There are formulas for pipe diameter and length,I've posted them here before I think,but as my books are still packed away I can't find them (sunday afternoon project,unpack my books?) The exhaust gases and the exhaust noise are two different things,one travels down the pipe at aproximatly the speed of sound,the gases are needed to move at around 300 ft/sec at max rpm,the smaller the dia the faster they move - most stock pipes are about one size too small as this boosts bottom end HP.Very early Triumphs had huge fat pipes because they thought that was a good idea,but the gases traveled too slow - so later models,say 60s models,actualy stepped down in size from the exhaust port....check out a 69 Bonnie.I'll post some formulas when I find my books later.
Found them - exhaust pipe length...L=V 120/N
L=length of pipe
N= engine speed in rpm
V= velocity of wave in ft/sec
Velocity of the wave is variable to some degree,if you use a figure of 1700ft/sec it'll get you close enough.
Pipe dia formula is - V=piston speed/60 X D squared/d squared
V=gas velocity in ft/sec
D= piston dia
d=inside pipe dia.
piston speed=Stroke X 2/ 12 X rpm,this gives ft/min so divide by 60 for ft/sec.
It all sounds pretty complicated but it's fun to play around with - I used to do this stuff before calculators....and I didn't take maths as a subject at school.Enjoy yourself,I do.
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