OK... here goes...
The theory of long intake VS short intake has to do with pressure waves that reflect back and forth inside your intake. Much like small waves lapping up against the edge of a pool and then heading back toward their origin, these resonance pulses will rebound and travel back and forth along the intake tract. The number of bounces the pulse incurs before being utilized by our tuning determines how we address the pulse and also the amount of pressure the pulse creates. For instance, the third time the wave bounces back and forth is called the (funnily enough) third wave or third pulse. Just like any other wave that bounces between objects, much of its energy is spent during the reflection process and so each each higher numbered wave will have much less power than the lowered number wave before it.
"Easy!", you say. "I want the most power and so I will tune for the first wave!" Well, that's exactly what we want, in theory, but this is often quite difficult to do in practice. The speed at which these pulses travel is variable depending on your intake conditions, but is roughly the speed of sound (1125 feet per second). Now lets examine your intake system a bit more closely so we can figure out how to best capture that rebound.
Before we begin with the math, decide which range in the RPM you wish to the effect to take place. As with nearly everything in engine performance, you have to choose a "best" and in order to make the most of your machine you're better off stacking all of these "best" points at exactly the same spot. For argument's sake I will choose 8000 RPM. For the following calculations, I will also assume the stock duration for a Honda 360 which is 221°.
1.) A 4-stoke engine rotates twice for every opening of the intake valve, and so we use 720° as a starting point.
2.) To determine how long our intake valve remains closed, we take 720° and subtract the duration of our cam at 221°. The answer is that the intake is closed for 499° of the crankshaft's rotation.
3.) Now we need to figure out the number of rotations per second by taking our 8000RPM figure and dividing by 60. We have 133.33 RPS.
4.) Now convert this number to degrees per second by multiplying by 360°. We have 48000°/sec.
5.) Next, take the number of degrees the intake valve is closed and divide that by the number of degrees of rotation per second and we have .010395 seconds. This means the time between the closing of the intake valve and its reopening needs to be .010395 seconds in order for us to capture the wave.
6.) Finally, we take the number of feet per second which the pulse is traveling and multiply that by the number of seconds we calculated at step 5. The answer is 11.695 feet. Now divide this number by two because the pulse which we are measuring is, first, traveling away from the closed intake port and then rebounding back to it. This gives us an ideal intake length of 5.848 feet in order to catch the first pulse. Obviously, a six foot intake is going to be longer than your bike and so capturing the first pulse is rarely, if ever, feasible. Even targeting the second pulse can be difficult and NASCAR builders usually aim for third pulse. Depending on your application you should try to get fourth pulse but can settle for as low as sixth. Knowing the necessary intake length for each pulse you capture is as simple as dividing the number we got from step six by the pulse number. For instance, to capture the fourth pulse, we divide 5.848 by 4 and get 1.462 feet, or 17.5 inches. Long, but probably more realistic than some of our other choices.
Because this is the total length of the intake and not just the length of the velocity stack, we need to first subtract the existing intake length before we can determine the length of the intake. The intake length from intake valve to carb venturi opening for a Honda 360 is 214mm. A quick metric conversion from 14.0352 inches minus 214 mm gives us 142.5 mm.
So for our particular application, we're looking for and intake that is 142.55 mm in length. Simple, no?
