Stephen wrote:
Crossbow prods don't really need to be pulled back far: almost universally the length of stock was equal to the distance between the prod tips and the prod was mounted at the end of the stock. That's not much of a draw and in later times, a self wood prod or bamboo leaf spring prod worked fine.
There are a few assumptions here that need to be assessed.
Crossbow lathes are bows and subject to the same physics as hand bows. The longer the power stroke a bow has, the more energy it can impart to an arrow. European crossbows went down a strange developmental path with shorter draw lengths and more massive bows to compensate for the reduced power stroke.
The length of the stock in the 1:1 ratio proposed is relative. Longer bows would end up with longer stocks. Qin crossbows, the immediate predecessors of Han crossbows, have quite large bows. Han pottery models of watch towers have model crossbowmen with substantial lathes with curvatures that imply they were composite.
Later crossbows are often considered to have been inferior and technical information suggests that they also used weaker and less sophisticated locks. Ming texts describe crossbows with ranges that are much shorter than previous dynasties. The large bronze and iron arrowheads used in the Qin and Han would have hardly travelled far if used in later crossbows. In fact, the military encyclopaedias show poison to have been used in the later dynasties which would have been unnecessary with some of the Qin and Han weapons.
This leaves the pottery figure to be explained. There are Han Dynasty reliefs in tombs showing small bows and crossbows being used to shoot birds in trees. It is possible the figure represents a hunter. There is good reason to believe that crossbows were common weapons and there is no reason to think that hunting and civilian bows would not have been of a lesser standard than the military weapons. You don't need a bazooka to shoot a turkey.
Regarding the multi-bow siege crossbow, McEwen made a replica of one of these using self bows. I think with the complex string path he ended up with a 42 inch draw. He made the two rear bows 40 pounds draw weight at 14 inches and the front bow as 20 pounds. This created a machine with a 100 pound draw weight at 42 inches. McEwen calculated the relative stored energies of a straight bow of 100 pounds at 14 inches, the experimental bow and a projected reproduction with composite bows. The two actual comparisons show a much greater stored energy for the multi-bow machine because of the long draw. The article is in Vol. 28 of the Journal of the Society of Archer-Antiquaries.