You can. In fact, I think heavy crossbows are assumed to have such. The problem with crossbows is that although the draw is strong, the application distance is small, so a crossbow gets less time to transfer that energy to the bolt. Net result is a crossbow IRL sends a bolt with not much more energy than an arrow. Worse, the bolt is less aerodynamic and actually has a shorter range than a longbow.
I did do some work on crossbows once...lemme dig it out...
I reworked all the crossbows into stirrup bows (replacing the light xbow) and winch bows (replacing the heavy xbow). So a stirrup bow could normally be reloaded as a move action and a winch could be reloaded as a full-round action. Then there are different strength versions that do different damage.
See this. It was written for 3.5 but I don't think anything much has changed.
The energy that goes into the bolt is the half the force times the square of the draw, less the amount wasted in moving the bow. A winch crossbow can have a huge force, limited only by the weakest part of the string. A pull bow has other limits, such as the stiffness and strength of the arrows, which must be longer than the draw; this is not so for a crossbow.
Well the physics is simple enough for longbow vs crossbow, and these numbers were crunched using recreated medieval weapons:
Longbow, 68lbs draw, arrow weight 2.5 Oz (0.070875 kg). The speed of the arrow was measured at 133.7 fps (40.75176 m/s) for a total energy of 117.7 J.
This is a light-weight longbow. Some of the medieval bows retrieved from the wreck of the Mary Rose had an estimated draw of 200lbs when they were in use.
Crossbow 740lbs draw, bolt weight 1.25 oz (0.0354375 kg). Speed of the bolt measured at 138.7 fps (42.27576 m/s) for a total energy of 63.3 J
The problem is that while the crossbow stores way more energy, the transmission of that energy to the bolt is very inefficient. Just like with a gun a longer barrels always give you a higher-velocity projectile, with bows the longer the distance of the acceleration (the draw distance of the bow or crossbow) the more efficient the transfer of energy. The clothyard arrow has about three times the draw distance to propel it than the foot-long bolt, and hence three times the efficiency.
In the above example, I suspect that if you used a heavier bolt, the crossbow would become much more efficient. The efficiency isn't really down to the length of the draw; it's down to what proportion of the energy is moving the projectile and what proportion is moving the arms of the bow. A 740 lb pull suggests a very chunky armature, which has to move its tips at half the speed of the bolt. So all that material is going 70fps.
This is one place where the materials / metallurgy of the crossbow will make a huge difference. The lighter, stronger and springier the arms, the more efficient the bow will be. Which is a case for Mighty crossbows being available for increased cost, weight aside.
Actually, it's a bit of an omission that mighty bows don't weigh more than normal ones; they must be thicker and heavier. Though compared to the clumsy bulk of the thing, the weight is perhaps unimportant.
Here's a feat I magically made up for ya'. The wording is still clunky.
Overdraw [COMBAT]
Prerequisites: Str 13, base attack bonus +1.
Benefit: By drawing further than the weapon is intended to go, you can add your strength modifier to the damage of a ranged attack made with a bow or crossbow, but with a -1 penalty to the attack. Rolling a natural 1 causes the bow or crossbow to gain the broken condition. Activating this feat requires using a move or full-round action for a crossbow, or a swift action for a bow.
Normal: You do not add your strength modifier to damage rolls with projectile weapons.
What you are looking for is an Arbalest. It does not add a STR bonus but does more damage and requires a 13 STR to load.
http://tinyurl.com/8d2kd85
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In the above example, I suspect that if you used a heavier bolt, the crossbow would become much more efficient. The efficiency isn't really down to the length of the draw; it's down to what proportion of the energy is moving the projectile and what proportion is moving the arms of the bow. A 740 lb pull suggests a very chunky armature, which has to move its tips at half the speed of the bolt. So all that material is going 70fps.
I disagree that the draw length is immaterial, because in physics terms you are delivering an impulse to the projectile. Impulse is delivered as force multiplied by time, not just force. The greater length of the draw means a longer time period. The lighter bolt will gain greater acceleration, which actually reduces the amount of time it is in contact with the string to receive power. If we assume it is in contact for half the time the arrow would be, for 1/3 of the distance, then the proportion of force delivered by the crossbow impulse will be 1/6 of what it would be for the arrow. Hence the 740lb draw of the crossbow becomes less than 124lbs in a 'real' comparison.
You are correct in that a heavier bolt will more efficient, however most of the mass of the bolt is in the head, and hence a heavier bolt will be more point-heavy and less aerodynamic, making it less accurate and have less range.
By all means, a heavier bolt could be viable - give it a damage bonus and an accuracy penalty, and half the range increment, and it's a killer. Indeed, crossbows were considered to be more accurate and lethal at close range, especially in amateur hands. If you wanted to kill at a distance, though, the longbow was king.
As an aside, Chinese crossbows were more effective because the Chinese perfected a trigger mechanism that allowed for a longer draw. However, these crossbows also had lighter draw weights, comparable to a bow rather than a medieval crossbow.
This is one place where the materials / metallurgy of the crossbow will make a huge difference. The lighter, stronger and springier the arms, the more efficient the bow will be. Which is a case for Mighty crossbows being available for increased cost, weight aside.
Agreed, and this is why modern crossbows are so much better than the medieval ones. The same can be said of modern bows, but since the law was repealed that required all males over the age of twelve to practice archery on the village green every Sunday there are no more people with the kind of muscle power comparable to that which medieval archers could ply. Hence drawing a real comparison between a longbowman and a crossbowman using modern materials is not viable save in theory.
Actually, it's a bit of an omission that mighty bows don't weigh more than normal ones; they must be thicker and heavier. Though compared to the clumsy bulk of the thing, the weight is perhaps unimportant.
True, have you seen the girth of the longbows from the medieval period? The difference between the composite bow and the longbow is that the longbow was all of a piece of wood, while the composite bow was made of wood, sinew and horn laminated together. It was also recurved for added power.