I've had this question open in a tab all week, but haven't had any time to actually write anything! Unfortunately, there's a lot to your question we can't answer. Archaeological evidence for crossbows in the twelfth century is very thin on the ground - really any time before the fifteenth century is pretty limited. That isn't to say we don't know quite a bit about crossbows in this time, but it does necessarily limit how technical we can get in our explanations.

First, let's talk about One-Foot, Two-Foot, and ad turnum crossbows. These terms are used to cover what was in practice quite a wide variety of crossbow terms, for example you might find a reference to a ballista de torno instead of ballista ad turnum, but the meaning was pretty much the same. These terms have long confused historians, and I don’t have time to get completely lost in the weeds about the many attempted explanations of what they meant. The important details here are that these terms were common in the twelfth and thirteenth centuries and that ballista ad turnum is generally accepted as meaning a windlass crossbow. One intriguing detail is that many references to these types of crossbows also include references to specific ammunition for them, i.e. 400 bolts for a ballista ad turnum. This has inspired speculation that specialist bolts were intended for use with these weapons. This is complicated partially by evidence for orders for just ‘bolts’ accompanying entries that included multiple types of crossbows. G.M. Wilson, former head curator of the Royal Armouries in Leeds and an eminent scholar on medieval weaponry, has proposed the very plausible explanation that while all three weapons could shoot a generic ‘munitions’ type bolt, in some cases specialist ammunition would be ordered for specific crossbows.

What would that specialist ammunition look like? The historian W.F. Paterson noted, and later evidence has supported this point, that a more powerful crossbow didn’t really shoot a given bolt any faster than a lighter crossbow. What made it more effective was that it could shoot a heavier bolt at that speed (or nearly that speed), and since impact is mass times velocity, increasing the mass would increase the impact. So, at its simplest the difference probably was that a bolt for a ballista ad turnum, which most historians accept were probably more powerful than say the one-foot crossbow, was probably heavier. Unfortunately, as I said at the start, we don’t really have any archaeological evidence to confirm this. There is better archaeological evidence in the Later Middle Ages, but even then, pairing surviving bolts with specific weapons is largely impossible so we can’t really say for certain that these bolts were for use with a light crossbow while those bolts were for use in a heavy windlass crossbow.

To give some indication of medieval crossbow bolt weight, some late medieval military bolts (13th – 15th centuries) currently in the Deutsches Historisches Museum weigh between 60 and 66 grams, while some early modern (15th – 16th centuries) military bolts weigh 84 grams. The heaviest bolt in the collection is an ornate early modern bolt that weighs 100 grams, the lightest bolts weigh 40 grams. It’s not exactly the most robust sample, but I think it’s a useful initial impression!

Windlass crossbows were used in both sieges and battles. As a few quick examples, we know that they were used at the Siege of Acre during the Third Crusade – which in addition to being a siege featured numerous skirmishes and even several all out battles between Saladin’s relief army and the fortified crusader camp that was besieging the city. There is also reason to believe that windlass crossbows were used at the Battle of Jaffa in 1192 – Richard I reportedly had his crossbowmen work in pairs with one person shooting and the other reloading, which would better fit a slower reloading weapon like a windlass crossbow. Windlasses were certainly used in battles in the Later Middle Ages, the Genoese at Crécy probably had them (certainly medieval images of them almost always depict them with windlasses). Some historians have argued that in late medieval warfare windlasses and cranequins had replaced earlier spanning devices. I’m less convinced, the available evidence shows that older spanning devices didn’t disappear and I’m inclined to think that things like belt hooks continued to exist alongside windlasses – to say nothing of the krihake which wasn’t even invented until the Later Middle Ages.

We don’t know as much as we’d like about how ammunition was managed in medieval warfare. Surviving medieval bolt quivers would have struggled to carry more than 6-12 bolts at a time, but more likely than not there would have been people whose job it was to bring new bolts from the supply lines back to the archers to ensure they had a steady supply of ammunition. In general, bolts and other ammunition was supplied by the commander in charge of the army – we have records of large purchases of bolts by kings and other rulers for their armies. Depending on the terms of their service a crossbowman may have been required to bring a certain number of bolts – possibly their initial quiver full for example – but they wouldn’t be required to show up with, like, a hundred bolts or anything on that scale. The evidence we have is rarely specific enough to determine what kinds of crossbows individual soldiers had so it’s not really possible to determine if archers with different types of crossbows had to bring different numbers of bolts – besides even if we could often these terms would be so hyper specific that it would probably reflect more on the status/relationship of the individual archer than any broad army-wide policy based on weapon type. To underline how tricky this can be for historians, there’s an excellent document from medieval Florence that outlines exactly the types of equipment each militia member had to bring with them to fight, including the specific fine you would pay for not having it. So, for example, if you were a man-at-arms and you didn’t have your shield you would pay x amount of money, plus another x amount if you didn’t have your helmet. However, under crossbowmen, it just says that they must bring all of the equipment necessary to perform their duties – no breakdown of what that was or even an indication that the document’s author knew!

For the crossbow bolt weights I used Sven Luken and Jens Sensfelder’s Die Armbrust: Shcrecken und Shonheit.

Guy Wilson’s article “What’s in a name? One foot and two foot crossbows” in ICOMAM 50 Papers on Arms and Military History 1957-2007 is the best breakdown of that whole issue.

Also, not to plug myself too hard, but I also wrote a whole book called The Medieval Crossbow: A Weapon Fit to Kill a King which is coming out with Pen and Sword books on the 30th of May. It doesn’t answer all of these questions directly, but it does include a lot more information about the development and use of crossbows.