# Thickness, tiller, and elongation...and how they relate

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jeb532
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After posting the two graphs for elongation (strain), I had one of those DUH! moments. Tell me if you agree with this....

To strain the wood equally along the limb, that is to say\...to stretch or compress the wood equally in all sections of the bow limb...a circular tiller is correct for a ONLY for constant thickness. If the limb thickness reduces from fade to tip, to maintain a constant strain, the bend radius must get tighter as you approach the tip...which would give you a whip tiller appearance. And if the limb gets thicker from fade to tip, then you would get an elliptical tiller shape.

Look at the graph again...elongation (strain) depends only on thickness and bend radius... to maintain a constant strain...bend radius and thickness must match.

So, following this observance...you should determine your bow's tiller shape by limb thickness only...and then, you should adjust the limb's width to make the stress equal for all parts of the limb...
2600 years ago Lao Tzu observed that in any generation..."only one out of ten will ever become self-aware" (i.e. know why they do what they do). The rest will be eternally driven by their emotions and/or confusion. Confucious thought Lao Tzu was a pessimist. Confucious stated that the odds for enlightenment were much better...at one out of eight!

Either way, that pretty much explains human history...

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Joined: June 3rd, 2005, 1:13 am
Jeb, you are absolutely correct! I have been preaching that for years. The thickness determines how far something can bend and the width determines how far it will bend. The string angles determine the proper lay out of the bow. What we often call beautiful tillers are often all wrong. Because of the geometry of a bow perfect adherness to these principles are not always possible but I do believe we should keep them in mind as close as possible. Steve

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Pathfinder78
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Joined: January 29th, 2008, 6:29 am
Ok guys, if I'm reading you correctly..
That means that for example the limbs of pyramid bows should be tillered circular? Because they are about the same thickness along the limbs?
How does this chart relate to "tiller to bend slightly at the fades, mostly midlimbs, and tips slightly stiff? Does it mean that the tips should be slightly thicker than midlimbs?
Any more graphic examples?
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Path, if you build a pyramid bow it should have a circular tiller, if you build a bow with paralell limbs and tapered thickness it should be elyptical tillered. Same with an elb, tapered withness and thickness suggests proper tiller would be increased bend from handle toward tips. performance excels and the amount of set a bow takes is greatly reduced when you follow these guidelines. This is one of the main issues I discuss in my Mass prnciple chapter. Steve

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Woodbear
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Joined: June 25th, 2005, 4:30 am
Jeb,

you are exactly correct, the bend radius is directly related to the thickness to maintain uniform strian, and the width must be adjusted in accordance with the bending load to achieve this bend.

One point of terminology; Elliptical tiller is commonly used to refer to the tiller of a uniform strain bow that tapers from thick at the center to thin at the tips. The flat part of the ellipse is thru the handle.

Path,

Tim Baker's "mantra"; "tiller to bend slightly at the fades, mostly midlimbs, and tips slightly stiff, is closer to elliptical uniform strain tiller than many would believe, the exception being the stiff tips. It is not needed to make the tip area thicker in general, as the extra stiffness happens almost automatically, because the "ideal" width goes to zero at the tips, but in practive, a finite tip width is needed to attach the string. Making a reverse taper makes the effect more dramatic.

Dave

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Pathfinder78
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Thanks for the additional explanation guys!
Buttercup: We'll never survive.
Westley: Nonsense. You're only saying that because no one ever has.
"The Princess Bride"

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gmc
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Joined: December 17th, 2008, 2:26 am
Jeb:
Very informative post.

Steve:
What you say makes perfect sense. Would you care to elaborate on your statement about string angle determining the design of the bow? I read your chapter and probally need to read it again but this certainly opened my eyes a bit.

Greg

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Greg explaining string angles gets complicted for e, I will give it my best shot but maybe someone can come in and expalin it better. A bow that bends out near the tips will have higher string angles in the outer limb and tend to put more pressure on the inner limb than a bow with stiffer outer limbs might. Every inch of the limb is responding to the angle of the string which remains constant, all parts of the limb are at different angles to the string at any given time. Often a pyramid bow with the outer limb eifel towered ( concaved width taper) will bend in more of a circular tiller than a straight pyramid. Just keeping in mind the thickness of the limb and how much it is bending and then using the width more for controlling it will go along way toward better performing bows. The string angles can tax my brain beyond it's ability to funtion! LOL. Steve

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gmc
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Joined: December 17th, 2008, 2:26 am
Thanks, Steve!

Sorry for hijacking the post for a moment Jeb, but I had to ask.

Greg

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Rod
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Joined: June 17th, 2005, 11:07 pm
I can see that uniform distribution of the stress would make a bow more durable, but am I right in thinking that it will not in itself maximise cast?
Rod.
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jeb532
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Rod wrote:
I can see that uniform distribution of the stress would make a bow more durable, but am I right in thinking that it will not in itself maximise cast?
Rod.

I think that utilizing all parts of the limb to their utmost would indeed increase cast and efficiency...otherwise you just have a lot of wood going a long for the ride...just like a certain political climate we now all face....
2600 years ago Lao Tzu observed that in any generation..."only one out of ten will ever become self-aware" (i.e. know why they do what they do). The rest will be eternally driven by their emotions and/or confusion. Confucious thought Lao Tzu was a pessimist. Confucious stated that the odds for enlightenment were much better...at one out of eight!

Either way, that pretty much explains human history...

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The main thing that uniform stress gives us is the ability to minimise the mass if we take advantage of it. Another thing is less wood fatique which makes a huge differenence in performance. I use more mass in my bows now than I did 5 years ago. I just put the mass where the bow is bending. Steve

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Woodbear
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Joined: June 25th, 2005, 4:30 am
The durability of the bow is determined by the maximum stress anywhere in the bow, the bow is only as strong as it's most highly stressed point.

