Mr Helmholz - simple model

[Robert Harris]

The Helmholz resonating system was originally developed for wind acoustical
instruments as a model.  We now routinely use it to create and size resonant
intake systems.  But some may still have trouble visioning it.

The pure model is a ball  "resonating volume"  with a pipe "tuning pipe"
attached.   Changing the temperature changes the local speed of sound within
the resonator - and thus the frequency of resonance changes.  Changing the
volume within the resonating volume changes the frequency - larger lower.
Changing the area/length of the tuning pipe changes the frequency.  

So everyone should see a ball with a pipe.   We now add some pipes - sort of
like porcupine spikes sticking out of the resonating volume - but part of the
resonating volume.  N -1 spikes are of the length and volume of the header
pipes running to the collector.  The Nth is the length and volume including
the volume of the cylinder with the exhaust open during overlap  N is the
number of cylinders firing into the common volume.  

The headers/runners can be individually ram tuned to a frequency somewhat
higher than the highest helmholz frequency and thus extent the top end as this
resonance swamps the helmholz effect.  

When a pulse of sound ( exhaust gas acoustic pressure front ) hits an open
volume it generates a negative pressure wave that travels back up the header
to the exhaust valve.  We want the negative peak of this wave to arrive at the
time both valves are open "overlap" to gain maximum effect.  That is the
theory behind ram tuning exhaust.  With the ability to swamp that effect with
the Helmholz resonance, think ringing a bell - with a variable sized bell - we
can retune the resonance downward as much as practical.

Since the only thing that matters ( assuming a reasonably well designed
otherwise exhaust system ) is the arrival of this negative pulse, we need only
measure the instantaneous port pressure in this crankshaft angle region and
then tune the system to a maximum negative pressure.

Adding blind volume to the resonating volume simply lowers the resonant
frequency -  a good thing since the additional volume does not have to flow
gas.   Adding area/shortening the length of the tuned pipe raises the resonant
frequency.  Perhaps multiple switched exhaust pipes?