[Dave]

i started writing a book to try and help out and then got lazy and stole someone elses

It’s possible to obtain greater than 100% volumetric efficiency in a naturally aspirated (non-supercharged) engine by using tuned intake/exhaust systems. How all this works isn’t all that complicated, but it takes a while to explain it properly. I think the first use of tuned intake runners were the vertical velocity stacks. They were generally of a length that put the open bell mouth somewhere around 15 to 18 inches above the back side of the intake valve. Although both the length and diameter of the runner are important, the length is what determines the specific rpm at which the runner is tuned to provide peak efficiency.

The velocity stack utilized the fact that air is a compressible fluid to produce its boost. At wide open throttle, with the engine turning at high rpm (the rpm that the intake is tuned for), a column of air is moving at a high rate of speed down the intake pipe while the intake valve is open. The column of air moves toward the cylinder in response to differential pressure; the pressure in the cylinder is lower than the pressure at the open end of the velocity stack. When the intake valve closes, the inertia of the column of air causes it to continue moving down the intake tube, stacking up against the back of the closed intake valve, causing the intake air to compress, and creating a higher pressure right up against the valve.

Now if the high pressure air sitting at the intake valve would just stay there until the valve opens again, life would be very simple. Only it can’t, because the pressure is now lower at the inlet to the runner. So the high pressure air bounces off the closed valve and tries to move backwards toward the inlet. Since the valve is closed, the entire column of doesn’t really start flowing backwards; instead it is more like a high pressure wave propagating back toward the inlet. This high pressure wave (or pulse) leaves a low pressure behind it, and when it finally reaches the inlet, the pressure at the inlet is now greater than the pressure in the intake tube. As a result of low pressure in the tube, air starts moving back into the tube, its inertia causing it to stack up against the intake valve again, which is still closed. If the engine is turning the proper rpm (whatever the intake tube is tuned for), the intake valve opens when this higher than ambient pressure is present at the valve.

Some of the design considerations are pretty obvious. If the diameter of the tube is too large, the velocity of the column of air will be too slow to create a good inertial pulse, or reflected wave. If the tube is too narrow it will restrict the airflow and cause a performance decrease. The length of the runner determines the rpm where any boost effect will occur. Earlier it was noted that the typical velocity stacks on old race cars were around a foot long. Since I think the reflected waves that set up inside the runner propagate at the speed of sound, I think the length is such that it is three times as long as the calculations would indicate it should be. These older types used a third order harmonic, or in other words, several of these waves would be bouncing back and forth inside there at any given time. Maybe some math people here can sort out whether this is part is correct or not. I think they used to use a foot (or foot and a half) long for an rpm around 5 or 6k. It seems like there used to be a formula that was used to make some sort of preliminary “length to rpm” calculation. Testing would still be needed to fine-tune a particular setup.

The way it was explained to me, using a length tuned to the third-order harmonic gives a very deep peak when you hit the resonate rpm, in other words a big kick. The problem with this is that it is not effective when you get off of (above or below) that rpm for which it is tuned. The much shorter stacks that are common today, and the tuned induction systems seen on a lot of cars must be using first- or second-order harmonics, I’m not sure, but that would have the purpose of making the thing effective over a significantly wider rpm band, but at the cost of not producing quite as high of a peak boost.

Exhaust systems are similar, but I think they are not quite as twitchy to get right as the intake runners are. The exhaust pulses have a significantly higher pressure differential, or power pulse, that you are dealing with, to begin with. But the process is similar, except the thing is tuned to have the exhaust valve open when the low pressure pulse is present at the back of the valve.