Crossbows vs. Longbows

[thejeff]

Or in other words:

Assuming 100% efficiency

You can't do this. It's a false assumption and that's where all the problems come from.

As the old physics joke goes: "First, assume a spherical cow..."

[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.

[Squirrelloid]

It should probably be noted that longbows tend to be fired indirectly, that is, with a high arc, and that the force behind a strike comes from gravity. Now, while the height an archer can put an arrow at is dictated by the energy released firing the bow, he can cheat additional striking power by occupying higher ground (and thus causing the arrow to fall farther than he sent it up).

[Knai]

You can do that with crossbows as well, but really, eventually the slower loading time just makes it pointless, though a lower, slighter arc is often pretty good just because of some angles you can get better with it. That said, slings get even nastier at higher angles. Comparable firing rates to a bow, but sling bullets are pretty heavy, and rather difficult to remove from people once they get hit by them.

The issue with a bow is that it is ultimately limited by how hard you can pull. Which can get ridiculous, but a crossbow can always go above that. Again I draw an analogy to a sling, what matters there is how fast you can get it, and there are ways to change that (sling length, wind resistance, etc.).

[Wrana]

Originally Posted by Knai

You can do that with crossbows as well, but really, eventually the slower loading time just makes it pointless, ...

This would have an additional problem as crossbowmen weren't usually trained in this due to a more flat trajectory common for crossbows and the possibility to aim along its "barrel" which made such training unnecessary.

[Maerlande]

Knai,

The issue with a bow is that it is ultimately limited by how hard you can pull.

If you read the previous post in this thread I suspect you will find I stated exactly this a dozen times. No matter how many times I say it, there appears to be folks who don't comprehend. And as I have said previously, a crossbow allows higher pull by using more time to do it.

Comparable firing rates to a bow, but sling bullets are pretty heavy, and rather difficult to remove from people once they get hit by them.

I'm curious. What makes you think sling bullets are heavy? Let's take the example of a one inch diameter rock. Assuming it is made of basalt it weighs 0.87 oz. As previously stated the mass of an arrow is about 0.54 oz. This is not exactly a huge increase. Can you back up your statement of generalities with some calculations or facts? So far it appears to be base generalization with no substance. I'm also curious to learn how a rock is hard to remove from a person? Perhaps it penetrates the stomach cavity and is therefore a challenge to extract?

Squirrelloid:

It should probably be noted that longbows tend to be fired indirectly, that is, with a high arc, and that the force behind a strike comes from gravity.

Quite a simplification. But I haven't the time tonight to analyze. I will get back to you.

[Knai]

Originally Posted by Maerlande

I'm curious. What makes you think sling bullets are heavy? Let's take the example of a one inch diameter rock. Assuming it is made of basalt it weighs 0.87 oz. As previously stated the mass of an arrow is about 0.54 oz. This is not exactly a huge increase. Can you back up your statement of generalities with some calculations or facts? So far it appears to be base generalization with no substance. I'm also curious to learn how a rock is hard to remove from a person? Perhaps it penetrates the stomach cavity and is therefore a challenge to extract?

Typical sling bullets were made of lead for one thing, or clay way back when. Incidentally the density of basalt is about 3 g/cm^3, compared to 11.54 for lead. That works out to 3.23 ounces for a 1 inch sphere, which is much higher than the .54 for an arrow. Rocks are really not high priority ammunition. Now, 2 1 inch long .75 inch diameter parabolas attached together (foot ball shaped ammunition, in common use.) is .471 inches cubed, compared to .523 for the sphere, and weighs only 2.9 ounces. Most sling bullets are in the 2-3 ounce range, though there are outliers. The Balearic slingers are known for using 5 oz bullets, but that is exceptionally heavy, though lighter than some of the Incan ammunition, which were typically very heavy, large rocks, with limited range. Note that I'll try to find the data I was looking at earlier for some of the specifics. Among them are Roman sling bullets typically weighed between 30 g and 90 g. 28g is about 1 oz (28.4 if I remember correctly), so 1-3 for Romans, which is a big difference. The sling is a very dangerous weapon, just difficult to aim for the obvious reason that it is an aim while firing weapon instead of an aim then fire weapon, and the projectile is a decent distance from the hand.

There are a few exceptions to lead bullets other than the Incans. Another is the Apache, who used obsidian in some cases, despite low weight. However, it was used differently, obsidian is rather brittle, and if an obsidian sling bullet shatters near you, it is going to cause some injury, not to mention being bad for morale. Though heavy armor helps hugely at this point.

As for removal difficulty, there are two main factors. The first is the difficulty inherent in removing an object that has fully penetrated. All of the sling bullet is inside the struck target, whereas an arrow is only partially inside someone shot. Furthermore, sling bullets were round, egg shaped, or shaped roughly like an American foot ball. If you can't get around to the back of objects shaped like any of these, you can't get a good grip on them easily, which means either stuffing your hand in an injury, pushing tissue out of the way, and pulling it out (which will lead to infection), or specialized tools (which probably still will lead to infection in earlier eras, but at least won't cause further immediate damage.) The Romans actually eventually developed some specialized prongs, which could still prove problematic. Note that an arrow or crossbow bolt, as a cylindrical pointed object, is much easier to remove, though it obviously has to be done carefully.

[Rookierookie]

I was under the impression that arrowheads are removed by digging it and any flesh attached to it out with a knife.

[Illuminated One]

Originally Posted by Maerlande

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.

Ignoring all "complicated" stuff like friction or speed-dependent forces it would still be damn hard to model, and flexible objects can only be really analysed via computerprograms afaik. However there are two simple points to add:
The energy put into the bow ( - losses) doesn't equal the energy of the arrow but the energy of the arrow and all the moving bowparts at the moment of launch. I can't calculate how a bow would actually behave but for a simple balista with rigid arms and torsion springs in the middle this should come to
E(bow) / E(arrow) = mass(bow) / 16 * mass(arrow)
With E(arrow) = (1/2) * mass(arrow) * speed²(arrow)
So speed²(arrow) = 2 * E(input) / (mass(bow)/8 + mass(arrow))

So if the bow weights 8 times as much as the arrow the catapult has only an efficiency of 50% (and that's not even counting entropy) a catapult which weights 24 times as much only 25%.
(While every real bowshape should be more energy efficient this still applies with different factors)

Now, so making the bow heavier (or changing its shape) makes it less efficient, why would we do so anyway? For one thing because we want additional draw weight.

And that makes two factors that limit the crossbows we can build. It's undoubtedly true that the crossbowman can put a lot more energy into the crossbow, but the question is could the medieval people build crossbows that could handle that extra energy while putting enough of it into the bolt to make a difference.

[Maerlande]

But Chris,

You aren't being suckered by the rhetoric are you? You understand my point that whatever the material the energy input is a human being. And I totally agree with you on the training of Yeomen. It's pretty famous. Which goes back to the original debate. Longbows were getting the shaft as far as I'm concerned. They are incredible weapons but do need training.

But of course if you want to submit fact you will be required to find those references I promise to read them.

And really, you can't say this

But the facts are that in medieval ages, in england for example, yeoman were required to spend a day a week in archery training.

without references. Because how do we know those are facts?

I'd love to see those penetration tests. I did some digging but best I could find were British naval round tests. Not irrelevant but the energies involved are orders of magnitude higher.