That Kakimoto NSX airbox looks really cool. I agree that there's a lot of math in a good design. You want the airspeed in the trumpets to get as high as possible without restricting the flow and the airspeed is determined, for the most part, by cylinder displacement, rpm, and the diameter of the trumpets. Then you want the trumpets to resonate and boost torque at a certain rpm so if you've fixed their diameter, you can vary their lengths to achieve that.
Pulses also play a role. When an intake valve closes and air stops flowing into a cylinder, a pressure pulse bounces off the back of the intake valve and travels back up the trumpet. If that pulse reaches the intake valve of another cylinder just before it closes, it will push more air into that cylinder – which you want. Designing the airbox to take advantage of the pulses given the shape and length of the intake trumpets requires math. But you should go further than that. I believe that optimally, you want the walls of the airbox to be at least a certain distance from the trumpet bellmouths (1/2 their diameter?). The plenum should be shaped so that it feeds an even amount of air into all the trumpets given where the entrance opening is. Also, the airbox can resonate and give your engine a torque boost at a certain rpm, similar to what the trumpets do, if designed correctly. That rpm is determined by its Helmholz frequency, I believe, which is a function of the plenum's volume and the cross sectional area and length of its inlet piping.
Assuming you know at which rpm a stock airbox gives a torque boost, if you keep everything else in the engine the same, you can play with the Helmholz resonance of the airbox to boost torque at a different rpm. Moving the air filter further away from the airbox increases the length of the vibrating air column in the inlet pipe and therefore decreases the resonant frequency and rpm at which the airbox gives a torque boost. You can calculate that with a simple formula. Increasing the diameter of the inlet pipe or the volume of the airbox has a similar effect.
If you change other factors as well such as when the inlet valves open and close, how much air the cylinders inhale, the length and shape of the intake runners/trumpets, etc., you will have changed several variables and I think it's going to be really difficult to design an optimal airbox without complex CFD (Computational Fluid Dynamics) software and/or empirical testing. Engines can often produce more horsepower with an optimal airbox than if they just inhale cool air from the atmosphere. However, juggling all the design variables to make that happen in reality is not a trivial task.
I'd image that companies that design intake manifolds for a living have the CFD software to design a good airbox if you give them information about your setup (displacement, firing order, cam timing, trumpet length and orientation, etc.) and your design goals (maximum rpm and the desired torque characteristics). I wonder what someone like Wilson Manifolds would charge for that.
..... Kaki must had too much sake.
