Customising bows

[malloyd]

Originally Posted by DanHoward

Yes crossbows were sometimes made of steel. So were regular bows (especially in India). No it wouldn't increase weight, it would actually decrease weight. Not sure how to handle it. Perhaps treat it like fine quality material with 10% weight reduction. They don't seem to perform as well as composite bows.

In fact, I think the basic physics of the situation dictate that a steel bow cannot be as effective as a wooden one of the same weight, let alone lighter. A bow is an energy storage device, and the elastic energy storage capacity of even spring steel is quite poor compared to wood. A steel bow of incredible power might possibly be more compact than a wood bow of the same power - which isn't necessarily a negligible issue, after all if the required draw length of the wooden bow is considerably longer than a human arm, it's a siege engine even if the springy bow part itself is quite light - but it will be heavier.

One thing I think is somewhat revealing is to go the other direction and consider the hunting slingshot. This is effectively a bow made of rubber (a somewhat better energy store than wood, but probably not by as much as the ratio of wood to steel). The actual bow equivalent part is the rubber tubing, the frame is equivalent to the stock of a crossbow, or the pieces of that siege engine holding the bow up, and you can get a fairly respectable weapon out of a few ounces of tubing. You can also quite reasonably say that some of the weight of a bow staff isn't storing significant strain energy and is also functioning like that stock, which means the steel bow isn't necessarily heavier by the same ratio as the elastic energy storage limit of wood to steel, and I think this may actually be signficant for steel crossbows vs wood, the substantially thinner steel bow may have more of its total volume close to the outer curve where the strain is maximized after all, but I can't see wooden bows carrying so much useless extra weight that you are going to overcome the materials difference - most wooden bows are flattened a good deal (oddly English ones seem to be more rounded, and presumably are carrying a lot of useless extra weight on the belly).

[nik1979]

Thanks Dan, this will fix my own bow tables.

[DanHoward]

I've just edited the original post (#2) and eliminated Range changes. All Ranges are now x15/x20. Try some reality checking. How much does a heavy longbow weigh? Is 3 lbs too light? A ST15 bow now has a range of 225/300. This seems more reasonable.

[whswhs]

I think I've figured out why the composite bow is as effective as it is. The energy is stored in strain. Well, it has horn on the inside, which is strong in compression, and can take a 4% strain; and it has sinew on the outside, which is strong in tension, and can take an 8% strain. And when the bow is bent, the inside gets shorter and the outside gets longer. But the wood, in between the two, approximates to zero length change! Its less ability to withstand strain doesn't matter, because it's not the part that's undergoing strain.

So if we figure that the bow overall can take a 4% strain, then 4 times 90 is 360 and 4 times 70 is 280; that averages to 320. This is better than 210 for spring steel and way better than 108 for yew.

(The point occurred to me that we're comparing part of the mass of the composite bow, the inner and outer strips, with all of the mass of the steel or yew bow. But that's not really true. Because just as the middle strip of the composite bow is not changing length, the middle strip of the steel or yew bow is not changing length, and thus not storing energy. The energy is stored in the same part of the material in all three bows.)

We have roughly an energy ratio of 1:2:3 for yew, steel, and composite. Since arrow velocity is proportional to the square root of energy, that implies a velocity ratio of 1:1.4:1.75. The range will vary with the energy. GURPS assumes that damage varies with square root of energy.

On the other hand, the composite bow is going to be lighter, and the steel bow heavier, for the same volume: their respective densities are 1/3, 1/2, and 8 times that of water. And aside from affecting the burden of carrying the thing around, this affects efficiency of transfer of energy to the arrow. If I'm not mistaken, the heavier bow will have less recoil and thus a smaller share of the total kinetic energy: MV = (km)(v/k) = mv, but 0.5MV^2 = 0.5(km)(v/k)^2 = 0.5kmv^2/k^2 = (0.5mv^2)/k, so if the bow weighs k times as much it gets 1/(k+1) of the energy, and the arrow gets k/(k+1). So the composite bow will transfer less of its energy to the arrow for the same volume.

On the third hand, if we're doing energy storage by bows of the same mass, the whole calculation changes. My brain hurts.

Bill Stoddard

[whswhs]

Originally Posted by DanHoward

I've just edited the original post (#2) and eliminated Range changes. All Ranges are now x15/x20. Try some reality checking. How much does a heavy longbow weigh? Is 3 lbs too light? A ST15 bow now has a range of 225/300. This seems more reasonable.

I seriously think that's a mistake. A fully drawn longbow is going to have a greater draw length than a fully drawn short bow. If draw weight and thus ST is the same, it ought to have greater energy and thus greater range.

Draw weight will be a function of BL, and thus of ST^2. Range will be a function of BL times draw length. So if you want to figure range, it ought to be a constant times BL. So you might take your bow as having a range of BL x5/x7; that would give a ST 15 bow, with BL 45, ranges of 225/315. A ST 10 bow, with BL 20, would have ranges of 100/140.

You could and probably should use smaller multipliers for a short bow. Say you took x3.5/x5. Then ST 15 would give ranges of 157/225; ST 10 would give 70/100. And a regular bow, in between, might give x4/x6 for 180/270 and 80/120.

