Charon
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Ain't theory wunnerful? If you are going to try to run a straight pipe, you are going have lots of fun. When the exhaust valve opens, a pressure pulse travels out the pipe at the local speed of sound, which varies with gas temperature. This pulse moves faster than the gas itself. When it reaches the end of the pipe (a discontinuity) it reflects back up the pipe as a negative pressure pulse. If all goes as planned, this negative pulse arrives during the valve overlap, just before the exhaust valve closes, and as the intake valve opens. The negative pulse thus helps to start the intake flow.
Because the exhaust gas isn't "air" and because its temperature varies along the length of the pipe, you have to make an estimate of the speed of sound. Estimates range from about 1400 to about 1600 feet per second. I'll use 1400. Let's also assume you want the engine to be "on the pipe" at 5000 rpm. 5000 rpm is 83.3 rev/sec. One revolution thus takes 12 milliseconds (1000/83.3). The time from exhaust valve opening until intake opening is about half a rev, 6 milliseconds. You will have to look up cam timings to get a better number. If sound travels at 1400 fps, in 6 milliseconds it travels 8.4 feet, 100.8 inches. This is the out-and-back time, so the pipe needs to be half this, 50.4 inches. Part of the distance is in the head in the exhaust port, so the pipe needs to be about 48 inches.
Now, the complications. If the engine is turning much slower, the pulse will return before the intake opens, and will be ineffective in starting the intake flow. If the engine is turning much faster, the pulse will arrive after the exhaust closes, and will be ineffective. So the straight pipe only works over a narrow range of speeds, though sometimes it will "sort of" work at half the design speed. When "on the pipe" the negative pulse actually travels up the intake manifold into the carburetor, and can affect mixture. This is why jetting can be tricky with open exhausts. A pipe with a discontinuity in the middle (such as a Jardine which opens from pipe diameter to a larger diameter, then dumps into the atmosphere) will cause a reflection first from the change in diameter, then from the end, so you'll have two or more reflected pulses to complicate the issue.
Intake tracts are usually shorter, because of the available space. The speed of sound in the intake is about 1100 fps, which would actually need a longer intake than the exhaust. But the intake also has an air filter, which will dampen pulses. The air box serves as a reservoir, and allows the engine to take a "gulp" of air from its volume. The air box has time to refill during the three non-intake parts of the engine cycle. Factories often arrange the intake side so as not to be resonant at the same speed as the exhaust, in an effort to smooth the torque curve and make the motorcycle more user-friendly.
Hope you enjoyed that.
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