Crossbows vs. Longbows

[Fantomen]

I can verify that material and construction matters a lot. A flatbow, along with many other types, depends on the dynamic between the elastic surface wood(front of bow) of the tree and the hard corewood(backside of bow). The bigger the difference between core and surface the more efficient the bow will be relative to its draw weight. That is why different kinds of tree are more or less suitable.

The bow is consequently built by first splitting the tree in four quarters and then you pick the one without branches or other defects. You work out the bow from the "back" leaving the elastic surface intact and carve away enough of the hard wood to get your preferred draw weight.

Laminated bows follow the same principle, but are built with materials of varying hardness/elasticity instead which are then glued or wired together.

You can elevate the effectiveness of your wooden bow by applying a string of elastic material along the front and some hard material on the back. The vikings of Iceland used sinews and bone for example.

[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.

[chrispedersen]

Originally Posted by Maerlande

Dhaeron,

Welcome to the conversation. The primary point of bumping this thread is to remind Lingchih that he can never live down starting it.

But I have some rebuttals for you

I don't agree with this. I shoot archery maybe 10 times a year. And I shoot a 55 lb recurve bow. It was my first bow and I've had it for 25 years. I can't shoot all day, but I can easily shoot 40 arrows which is a pretty big bunch for any quiver. And I'm a desk jockey. So it's not like I work out regularly or do anything in particular to pump my strength. I am strong and big, but it's all just native ability.

If I was a peasant forking hay onto wagons I would easily be able to shoot a 100 lb bow. Forking hay onto wagons is an over the head move. Also using a scythe builds massive arm and shoulder muscles. I used to be able to place a 60 lb hay bale onto a wagon above my head using a fork. A fork of hay is not light. Do that all day and you'd find drawing a big bow easy.

We all tend to forget that medieval peasants worked all day at hard physical labour. It's unrealistic to compare them to modern couch potatoes.

The mongols shot 150lb composite bows from horseback.

This is incorrect. The physics of the problem are reasonably simple. It's conservation of energy. The archer puts the integral of force times draw into the bow as energy (or the work done by the archer). If we want a simple calculation, using 100 lbs force for 28 inches (assuming a straight line force curve from zero to 100 lb on a longbow) the energy put into the missile is exactly 159 J or 0.15 BTU. I have converted to SI for the calculations.

Assuming 100% efficiency the missile when fired will have exactly 159 J of energy since energy is conserved. This does not account for energy lost as heat and sound in the string and bow but will be good enough for our calculation. The kinetic energy of the missile is then mass time velocity squared. I found some modern replica arrow heads online that mass about 2 oz each. Add that to the mass of a 1/4" diameter by 36" long cedar arrow (the material I use) we get a total mass of 0.54 oz. The velocity of the arrow is then 333 ft per second.

Let's now try this with a simple goat's foot type crossbow with perhaps a draw of 200 lbs. The draw length of a goat's foot crossbow is about 12 inches. Assuming the same type of force curve we get a input energy of. If the bolt is made of cedar as well with a similar point, it's mass is now 0.27 oz. The bolt velocity is 436 feet per second.

So basically, the velocity of a missile fired from any type of bow is a function of the input energy and mass of the missile. There is no direct comparison possible between crossbows and bows. It's all variable.

This is also why the material of the bow is irrelevant to the discussion. For what it matters, the bow could be made of adamantium or kevlar. The input energy doesn't change since it comes from the human archer. And a human archer has a very strict limit on the energy available. Crossbows can put potentially more energy into the missile because they over come the limits of human power by mechanical leverage. The trade off is loading time.

Of course, someone will argue that the bolt could be made of steel. And it could but then carrying them would be difficult. If we change the bolt shaft to steel the bolts weigh 4 oz each and then 40 bolts would weigh 10 lbs. Pretty heavy but I suppose not impossible. The worst problem is that the velocity drops to 113 feet per second which is so slow that you could simply step out of the way and the ballistics are such that range would deteriorate.

Summary

It is a standard rule of thermodynamic analysis in energy conversion that finding the output from a certain input you do not require to know anything about the internal workings of the energy conversion machine. A simple efficiency rating (to account for losses) is adequate. In the case of bows, they convert human force and distance into kinetic energy. On this basis, the materials, shape, construction, etc are irrelevant. All that matters is the input energy and the efficiency of conversion.

As far as output energy, a crossbow simply does one thing. It increases the energy input by allowing more time for the human to apply the energy. Whether it's simply a goat's foot, windlass or lever action, the job of a crossbow is to mechanically leverage the force of a human. And it takes more time to do so.

I can keep going, but let's see if anyone has the knowledge to try to refute my facts. So far, 80% of this discussion is simply annecdotes and opinion. It's very shy on fact.

For anyone interested, I can share my calculation pages by irc or here.

I'll take a pound of actual results over a two pages of reasoned theory, any day.
(Not to comment on the discourse.. it was pretty good so far as that went).


But the facts are that in medieval ages, in england for example, yeoman were required to spend a day a week in archery training. EVERY yeoman, unless they arranged exceptions. And this was to increase accuracy, and stamina.

Up until the 14th century, and probably well into the 14th century velocities and penetration were almost identical. This wasn't theoretical - the british did penetration tests, both vs oak planks and plate mail.

British quartermaster records go back that far - sadly, I don't recall the name.

Finally, english steel was notoriously poor quality, due to the poor quality ores. HIgh quality steel was done on the north coast of spain (bilbao area), toledo, and damascus.

[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.

[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.