As Shrew and others have said exhaust manifold design is actually very complex and involves compromises throughout. But your point about pipe volume is not actually the crucial factor. It is the length from the valve to the outlet of the pipe which is a critical factor (where it changes diameter at the secondary) as a pressure wave travels down the pipe to the end then a negative wave goes back up the pipe to aid cylinder filling when the exhaust valve is open again.
Also though there is the effect of the velocity of the exhaust gas in the pipe - which is higher for smaller diameter pipes - but then there is increasing friction effect for smaller dia pipes....and the temperature of the gas has an effect on wave speed - and the temperature varies with engine speed.....and distance down the pipe.....
Leave it to Shrew! Experience is a great textbook in these matters!!
you should re-doe my diy website Phil!
thank you very much, i wouldn't normally boast that statement myself, i tend to kind of dance around it a bit, so thank you.
as i touched upon before, the maths are very relevant, the physics very real, but the reality is still full of compromise,
take a peak at some of the better more in depth calculators, and you'll find that you can predict and to a degree build in both primary and secondary power hikes by tuning the lengths, there are some clever maths behind it, but it can also bog you down and keep you going in circles striving for that perfect exhaust, which in all reality, is largely unavailable in the real world, without NASA backing!!!
because our engines have to produce useable power and torque over quite a large rev range, the exhaust is full of large compromise straight away, which in fact almost makes a race exhaust slightly easier in design, not neccessarily in build, but at the extreme end of things, a full race drag engine's exhaust, only has to work efficiently over a very narrow power band, right at the very very top of the engine rev's, flat out in other words!
you don't drive a top fuel alcohol fired 5000hp monster through McBellyaches Drive Thu, crawling around in low geared town traffic eh?
so the exhaust can be spectacularly less full of compromise, by being spectacularly less! ha ha!
we need things like secondaries and collectors and an exhaust system to follow, all to satisfy the compromises caused by needing it to work at least reasonably well over a much larger rev range.
as many car manufacturers, including Alfa on the twin spark motors, have played with variable length inlet tracts, so should they apply the same gas harmonic theory to the extraction side, but simply put, budget restrict us from having an exhaust manifold that can change length for example with increases in engine revolution, and it would also mean a plethora of additional unreliable bosch sensors and brains to do it properly no doubt!
you can imagine how it would work quite simply, the higher the revs, the shorter the headers need to be to evacuate the spent gas at a greater gas speed, and the less reliance upon the reverberation pulse to aid cylinder filling.
this is where the motorcylce manufacturers are way ahead, and have been using a reasonably cost effective way of cheating this theory into practice for 20 years!
yamaha first patented it as the EXUP valve, which is a butterfly valve sitting right across the whole internal bore of the final 4 into 1 collector pipe.
it meant that the bike could have relatively short header pipes and a straight forward 4-1 design, leaning more towards the drag style we mentioned that suits top end rev range power, so the butterly would be partially opened at idle, and progressively more and more open as the revs increased until fully open and straight thorough at around 6-7k, out of a possible 12k redline iirc.
this fooled the engine basicly with back pressure, reverberation pulse, call it what you like, and so the cylinder filling behaved as if the pipework was a longer tuned length exhaust primary, getting progressivley shorter as the engine rev's increase.
Clever, and Cheap!
i have thought about ways of incorporating something like that into an exhaust one day, but it might be a little wasted until i have a car engine that can rev well into the double figures!
until then, i'll go with what i know so far, which to the best of my description, is juggling with the compromises!
and they all lived happily ever after,
oh, you're asleep already,