Working limb and bow length based on stiff tips, recurves and other features?

[gfugal]

I have been thinking lately about an equation for bow length that takes into consideration different design features such as stiff handle or bendy handle, or recurves. Depending on what you chose it woukd effect how long it needs to be, so a simple 2-something times the draw length doesn't address that. What I've come up with so far is 80% the draw length x2, plus handle and fade length, and plus the length of non working tips x2. For example, if you have a 28" draw you get (28×0.8x2) + 8 + (6×2) = 64.8" long. I wanted to basically figure out how much working limb length you actually need. Most bows of about 64-65 inches have significant non-working handles and stiff tips. If i could figure out the necessary working limb length then I could add or remove design features at will (like bendy handle, molly levers, large static hooks, ect.) and avoid the chance of over or under-stressing the design.

But then I was thinking of doing just this by trying to figure out how to incorporate recurves. It's been said that recurves shorten the working limb and thus put more strain on the bow. But if your supposed to tiller with stiff tips anyway, why would recurves smallar than the normal 4-6 inches of stiff tips make a difference on working limb length? Do you think smaller recurves increase the stiff limb length further than 6"?

[Badger]

   I don't think a formula for length can exist because the width and thickness of the bow will have a lot to do with how far it can bend. If you are primarily looking at string angles then I think your formula would work out pretty good. Working limb doesn't mean all that much because we gain a lot more draw from working limb near the fade than we do working limb mid  or outer limb. A smaller handle can add quite a bit more potential to draw length.

[simk]

if you want a formula you'd also had to consider wood-species and draw weight i think. i lately broke a nicely tillered rowan bow - i think it didn't broke if it was a little thinner and had a little less draw weight. it probably also didn' broke if it was of osage....cheers 

[gfugal]

I should have phrased my question better. While I am interested on creating a general formula to give me a starting point, I'm not attempting to create the end all be all formula. I just want something that's a little more helpful than 2 to 2.5 times the draw length. But that a side, my main question was on how much certain features, like recurve, actually add or subtract from the working limb, and less on creating a perfect formula. You guys are right, there is no perfect formula and there won't ever really be one (at least that's any use for me, it just gets too complex). I knew that adjusting variables like material and width can effect what length you need. However, what I hadn't thought about before was how the part of a limb closer to the fades have a greater impact on the draw length than the part of the limb further away from the fades, even if they are stressed the same. thanks for that insight badger.

What I'm still wondering is if you or anyone else thinks small recurves that don't extend past the normal 6" stiff tip (that are tillered the same as a straight limbed bow of equal material) would have less working limb, or be anymore stressed, than the straight limbed bow?

[PatM]

They have  essentially the same amount of working limb which is stressed more.

[gfugal]

They have  essentially the same amount of working limb which is stressed more.

Interesting! I thought something similar or thought maybe we extended the stiff section of the tip just a bit further. One of the two. I wonder why it would increase the stress? One thing you do by recurving is decreasing the mass moment of inertia, or in other words shortening the limb length. Similarly, If you pike the same amount off each limb of a bow you increase the poundage. But in that case if the working limbs aren't decreased, an increase of poundage would only mean you would reach your target draw weight sooner, theoretically stressing the limbs less not more. But recurves aren't as simple as piking the bows length, and probably has other factors in play. It would be curious to see if someone had a straight limbed bow with 6"stiff tips, then chose to put 3" recurves on without retillering, and see what it did to draw weight and how far the working limbs bend.