Jay , as you point out ..." Basically put...imagine the engine as nothing more than an air pump, quite literally.  Anything that one can do to ease the restrictions on air flow through the engine is beneficial both from a power and efficiency perspective.  That being said, the real purpose of the muffler system is merely to reduce the audible noise level to an acceptable level - "........

We are looking at an "air pump" but the introduction of a fuel charge into the "pump" makes it much more complicated , and do not overlook the need to "exhaust" the burned air/fuel residue before charging it with air and fuel for the next explosion . The most efficient engines operate over a very narrow RPM range , to get an engine to start idle at 750 then make power to 7,000 rpm requires many compromises . The length of the intake runners maximizes power at a specific narrow rpm range , the S-4 Flappy Valve opens an alternative air path tuned to a different RPM hence the two torque peaks evidenced for an S-4 . The first "natural resonance" occurs at 2,700 rpm the second at 4,000 rpm . The same is true of exhaust systems , each exhaust pipe length functions best at a narrow rpm range . Back pressure in the exhaust helps to "hold "the new air/ fuel charge in the cylinder and at certain rpm reversion can occur to push air/fuel back into the cylinder to "overfill" the cylinder . Small 2 stroke race boats used a trombone exhaust pipe , the driver manually lengthen and shortened the exhaust pipe for more torque in the corners and more top speed HP in the straights . Some Honda race bikes ran a throttle body , butterfly in the exhaust for similar tuning benefits . Camshafts are a huge compromise , hence the different Vario Cam timing arrangements used on newer engines including the 968 Porsche 4 cylinder to try to broaden the "sweet spot" . It also explains the benefits of advancing or retarding the camshaft timing to either raise or lower the rpm where an engine is most efficient , a gain at one end in exchange for
losses at the other . All of the above must be factored into the engine design to determine at what RPM it will be efficient - simply stated IT IS NOT SIMPLE ..... an engine with no intake runners and no exhaust manifold runs like crap --- the old Cox .049 model airplane engine is a perfect example , a little diesel engine that chops out part of the air/fuel that is flowing through it and pops it off with a glow plug .... Even Top Fuel dragsters , thousands of horsepower supercharged , Nitro use exhaust pipes .


Jim Bailey
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Taken from a dyno run from George Suennen. The green area is what the flappy takes care of.

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With the intake flap closed you have two separate intake systems closed off from each other by the center valve/flap. Each side plenum is fed from the common plenum underneath the manifold which is fed by the common throttle. Each side plenum in turn feeds two cylinders on each side of the engine. Those cylinders will generate intake pulses every 180 deg of crank rotation. That's why two cyl from each side are required because if using all four cylinders on one side for each side plenum, the intake pulses wouldn't be evenly spaced due to the type of crankshaft. Without evenly spaced intake pulses, you wouldn't have the tuned resonance characteristic of the side plenum. Parameters that determine the frequency (RPM) of the Helmoltz tuned intake is the volume of the plenum, the volume of all four intake runners, and the size and length of the tube feeding the plenum. That tube is the short tube connecting the lower plenum to each side plenum. That all works to give the torque peak (increase in VE) at around 3000 rpm. The Helmholtz resonance gives a rather big boost to torque at the peak, but it's pretty narrow and if left functional above the resonant RPM area will cause a loss of torque. That's the dip after the peak and where the flap opens to destroy the resonance in the side plenums. Then they act simply as an air chamber to feed the intake runners which have their own resonance RPM. The runners are not equal length so the torque (VE) increase from their tuned lengths is distributed throughout an RPM range roughly in the 4300 to 5000 area. The Helmholtz tuning comes in to play again at a higher RPM so the flap closes around 5500 to help a little bit on the top end. The help at the top end is not a lot as compared to the 3000 RPM resonance.


Louis Ott
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The defaults (available in the screen shots of the SharkTuner User Manual, available for download from my website) are :

Flappy opens at 3600rpm, flappy closes at 5880rpm. Load threshold 39 (on a scale of 1-255).