Stored energy goes up with each inch of draw. Calculate the area under a triagle. One has a 50# peak at 27" and another has a peak at 28". One-half of the base times the height equals the area of the triagle. A longer draw with the same draw weight has more stored energy than a shorter draw. Simple.
Therefore, with dynamic efficiency staying about the same at most normal draw lengths (see our website's description of "energy storage") then the longer draw length (at the same draw weight) will shoot the same arrow faster because it stores more energy than the shorter draw length.
As much as we'd love to, none of us can fool Mother Nature or the laws of physics.