Efficiency?

[Wooden Spring]

OK, if you've got two bows of equal draw weight, equal length, equal mass, and equal materials, which would be more efficient - that is, cast an arrow faster?

1) the bow that is wider and thinner
2) the bow that is narrower and thicker

(assume every other quality of the two bows are equal)

[Badger]

  The bow with the least hysterisis all other things being equal. The wider bow may have less hysterisi but not neccessarily. The norrower bow might be built well within it's ability to handle the bend and in this case the lower mass would win. I have examples of both and either can win.

[Slackbunny]

I think that the bow that is wider would be more efficient because it would be getting the maximum work out of all the fibres, with the least set.

Isn't that why we go wider on woods that are less than top notch, to get a more efficient and thus less stressfull design?


Edit: I'm not so sure all the variables you listed could be all made equal with two identical pieces of wood. When you remove 1mm thickness, you would need add 8mm in width to maintain the draw weight. But in doing so I think you would increase the mass, unless your length changed which you require to be fixed.

[son of massey]

Predicting cast is tough. If they also have the same set my gut would say that they are the same efficiency. If they do not that would be a good thing to look at.

There are diminishing returns to either model-if you imagine a hugely wide and thin limb there is a very well distributed amount of stress on the limb-but it is going to be large enough at some point that wind resistance comes into account. The limb is basically a sail. If you crunch the sides in so that the limb becomes narrower you get more stresses centered at the highest points along the back and the belly. If those stresses become more than the individual wood fibers can handle-and as you narrow the limb you are decreasing the number of fibers sharing the load-they will be crushed on the belly or break on the back resulting in either set or a broken bow.

Assuming the same mass with different dimensions does make it interesting, and I would think in that case you are either dealing with one bow that is too narrow and one that is less so, or one that is wide enough and one that is more than wide enough-unless you straddle the line just right such that one is just right and the other a little too narrow/wide.

So the most efficient limb would be wide enough to distribute stresses appropriately but not wider.

[Badger]

  Massey, you can't go entirely by set. Often times a strong tension wood will pull the bow back into shape better than a weak tension wood. For the most part early draw weight would be a good indicator of energy stored in the bow. Efficiency is more a product of mass and hysterisis when the design is the same.

[son of massey]

I agree that in general you cannot use set alone, but is that the case in the hypothetical 'identical materials' case? Here there is no difference to the tension/compression values between the two bows, and I would think that the bow with the less set ought to have a higher early draw weight. Is your impression that even in this case the two would not go hand in hand?

SOM

[Badger]

    For the most part I would agree with that. In the case of a bow that was not properly tillered it might not apply. I have seen and screwed bows up myself where they didn't take much set but were on the weak side at brace height because I had overstrained the limbs and they got way I call kind of a rubbery property where they were easy to flex back and forth a few inches if you pushed thm to the floor.

[son of massey]

Yes, tiller is a big part of it. I guess I was just holding variables like that constant.

And you were correct before, I wouldn't want to mislead anybody and should probably be a little clearer that set is not what defines efficiency. A very efficient and highly strained bow may take set but still impart a lot more of the stored energy to the arrow than an improperly tillered overbuilt bow with a spring for a string.

I just thought it may be interesting that in this case, assuming so much was exactly the same between the test cases, that it would actually be a good indicator-so it is not the thing that defines it but it can be an indicator.

SOM

[huisme]

Dare I open the mollegabet debate?

Light outer limbs and even tiller make for my fastest bows, and my molles have been just a step above my full working limbed bows.

I might have just been more careful with the mollegabets than with the flat/pyramid/character bows, so take it all with a grain of salt.

[diliviu]

But is it possible to have equal mass if you have egual draw weight, egual lenght, equal material (and equal tiller and same design and equal reflex/deflex), but one is thicker and the other wider and thinner? I thought in these conditions the narrower one is always lighter, it can't be equal mass. ? Assuming thicker will be lighter, up to a certain ratio [draw length/bow length] the ticker wins. Over that ratio (when bows, but especially thicker one are forced very close to the limit) wider might have a chance to win.

[Buckeye Guy]

Not that Marc
I wonder too
When done well there does seem to be difference and Black locust seems to be the best candidate for showing it off that I have seen !
Of coarse you folks know that is just an opinion from a worthless old nut with no way of measuring except a whole bunch of years of playing with bows ! 
Have fun
Guy