It seems Dr. Grant's research supports this....beyond 30 yards. At 20 yards it would appear that a deer can't really drop enough to avoid an arrow no matter the speed. At 30 a faster bow will hit the target, while a slower bow will not. I think Grant tested a bow shooting high 300's vs, one shooting high 200's. Beyond that, yes, there then appears to be no difference between a fast and a slow arrow. Both missed at 40 yards. At 30 and under a faster bow will indeed reduce the string jump effect. He also suggests an interesting theory that deer with their head down at arrow release can drop faster than deer with their heads up.
Not a whole lot of research is needed here. With all the hunts that are recorded these days, it is very easy to document string jumping. Here is the post I was referring to with the pictures:
http://www.habitat-talk.com/index.php?threads/crossbow-noise.9885/#post-179849 The math is also in that thread.
The pictures there come from a video. We marked the frame before the bow produced noise in the audio channel and marked the position of the deer's shoulder. When you go through the video frame by frame, you can pick the frame where the arrow arrives at the deer. This particular video was shot at 30fps in standard definition, but we were lucky and happened to catch it as it passed the deer. Higher speed videos in HD make this even more obvious. At this point, we marked the position of the shoulder again. Given the typical shoulder height of a doe in that area, we can pretty accurately estimate the amount of drop when the arrow arrives. This was a 300 fps arrow.
There are certainly examples of deer not dropping this much at 20 yards, but that is the problem. You can't count on string jumping. It may or may not happen and the amount can vary. The slide I posted in the other thread I reference simply shows what deer can do at 20 yards, not what they will do. So, regardless of bow speed, at 20 yards your 9" target can move 18"-22" by the time the arrow arrives.
One more thing to consider. The deer avoiding the arrow is a good thing! I would much rather that happen than the deer almost avoiding the arrow. I would prefer a clean miss to wounding a deer and not recovering it. Depending on the angle of the shot, a movement of only 6" can be the difference between a recovery and a loss.
I'm not suggesting shooting 200 fps bows. My old Mathews Switchback shoots about 320 fps but is deadly quiet. Crossbows have a different challenge. Stored energy is the area under the draw curve. Traditionally, crossbows have made up for a short draw length by over doubling the poundage compared to a compound bow. New designs are experimenting with all kinds of configurations. The marking push is speed, but the difference between 300 fps and 400 fps in inconsequential. In either case, if a deer jumps the string you will likely miss or wound it, even at 20 yards.
I'm simply suggesting that once you get around 300 fps, you've accounted for sufficient ranging error inside 30 yards given todays ranging technology. If you can range a target inside 30 yards with 2 yard accuracy, ranging error doesn't contribute more than an inch or so at 300 fps. Rather than focusing on making a bow faster at this point, folks selecting a design that minimizes the intensity and character of the noise that contributes to string jumping will have more harvests and less losses than folks selecting designs that maximize speed at the expense of quieting.
Thanks,
jack