The material the bow is made of would add a further set of modifiers.

Bill Stoddard

[DanHoward]

Originally Posted by whswhs

I think I've figured out why the composite bow is as effective as it is. The energy is stored in strain. Well, it has horn on the inside, which is strong in compression, and can take a 4% strain; and it has sinew on the outside, which is strong in tension, and can take an 8% strain. And when the bow is bent, the inside gets shorter and the outside gets longer. But the wood, in between the two, approximates to zero length change! Its less ability to withstand strain doesn't matter, because it's not the part that's undergoing strain.

Which might explain why some composite bows have no wooden core. They are made of horn and sinew only.

So if we figure that the bow overall can take a 4% strain, then 4 times 90 is 360 and 4 times 70 is 280; that averages to 320. This is better than 210 for spring steel and way better than 108 for yew.

But yew is so good for bows because the sapwood and heartwood have different mechanical properties. The heartwood is good in compression while the sapwood is good in tension. It won't produce a bow as good as a composite bow but it is better than any other type of wood. I think 108 is undervaluing the effectiveness of yew.

[DanHoward]

Originally Posted by whswhs

I seriously think that's a mistake. A fully drawn longbow is going to have a greater draw length than a fully drawn short bow. If draw weight and thus ST is the same, it ought to have greater energy and thus greater range.

true

Draw weight will be a function of BL, and thus of ST^2. Range will be a function of BL times draw length. So if you want to figure range, it ought to be a constant times BL. So you might take your bow as having a range of BL x5/x7; that would give a ST 15 bow, with BL 45, ranges of 225/315. A ST 10 bow, with BL 20, would have ranges of 100/140.

You could and probably should use smaller multipliers for a short bow. Say you took x3.5/x5. Then ST 15 would give ranges of 157/225; ST 10 would give 70/100. And a regular bow, in between, might give x4/x6 for 180/270 and 80/120.

OK. [trying to keep BL out of the rules to make things simpler]. Suppose the initial basic bow has a range of 8x/12x. For every +1 ft the range increases by +1. For every decrease of -1 ft the range decreases by -1. So the ST10 longbow has a range of 90/130 and the ST10 shortbow has a range of 60/100.

The material the bow is made of would add a further set of modifiers.

At the moment the material affects the ST of the bow. Will it affect Range enough to add an additional modifier or can it be subsumed into the increased ST?

[whswhs]

Originally Posted by DanHoward

At the moment the material affects the ST of the bow. Will it affect Range enough to add an additional modifier or can it be subsumed into the increased ST?

I don't know. Tell me the stave lengths for a short bow, a long bow, and a middling bow, and I'll see if I can come up with estimates of stored energy.

Bill

[Polydamas]

Originally Posted by DanHoward

I've just edited the original post (#2) and eliminated Range changes. All Ranges are now x15/x20. Try some reality checking. How much does a heavy longbow weigh? Is 3 lbs too light? A ST15 bow now has a range of 225/300. This seems more reasonable.

Yes, that was what I was thinking of. For an added complication, different arrow types could have different range and damage. I think you suggested it and I gave some figures here.

Originally Posted by whswhs

I seriously think that's a mistake. A fully drawn longbow is going to have a greater draw length than a fully drawn short bow. If draw weight and thus ST is the same, it ought to have greater energy and thus greater range.

Draw length is actually a function of bow length and material. The force required to draw a bow varies with the distance of the current draw; the area under this curve is equal to the energy used to draw the bow. Usually, the further you have drawn the bow already, the more extra force needs to be added to draw it another cm.

Draw length is limited by that force-draw curve (at a certain point, each cm of extra draw gets very hard), and the danger of snapping the bow. You can get a similar draw with a 6' selfbow and a 3-4' composite bow because the composite bow is more flexible. Right now, you can get a ST 11, min ST 10 longbow 6' long, or a ST 8, min ST 10 shortbow 3' long, and that makes the longer bow more powerful for the same draw weight (Min ST) which is correct.

I think the use of steel crossbows has to do with self and composite bows getting inefficient as they get too thick. This may counter out the normal advantages which wood or composite construction have.

[DanHoward]

Originally Posted by Polydamas

Draw length is actually a function of bow length and material. The force required to draw a bow varies with the distance of the current draw; the area under this curve is equal to the energy used to draw the bow. Usually, the further you have drawn the bow already, the more extra force needs to be added to draw it another cm.

Draw length is limited by that force-draw curve (at a certain point, each cm of extra draw gets very hard), and the danger of snapping the bow. You can get a similar draw with a 6' selfbow and a 3-4' composite bow because the composite bow is more flexible. Right now, you can get a ST 11, min ST 10 longbow 6' long, or a ST 8, min ST 10 shortbow 3' long, and that makes the longer bow more powerful for the same draw weight (Min ST) which is correct.

So does this mean that there is no need to have different ranges for different length bows? If so then is 15x/20x reasonable?

I think the use of steel crossbows has to do with self and composite bows getting inefficient as they get too thick. This may counter out the normal advantages which wood or composite construction have.

So what sort of modifier do we use for ST10-15 steel bows?

I forgot to account for recurving. Would that reduce MinST by -1? Why weren't English longbows recurved?