[Maerlande]

Of course if you are saying when I have a bow made from material x that shoots an arrow weighting y with the speed z and another bow from material q that does exactly the same thing with the same arrow than yes, the material matters not (ignoring all other things that might be important for a soldier like weight or ruggedness), then yeah, but that's a truism.

You are correct. And that was what I was saying. But more important, the available energy is no more than can be put into the bow by an archer. The previous posters were confusing the issue with discussions of using modern materials vs. wood, sinew, horn and bone. Making a kevlar bow has no effect on the input energy. It might have some effect on the energy conversion efficiency. But tastles on the string to reduce noise generation do that as well and don't require modern materials.

This all started with, to paraphrase, crossbows are stronger than longbows. This is an irrelevant argument. Given enough time, a human being can load a 1000 lb draw crossbow if he wants to. And the material discussion keeps distracting for the key energy requirement. In no way can a human fired bow store more energy than the human can put into it.

You'll have a maximum velocity that you can archieve, as that's the maximum velocity with that the bow snaps back into shape.

Excellent point and one I did not address. Easiest way to model it mathematically is by an efficiency factor. I don't know the details sufficiently to make an analysis of this effect but I would be very interested if you can find some references or can supply some more information. Along with that same point there is a serious problem with the arrow flexing. It is my understanding that this is why modern hollow shaft metal and composite arrows are much more effective. They fly faster and straighter. But frankly, modern materials are not relevant to this discussion. We are talking about medieval bows and crossbows.

Another point I wish to address again is the fallacy that wood, bone, sinew, and horn are not good materials. They are brilliant materials and are still used in serious engineering work for the simple reason that they do certain jobs better than any modern materials. A wonderful example is the mosquito bombers made in England of plywood and glued with cassein. As an engineer I am intimately familiar with the tendency of engineers to limit themselves for manufactured materials. It's a terrible shame because many natural materials have superb properties nearly impossible to duplicate with man made materials.

Fantomen: I completely agree and I think you will note that I mention in passing composite bows used by Mongols. I am familiar with the use of high tensile strength elastic materials on the front of the bow and high compressive strengths on the backside.

But going back, this discussion has been about the relative penetration abilities of longbows vs. crossbows. I have previously provided references respecting the engineering properties of medieval materials and they compare quite favourably to modern materials. In general, the most important difference is in manufacturing cost. A steel bow can be built for a few dollars today. A hand made sinew, yew wood, and horn composite bow is extremely pricey. I can build a reasonably effective crossbow prod from a used car leaf spring in about 2 hours for $5 from the auto wrecker. It would take me days or weeks to build the same quality prod of sinew, wood, and horn. And that assumes I have the skill which I don't. But this is a modern view. In the medieval period, quality steel was hand made from wootz ingots folded numerous times to ensure the perfect carbon iron ratios, quenched, tempered and then ground. A bow could be built by a peasant artisan from materials scrounged from the yard.

TheJeff: Of course the efficiency of a bow or crossbow is not 100%. The point that I think you missed is that the resulting velocity of the missile when comparing a bow and crossbow is a function of the input energy and the mass of the missile. I can repeat the analysis at 50% efficiency or 80%. But the general implications are the same. Short draw requires more pull to get the same energy in the missile. Lighter missiles will go faster (and of course I accept that there are fixed velocity limits).

And for you three debaters and all the rest: I challenge you to put the same effort to do the calculations that I did.

I realize that I have written a wordy response. Let me summarize again.

1) The energy put into a bolt or arrow will never be more than the energy put into the bow by the human archer. And this is fixed by physical limitations of human beings.

2) A crossbow can store more energy because mechanical leverage allows the human to spend more time putting more total energy into it.

3) The trade off is speed of loading versus missile energy.

To get more energy into a missile you require a way to store energy in more compact forms. The most practical example of this is gunpowder.