Tiller/strain/etc

[DC]

I'm trying to wrap my head around this so if you can point out errors in my thinking, please do. To my way of thinking the only way to get a bow to shoot faster is to strain it more. The idea being to tiller so that the strain is as evenly distributed as possible. I've read that narrower and thicker has less mass and so is faster than wider and thinner. I've also read that wider and thinner can bend further without over straining the wood. This lets you achieve the same DL with a shorter bow. Shorter bow has lighter limbs and faster return. Is there a point where thin, wide and short trumps thick, narrow and long? I have noticed that horn bows are short but they have a materials advantage.

[Pat B]

DC, narrow/thick does decrease physical weight without reducing strength and for the outer limb that is a good thing but, depending on the wood you use it is not necessarily the best for the entire limb. Straining the limbs is how you get more out of them but you first want to educate them to bend but also to return to their original shape. Straining while tillering isn't a good idea. You want to finesse the limbs to bend evenly and together without over stressing the limbs as you tiller the bow.

[mmattockx]

I've read that narrower and thicker has less mass and so is faster than wider and thinner. I've also read that wider and thinner can bend further without over straining the wood.

I can't comment on the speed thing, being a complete newb to bow making, but I am also an engineer and can talk about the stresses/strain/etc. that drawing a bow causes in the limbs.

What is being balanced with the limb dimensions is stiffness versus strength. They are not the same thing at all. Think of a yardstick. Place it on edge and try to bend it and you will find it is very stiff. If you lay it flat and bend it you will see that it is much more flexible.

If we consider a piece of wood that is 1" wide by 0.25" thick and calculate its stiffness and strength we find that it is 16 times as stiff in bending on edge compared to flat, but only 4 times as strong in bending. Stiffness equates to how far it will bend under a given load while strength equates to how much load it can carry before it fails.

Regarding bows, we are trying to size the limbs such that bending stresses are equal along the limb length (I think, if I'm wrong a correction would be appreciated) and to maximize the stresses within the material limits to get the most energy possible into the arrow. This would be why you can make a narrow, thick limb weigh less and still carry the loads, because that cross section is stronger in bending than a wider, thinner section.


Mark

[RyanY]

I've read that narrower and thicker has less mass and so is faster than wider and thinner. I've also read that wider and thinner can bend further without over straining the wood. This lets you achieve the same DL with a shorter bow. Shorter bow has lighter limbs and faster return.

First off, I've underlined what looks like a few contradictory ideas.

I think the overall question is more complicated than just looking at strain itself. Hysteresis should be taken into account as well and that may have more of an impact on performance depending on cross section of the bow limbs. For example: if a wider limb with less strain also has less hysteresis. Then you can also have both types of cross section in the same bow limb such as on a mollegabet style bow.

[DC]

I've read that narrower and thicker has less mass and so is faster than wider and thinner. I've also read that wider and thinner can bend further without over straining the wood. This lets you achieve the same DL with a shorter bow. Shorter bow has lighter limbs and faster return.

First off, I've underlined what looks like a few contradictory ideas.

I think the overall question is more complicated than just looking at strain itself. Hysteresis should be taken into account as well and that may have more of an impact on performance depending on cross section of the bow limbs. For example: if a wider limb with less strain also has less hysteresis. Then you can also have both types of cross section in the same bow limb such as on a mollegabet style bow.

Just to clarify are you saying that "narrower and thicker has less mass" is contradictory within itself or that it contradicts something else that I wrote?

[bradsmith2010]

The wider thiner shorter limb,..might have more mass to make weight,,.. Not taking set....but a bit slower,..

[mmattockx]

I think the overall question is more complicated than just looking at strain itself. Hysteresis should be taken into account as well and that may have more of an impact on performance depending on cross section of the bow limbs. For example: if a wider limb with less strain also has less hysteresis.

That is an interesting question to consider. I'm not sure they would be much different between the two limb sections at the same stress/strain levels, but small differences can make a significant difference in the end for things that happen at high rates of speed such as launching an arrow.

Then you can also have both types of cross section in the same bow limb such as on a mollegabet style bow.

Yeah, but that is done to have a stiff, non-active limb tip and force all the bending into one defined portion of the limb rather than as a performance optimization of the entire limb. Or have I misunderstood that?


Mark

[Badger]

   Shorter bows tend to have faster dry fire speeds but longer bows tend to be faster with normal weight arrows. Between about 64" and 68" seems to be the fastest I have seen. I built a very short lived bow that shot 215 fps with 10 grains it went down in speed with every shot but the first 3 shots were all over 200 fps. The osage bow was about 3 1/2" wide, I don't believe narrower is faster. What ever the minimum width is that will give you no set is the fastest.

[RyanY]

Might be my misunderstanding. You said shorter limbs return faster but also that they need to be wider to bend further, wider being more mass and possibly slower than narrow deep limbs. This is what sounded contradictory.

[DC]

Might be my misunderstanding. You said shorter limbs return faster but also that they need to be wider to bend further, wider being more mass and possibly slower than narrow deep limbs. This is what sounded contradictory.

Sorry, I've been thinking about this kind of thing for so long that I forget to mention the stuff that I take for granted. My thinking always revolves around 40#DW, 28"DL. 10GPP arrows(so 400gr) and minimal set. There's probably others. So when I say thinner limbs I'm also thinking wider in order to maintain the 40#, shorter limbs means they have to bend more to maintain 28"DL.

   Shorter bows tend to have faster dry fire speeds but longer bows tend to be faster with normal weight arrows. Between about 64" and 68" seems to be the fastest I have seen. I built a very short lived bow that shot 215 fps with 10 grains it went down in speed with every shot but the first 3 shots were all over 200 fps. The osage bow was about 3 1/2" wide, I don't believe narrower is faster. What ever the minimum width is that will give you no set is the fastest.

I'm also finding that 66-68 seems best but I wonder a bit about that because the recurves use up 4-6". I have always made these booyews about 1 1/4" wide with a constant taper but I noticed that I was getting a little set on the inner third so I made the next two 1 3/8 and 1 3/4 but still with the constant taper. The last one took minimal set and it was mid limb so I'm thinking about a 1 3/4 tapering to 1 1/4(where it was 1) and then down to 3/8 tip.

[Badger]

    DC, you might be interested in this. Several years ago I figured out a test that would isolate the amount of hysterisis in a bow. And then I figured out how to identify how much of that comes from set. The test is time consuming and a pain in the ass but I did learn from it. Bottom line was a bow that has absolute zero set has about as much hysterisis as a fiberglass bow maybe less that 3%. As even minor set starts to take place that number rises fairly rapidly. Thats really all we need to know.

[Yellowstave]

I would love to hear how you did this badger. I dig time consuming pain in the ass things. Thats why were all bowyers right?

[bradsmith2010]

DC,,.sounds like a good plan on your taper

[Badger]

I would love to hear how you did this badger. I dig time consuming pain in the ass things. Thats why were all bowyers right?

   I think I posted a write up on it in the flight shooting board. I don't even remember how I did it now. It was one of those things that I would never need to do again. It just verified that set contains hysteresis.

[Badger]

I would love to hear how you did this badger. I dig time consuming pain in the ass things. Thats why were all bowyers right?

   Its coming back now. You plot a very accurate force draw curve and shoot the bow through a chrono. You determine the virtual mass in the limbs. Once you have the virtual mass you start shooting various weight arrows. On a bow with little or no hysteresis the virtual mass stays relatively stable while a bow with hysteresis will show more virtual mass as the arrows get lighter because hysteresis is time sensitive.