thedukeofhunslet wrote:One factor is known. By forcing air through a small aperture you increase the atmospheric pressure - this causes friction and hence creates heat.
Nothing you or the bike does increases atmospheric pressure. Only the forces of nature (or God, if you're so inclined) can do that.
Forcing air through a small aperture at a fixed pressure (created by a combination of atmospheric and the function of the speed that you're travelling at) will tend to increase its speed, not its pressure. Anyway, because the entrance to the intake is the smallest cross section in the snorkel (judging by your photo) you're not actually accelerating the air through a restriction at all - that would be the case only if the intake was large and the cross section then reduced further back. This is just restricting the amount of air that's allowed in, probably as suggested as a secondary effect of reducing the amount of induction noise.
Creation of heat? Not measurably at the air speeds and pressures involved here.
The principle of ram air (forcing air down a forward-facing intake) is to increase the pressure inside the air box to above ambient, but in that case designers try to create as straight a path as possible without restrictions (this is why it's becoming common to route the air intake from the headlight area, where pressure is highest, straight through/past the headstock) and having a reduced cross section at the entry point is not good for air flow.
thedukeofhunslet wrote:Heating the air up may assist fuel atomisation but immediatly reduces the amount of air supplied to the engine.
Cold air is generally better.
Heating up the air won't assist atomisation in an injected engine - this is controlled by the fuel pressure and injector design. Cold air is better because it's denser and contains more oxygen per cubic volume than warmer air.
thedukeofhunslet wrote:Given the size of the filter and throttle bodies I just don't see it - try sucking through 1 drinking straw and then through three and see the difference in the energy that you expel in drawing the same amount of air.
But there is a limit to the "bigger is better" argument. Try sucking through 30 drinking straws. Other than the packaging difficulties (fitting them in your mouth) your body may not need the amount of air that can theoretically be sucked through 30 straws. Physical filter size could mean anything - depends how efficient it is at flowing air. Throttle body cross section is the nearest comparison although it's rarely that simple.
thedukeofhunslet wrote:Perhaps the only way to solve this is with a Dyno.
Unfortunately that's unlikely to fully answer your question because you won't be able to replicate the forced-induction effect (if there is any) on a dyno. You may notice some difference with a larger intake but 'seat of the pants' testing on the road might prove to be more indicative, not to mention cheaper!