@troppo, to get you started, here's my learned summary of header design theory for the 4-stroke 4 cylinder CB750:
1) Length and width of header, collector, and megaphone sections
From experience, optimal pipe width has been shown to be around 75% - 95% of exhaust port diameter. At this ratio forces gases to escape with added speed and allows the sound pressure waves to have some influence as well. Wider than this and exhaust gas speed and hence heat, is a problem. Narrower than this and back pressure and loss of power is a problem.
Collector pipe volume = sum of volumes of inlet pipes. Hence, with 4 pipes, Collector diameter = 2 x header pipe diameter.
Megaphone section length adds to overall resonant length, and when combined with header section length, will determine the system's resonance characteristics.
2) Temperature
Break mean exhaust pressure (BMEP) is a good tool to calculate average exhaust temperature (EGTav). BMEP = K x power (Hp) / displacement (cc) x rpm, k= 447420. BMEP x 60 = approx EGTav. At 6000 rpm, the CB750 may have a BMEP of 6.8, which means an EGTav of 410oC. At 410oC sound travels at about 58,000 cm/sec. (Pipes will blue at about 600oC)
3) RPM
Pipes will resonate at precise sound frequencies. RPM determines the sound frequency at which each cylinder is running. Resonance is key to pipe design, and that means we must establish at what frequency a motor operates, or more precisely at what frequency we want our pipes to resonate. I’ve chosen 6000 rpm as the target design point.
Since a burst of sound comes every 4 strokes or 2 revolutions, each cylinder's sound frequency at 6000 RPM is therefore 50 Hz. Because there are 4 cylinders, operating at 2 opposing strokes, the combined sound frequency of the exhaust system at 6000 rpm is 50 x 2 = 100 Hz.
Also note that 6000 rpm = 0.01 seconds per revolution (inverse of rpm) or about 0.005 seconds/stroke.
Putting this together, you get; that in the interval between the power stroke and the beginning of the exhaust stroke, at 6000 rpm, sound would have traveled down an exhaust pipe, a distance of about 72.5 cm (28.5") Call this the Header Tuned Length (TL). Actual exhaust port timing is more precise than merely assuming ½ stroke (90o), but for this illustrative example its close enough.
Pipes will resonate (that sweet sound) if their length is a multiple of their resonant frequency. From above, TL= 72.5cm and that means 2/1 or 1/1 or 1/2 or 1/3 or 1/4 etc of 72.5cm (1/1 = 28.5”, ½ =14.2”) are harmonic. All other lengths will dampen the sound.
4) Sound pressure and pipe length
Sound waves have pressure - they can move the air (exhaust gas in our case). Also, sound waves can interfere with each other and can be inverted by bouncing them off of objects. This can be accomplished by using bends, divergent cones (megaphones), pipe length and in the case of multiple pipe exhaust systems, by timing the arrival of sound from one cylinder with the port timing of another cylinder. At 6000 rpm, a pipe of TL/2 cm would present a wave front to the opposing cylinder at precisely this moment. Hence placing the first bend at 36cm in a header pipe length of 72 cm would achieve maximum extraction at 6000 rpm. Thanks to harmonics, any multiple of TL will also work, just to a lesser extent. Conversely a pipe length that is not a multiple of this length, will have adverse effects. If actual exhaust port timing were to be used, then a slight adjustment to this length would be necessary.
5) Speed of exhaust gases and pipe length
Gases will speed up through a smaller diameter pipe and slow down in a larger diameter pipe. Correspondingly, pressure will rise in a smaller diameter pipe and drop in a larger pipe. Ideally, as the sound front hits the gases it speeds them up precisely when needed, and a reverse sound front slows them down precisely when needed.
The speed of sound is generally much faster than the speed of escaping exhaust gases. Stroke of a CB750 is 63mm. Since all the gases must escape within the span of time the piston moves this distance, we can determine the speed of the escaping gases. The volume of gases = 63 x 61 stroke x bore = 184.1cc (under pressure). Under the same pressure, that volume would take up 23 ¼ cm of a 1 ¼” I.D. exhaust pipe. At 6000 rpm, this volume of gases have about 0.005 seconds per stroke to escape, hence the speed is 23 ¼ / .005 cm/sec = 4,650 cm/sec. This would only be true if there was no pressure differential in the exhaust pipe. However, since gases are highly compressible, the actual speed is a fraction of this rate calculated as a ratio of pressure (about 50% actually), in any event, a far cry from the 58,000 cm/sec that sound travels at. Seen another way, the exhaust gases could have travelled an average of about 5”- 9" down the header pipe when the sound from the next cylinder hits them and forces them to pause.
Summary
CB750 pipes tuned to 6000 rpm
Single pipe dimensions 1 3/8" O.D. - 1 1/4" I.D up to 1 ½” O.D. – 1 3/8” I.D.
Actual Header Length = resonance frequency multiple of TL = 36 cm in our example
Collector diameter = 2 1/2” to 2 3/4”
Megaphone length = resonance frequency multiple of TL = 72 cm (for example)
Total exhaust system length = 108 cm (43”)
So there you have it, 4-stroke exhaust pipe design in a nutshell.
