 * 86 * 72 * 6 : 1000 = 2492,15616 = 2492)
2492 rounded-up is 2500 divided by ten is 250Effective is 6333 (3,141592654 * 103 * 103 : 4 * 95 * 8 : 1000 = 6332,539727767480 = 6333) The 6332 come from the fact that for Pi exactly four digits after the comma are used, that gives
6332,352965, but as soon as one uses five or more or the Pi function in Excel it is at least 6332,534379 which is rounded-up to 6333 - but that is another story... Pi Effective ccm 3,14 6329,3294 3,141 6331,34511 3,1415 6332,352965 3,14159 6332,534379 3,141592 6332,53841 3,1415926 6332,53962 3,14159265 6332,539721 3,141592654 6332,539729 Excel function 6332,539728Tax is 6289 ccm (0,78 * 103 * 103 * 95 * 8 : 1000 = 6289,0152 = 6289)
6289 rounded-up is 6300 divided by ten is 630 = 6.3
Effective is 6834 ccm (3,141592654 * 107 * 107 : 4 * 95 * 8 : 1000 = 6833,937915280410 = 6834) but tax is only 6786 ccm (0,78 * 107 * 107 * 95 * 8 : 1000 = 6786,9672 = 6786)
6786 rounded-up is 6800 divided by ten is 680 = 6.8 The reason here is simple: The Rolls-Royce Silver Shadows and the Camargue had engines with effective 6.75 litres ((bore = 104,1, stroke 99,1, V8, 6747,687820037850 = 6748 ccm) which would be rounded-up to 6.8 litres in normal speaking (although German tax ccm was only 6681) - MB simply wanted to have a bigger number than 6.8 on the trunk lid so it became 6.9.Effective was 2746 ccm (3,141592654 * 86 * 86 : 4 * 78,8 * 6 : 1000 = 2746,402917235300 = 2746) and tax 2717 ccm (0,78 * 86 * 86 * 78,5 * 6 : 1000 = 2717,14248 = 2717)
2717 rounded-up is 2800 divided by ten is 280As said my former post simplified matters - when you calculate German car tax displacement (so-called _Deutsche Steuerformel_ = German tax formula) it is clear that traditionally the designation on the trunk lid comes from the tax displacement rounded up to the next full 100 ccm and then divided by ten, see the examples above.
Or am I missing something?
Also kind regards to you from sunny Germany
Juergen