Sorry for intruding into something is not my field. I also ask for forgiveness for any barbarisms, I've been reading about it for three months, so I have no knowledge but "dangerous ignorance"...
However, I'm anxious to test my new knowledge on the "forum-test", to learn a bit, if someone contributes and corrects this post.
I become involved into the tuning of a motorcycle, so I "discovered" the Helmholtz theory.
The idea is that you can model the piston and the moving mass of air as a spring-mass system, known as a Helmholtz resonator. I'm fairly used to this, as is the base of the asphalt roughness measurement (modelling the suspension in a similar way), but I digress.
The first thing that seem curious to me is that the air behaves like a spring, with a "stiffness" (if I compare the equations to the ones of a suspension) given by:
where a is the speed of sound, A is the area of the piston,
is the density of air, V is the volume of displacement of the piston. Thus, the stiffness of air is proportional to the speed of sound! Beautiful.
Now, if you plug the frequency
of the system into the basic equations, for a trumpet length L, you arrive to:
Which I believe is the basic equation for trumpet length L. I used it (rather naively, I imagine) to define the tuning I talked about. Notice that the frequency
you have to use, is the one of the piston, same goes for the volume V and the area A.
In the end, it's clear from the equation (I hope) that for faster traveling waves, a shorter pipe is needed.
I wonder if you could construct a manifold with an "extra path". This extra-path could be controlled by a valve, which could be opened or closed depending on RPM. Has this ever been tried?
Is it legal? Would it be useful?
On the other side, I read about "organ pipe theory" (but I did not used it).
What I got from organ pipes is this:
When the cylinder goes down, the pressure in the intake drops, thus an "expansion wave" is produced. This wave travels through the intake up until the junction where all the individual intakes begin. There, the wave "sees" a larger area and it reflects. This reflected wave becomes a compression one. This compression wave travels down the intake, "in reverse".
The key is to dimension the intake in such a way that this compression wave arrives to the intake valve right when the valve closes, so this wave will help to "fill" the cylinder. Waves move at the speed of sound, so for you to get this effect you have to be very precise about the length of the trumpet.
At the exhaust, everything seems to happen in reverse: the geometry of the exhaust creates a reflected expansion wave that helps to empty the cylinder.
Am I wrong?
So, to summarize, I agree with G-rock: area should be more or less the same as the valve area (so you do not restrict the flow) and lower RPMs need longer trumpets.
LMAO
