id like to apologize for my novella in advance..

not saying you could cheat but i am saying that theres a physics based reason why one is faster but less powerful than the other. the hypothesis for that was it had to do with the frequency/velocity of that wave as it traveled through the runner and if it was a harmonic resonance. if one could figure that out, one could understand the whole relationship in a way that could help in the future.

the basis for that is the assumption that with a properly short, tuned, runner, it takes advantage of a higher resonance frequency (higher peak power, lower avg) but the longer runner takes advantage of a lower more advantageous frequency (lower peak power, higher avg). from that i get: shorter runner means the cylinder fills best at one point but fairly inconsistently throughout the higher rpm range. while the longer runner may fill less overall, it fills the cylinder on a more consistent or steadier basis through out the reduced rpm range.

we know it works and the engine parts that make it work but, scientifically, it could be clearer been trying to dig deeper into it beyond parts matching based on experience.

err.. ok, through writing this response i had a thought (it didnt hurt!): if we relate RPM directly to the intake pulse wave frequency, we have exactly why it acts as you describe and what ive stated. here goes:

in the upper rpm, the frequency is much higher as a direct result of the cycle speed of the valves opening and closing (though there are other factors). with the short runners, you are finding the resonance frequency of the pulse wave on the high end which is a very small window. with the longer runners, you are not killing rpm or even "leaving power on the table." you are taking advantage of the lower speed of the engine and the lower resonance frequency created by the lower RPM/valve event cycle of the engine. the wave length/pulse duration would be longer over a broader range causing the higher torque and higher avg power(lower peak with less rpm. if thats the case, it also means literally slowing down the cam (engine rpm) can aid in cylinder fill (cylinder airmass). it ALSO explains the faster recovery time after gear shifts or other rpm drop offs (the pulse wave lasts longer along more of the rpm range than in short runner intakes). all jusst theory though..

the 1 question that remains is: what is the physics model that can explain this? (general question, not really directed at you or anyone specifically)

 

I think the discussion is going in two different ways.

You are asking more about optimal runner length.

A 4 pattern camshaft is a crutch for an intake that has 2 different length runners (old carb style intakes)

If I am processing all of the responses correctly, a 4 pattern cam is essentially of no value (in almost all applications) for an equal length runner intake.

I am sure if you were running a spec series that required a stock intake (LS), but unlimited camshaft, there may be a place for determining any flow difference between runners and crutching them appropriately.

 

it went from discussing the basic 4 pattern, to runner length vs plenum, to cams that manipulate the intake pulse wave in various runners. not exactly what i asked originally but not outside the overall subject of why they would work.

 

If I am reading right, in a equal length runner system, this should be unecessary.

never meant to imply it was out of scope, more trying to keep it all straight.

 

something that helps explain some of it, i think..
http://www.chem.mtu.edu/~fmorriso/cm...sible_flow.pdf
and this one
http://www.scirp.org/Journal/PaperIn...x?paperID=7749

 

What you may be looking for can probably be found here. One thing to note is that most of the formula's for compressable gases allow for mach 1 air velocity, while all head porters and cam designers limit the velocity to mach .5
http://www.grc.nasa.gov/WWW/k-12/airplane/shortc.html

Since the heat variable skewed the results by 20% due to lack of heat transfer at speed, it is going to very difficult to accurately predict the pulse in varying atmospheres. I can see your hair looking like Einstein's when you allow for temp change at the beginning of the run ( low heat) vs. the End ( high heat) and as the atmospheric conditions changes. Varying pressures of forced induction, positive pressure as a result of a forward facing air intake at speed can all skew a perfect model.
I think the test and see is probably the best case you will get and that won't be perfect for all conditions.

 

theory that helps account for subsonic flow and the fluctuation of the speed of sound in a fluid based on temp.
http://en.wikipedia.org/wiki/Rayleigh_flow

the air itself is subsonic, the pulse wave that is causing it to compress on hte back of the valve is moving ~mach 1. at least from what you are saying anyways.

i believe one could actually use a corrected temp bias calculation to determine temp as well.