I'm doing some back-of-the-napkin engineering for a friend who runs F500 (500cc Rotax engine). 
He's a member here, but hasn't used the forum much.
He wants to design a Helmholtz resonating airbox for the car, and I'm very nearly done with my preliminary calculations.
My question is this: what volume of fuel/air mixture can you squeeze into a 250cc cylinder with scavenge? Lets assume well-tuned exhaust and intake chambers.
Thanks.
Heh. Just saw that featured on readers rides a few minutes ago.
You're working with the rotary valve rotax engine? Or is it the reed valve engine?
I'm not sure how much you can gain by forcing more air in without making changes to porting and exhaust to take advantage of the additional fuel air mixture. You may get more in, but just end up forcing it out the exhaust without proper tuning. There is a lot that can be gained with modification of ports.
Since its a 2 stroke, the mixture will be squeezed into the crankcase and cylinder under the piston first, and then the piston moving down will force the mixture through the transfer ports and into the cylinder above the piston (and out the exhaust port until the pressure wave forces it back into the cylinder).
The crankcase volume and cylinder volume under the piston will be the area of interest. I'd consider measuring the crankcase volume (fill with and measure volume of gas/oil) at TDC and BDC to better understand the volume and the change taking place. That way you can take into account any volume change due to transfer ports, port modification, counter weights, and piston thickness/style.
If it is the rotary valve engine, I would look into the timing and duration of the rotary valve first to be sure that isn't going to limit the air you can squeeze in. That may also be an area to gain some performance. It can also be used to move the powerband if necessary to match clutch tuning and track style.
Another thing to look into is if that engine was available in a snowmobile with RAVE valves. A set of RAVE cylinders would be a way to widen the powerband by making the top of the exhaust port variable improving low end while keeping the top end.
I'd start with, is he running a tuned pipe? If not, then any fresh charge pulled or pushed out of the cylinder by scavenging is just wasted. If he is then you need to figure out how much charge the pipe can cram back in the cylinder after the intake ports are closed. That's probably going to be more in the exhaust design rather than the intake.
I would think you would also need to figure out crankcase volume in there.
There used to be an outstanding book on 2 stroke tuning. It covered everything, but for the life of me I don't remember who wrote it or even the name of it. I've probably got a copy somewhere and will keep an eye out for it.
As has already been mentioned, we need to know more about the 2 cycle engine in question to give a good responce, but induction type, port design, exhaust port power valve (or lack there off) and proper expansion chamber design will all have greater influence on a 2 cycle engines performance than air box design.
Is this being run in some type of spec racing where the engine can't be touched?
This is the book, I have it in hard back. Found a link to the .pdf on supermoto junkies with a quick google search
http://www.vintagesleds.com/library/manuals/misc/Two-stroke%20Tuner%27s%20Handbook.pdf
Here's an Amazon link to A. Graham Bell's Two Stroke Tuning Performance book too, heavy on the technical side for sure http://www.amazon.com/Two-Stroke-Performance-Tuning-A-Bell/dp/1859606199/ref=pd_sim_sbs_b_1
I've got that PDF already. 
The engine is a Rotax 494, same unit they used in snowmobiles. I'm not sure on the workings of the engine; in prior emails he has said the intake duration is 147degrees, but that's the best I can tell you at the moment.
According to teh wiki: "The 494 cc Rotax engine is a rotary-valve engine. Like the AMW, the Rotax utilizes a 2 into 1 "Y" exhaust manifold and a single tuned expansion chamber exhaust."
He's running an aftermarket tuned exhaust (single expansion chamber), has been dyno'ed successfully for a significant increase in power.
The series is SCCA's F500 class. I don't know what the regulations on engine modifications are.
Just for the sake of clarification, I want to ensure the resonating airbox is larger than the largest slug of air that the engine could pull in a single revolution taking scavenge into account. I'd be stabbing in the dark if I tried to put a number on that. 120% of cylinder displacement, or 150%, or 102%, I've no idea. I'm aware that there's LOTS more engineering ahead of me if I'm going to get this right, but what I think I want right now is a "close enough" figure that I can use as a baseline for my airbox design.
Eric Gorr is THE man on ringding theory and practical application. http://www.eric-gorr.com/
Two strokes have the unusual problem of, as Toyman noted, crankcase volume to consider. Since the piston compresses the fuel/air mixture on the downward stroke to force it into the transfer ports, it's important that the crankcase volume be considered when building any sort of airbox system. It seems there is a formula for calculating the ideal crankcase volume, IIRC it's supposed to be something like 120% of the combustion chamber volume to keep the compression ratio under the piston from being too high.
Reed valves (if used) will change the resonance as well.
In reply to Curmudgeon:
I'll ask him if he can get me the crankcase volume.
If I understand the workings of the rotary-valve two-stroke correctly, the airbox resonations would be tuned to pre-pressurize the crankcase volume (to something like 122 or 125% of cylinder volume) during the intake stroke (piston traveling up), which would increase the pressure ratio under the piston slightly. Then the exhaust's job is to scavenge the now-slightly-higher-pressure charge back into the cylinder.
If we change the crankcase pressure, will the exhaust need to be significantly retuned?
Also, I found a pdf copy of Graham Bell's Two Stroke Performance Tuning, so I'll be browsing that over the next few days.
I saved this same doc off another site but can't find the link. But this might help some
http://www.vintagesnow.com/SledU_Folder/delivery_ratio-1.pdf
http://edj.net/2stroke/jennings/
Found the other link on the opening page theres loads of other links lower left. Best of luck.
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