As far as the trick shooter... double checked... he's using a 30-35lb modern recurve shortbow/horsebow. I don't doubt some aspects of what he does. But he's not using a 100+ lb longbow. Bows like that get drawn with the back muscles and not the arms. He's also only using partial draws so effectively only has the power of a those cheap fiberglass childrens bows you might have fired at boy scout camp as a kid. I'm bringing this up because it then goes directly into the PVC bow problem... He's directly sacrificing power for speed, and is directly benefiting from modern materials not available back then. (steel tipped target arrows are actually superior to the long iron bodkin points which were prone to bending on hits and which didn't work as well against steel armor; the reason was simply cost... iron was cheap... steel was really expensive... and not wasted on ammunition like arrows)
The problem with your on the cheap PVC is that it falls into the crossbow trap. Just because the draw weight is 50 or 100 or 500 lbs does not mean you're imparting all that energy efficiently into the arrow. At the end of the day only three things matter... the kinetic energy of the arrow on release and the mass of the projectile.... and that most of that energy isn't in the form of a flexing arrow (when fired arrows bend like a twig, and if too light break like a twig; or they simply flex like a spring while flying hammering their accuracy).
Crossbows were not adopted because they were superior to bows... but because they were cheaper to train conscripts to use them on the quick. It took years (or preferably a lifetime of use) to train archers... crossbowman could be trained in a few weeks. Experienced crossbowman could also benefit from having 'loaders'. People who'd just load crossbows and hand them one after another to the experienced shooter.
Trying to think how to explain this better... the more the limbs flex, and the heavier the limbs are, the more energy which is lost moving the limbs and not imparted into accelerating the arrow. Also longer draw lengths are generally more efficient than shorter ones. Therefor longbows are more efficient than shortbows, and lighter materials are more efficient than heavier materials generally. The other problem is if you accelerate a lightweight arrow too much it snaps in two... hence why I commonly refer to the classical shadowrun trollbow as needing to fire crowbars (the size and length of the arrow is based on the size of the shooter and his draw length). If the arrow is going to be going through both sides of an armored vehicle while not snapping in half while fired... it's going to have to be that strong and rigid (which will limit its speed... heavier the arrows slower it goes... but more momentum it has).
Crossbows had the problem historically of being extremely inefficient... they are effectively very short bows mounted horizontally. Using heavy steel springs which had to flex a lot. They also had extremely short draw lengths compared even to shortbows/horsebows.
The PVC bow has the same problem... you could pull out a modern olympic recurve with a 50lb draw weight... and the PVC with a 50lb draw weight... and I guarantee the olympic bow is firing arrows with higher velocity simply because it's drastically more efficient (more energy... damage to the target).
Oh well, here's a link rather than trying to explain... many people have taken some issue with the figures given here. As is to be expected over a few hundred years of history there are a lot of different data points some better or worse than the ones given here. Higher draw weight bows... or more efficient crossbows... 740lb crossbow vs 68lb longbow. Longbow has roughly equivalent projectile speed! And the projectile has twice the mass... so it has a lot more kinetic energy and more importantly momentum... (it doesn't decelerate as much from air resistance). This is simply because the crossbow uses brute force and a lot of it, but it does not use it very efficiently.
http://www.thebeckoning.com/medieval/cross...ross_l_v_c.html