As steeve said, making the whole bow (or as much as possible) work at the same stress minimizes the total mass of the bow for a given stress level, which moves in the direction of better efficiency. However, this is only part of the story. You can have the whole bow at an excessively high stress level, and induce excessive set through out the bow. The efficiency of such a bow may be OK, but the stored energy will be low reducing cast. It may also be that having some parts of the bow stiff, like the tip area, resists vibration in the bow and increases efficiency, in a manner that is in addition to reducing the moving mass. In this case, working the stiff outer parts of the bow at the maxium stress may not provide the optimum cast.

I do have to add, however, that the bows I have made with uniform stress perfrorm quite well. I think bows designed with uniform stress, and at a stress level that provides "low" set will tend to be above average in performance.

Dave.

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Springbuck
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Joined: July 2nd, 2008, 3:54 am
Pathfinder: If the bow limb is cut to an actual pyramid shape, the tiller can't help but be circular. Take a material of even thickness and taper to an elongated triangle, apply pressure at 90* to the tip and it will bend to the arc of a circle. Wood is not totally homogenous, but you will be VERY close to finished.

When I learned this, along with the rules of thumb about thickness and width, everything about my bowmaking improved. In my mind I can take this pyramid ideal as a starting point and know ahead of time what will happen when I change any aspect. I mean, like, "so the pyramid bow looks like this, so if I thickness taper here instead, narrow more severly here, and straighten out the side taper here, it will look like this....." Great place to start with any design.

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Springbuck
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Pathfinder, to add to this: "Tim Baker's "mantra"; "tiller to bend slightly at the fades, mostly midlimbs, and tips slightly stiff, is closer to elliptical uniform strain tiller than many would believe, the exception being the stiff tips. It is not needed to make the tip area thicker in general, as the extra stiffness happens almost automatically, because the "ideal" width goes to zero at the tips, but in practive, a finite tip width is needed to attach the string. Making a reverse taper makes the effect more dramatic.

Leverages are reduced further out along the limb, so along with what Woodbear is saying, often you can have stiffer tips by just tapering less in either direction, or keeping a consistent thickness and changing side taper.

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Springbuck
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Joined: July 2nd, 2008, 3:54 am
Pathfinder, to add to this: "Tim Baker's "mantra"; "tiller to bend slightly at the fades, mostly midlimbs, and tips slightly stiff, is closer to elliptical uniform strain tiller than many would believe, the exception being the stiff tips. It is not needed to make the tip area thicker in general, as the extra stiffness happens almost automatically, because the "ideal" width goes to zero at the tips, but in practive, a finite tip width is needed to attach the string. Making a reverse taper makes the effect more dramatic.

Leverages are reduced further out along the limb, so along with what Woodbear is saying, often you can have stiffer tips by just tapering less in either direction, or keeping a consistent thickness and changing side taper.

Steve said: "The string angles determine the proper lay out of the bow. What we often call beautiful tillers are often all wrong." I would add that the tiller might be perfect, .... for another style of bow....until you see the bow from the front and then it's all bass-ackward to how it should be. For instance: let's make a 52" long ambush bow, but give it very soft tips and a really whip-tillered side profile. That bow will stack and have very poor energy storage due to a terrible full draw string angle. Exact same side profile might be great on a bow 72" long or more.

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Springbuck
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Rod said: I can see that uniform distribution of the stress would make a bow more durable, but am I right in thinking that it will not in itself maximise cast?
Rod.

There is tweaking to be done for sure, but actually, depending on several factors, pyramid bows with rectangular cross sections have proven to be some of the better performing straight bows. Limb strain is even, a lot of bending (energy storage) is taking place where there is mass enough to handle it, and the tips are automatically fairly lightweight and stiff.

One fly in the ointment is that the string does not exert pressure against the tip at 90* throughout the draw, so the bend is NOT arc-of-a-circle throughout the entire draw sequence. I have a theory, as yet untested, that some ratio of limb length to draw length will give optimum performance, esp. with pyramid bows. If you and I shoot 66" pyramids side by side and you draw yours 27" while I draw mine 31", our string angles will be quite different, right? So our force draw curves are different, too. At some point the string angle is perfect, and past that stacking occurs, even if not felt.

Now, to punctuate what Steve said, if I take a pyramid bow and make the tips stiffer, I probably do that by adding thickness, right? Possibly narrow at the same time. Just by itself this will lower draw weight, if I change nothing else. NOW if the limb tip is stiff, I have a better string angle later in the draw, BUT, I have several inches loafing, so the inner limb section has to bend to a tighter radius (more tension elongation) so we have to make it a tiny bit thinner to avoid a lot of set, but we still want the draw weight so we make the inner limb wider as well, or reduce the side taper through that section and give it a slight thickness taper. See? Everything we do to one section of the limb affects others.

If you had like a long enough 2 x 4, you could string it at 6" brace and shoot it at 50 lbs if you wanted, BUT, with no taper the bend would be parabolic, with tightest radius at the middle, and WAY too much mass toward the tips. Great string angle, but horrible mass placement.

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Springbuck
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Joined: July 2nd, 2008, 3:54 am
Woodbear said: "The durability of the bow is determined by the maximum stress anywhere in the bow, the bow is only as strong as it's most highly stressed point."

Complete agreement, but let me add that strain or stress can come at ya from different angles. If you bend a thick limb as FAR as a thinner limb, it will be under more strain/stress and will take set or possibly break. BUT bend the thicker limb a little less and you still might have the same or even more energy stored as you would bending a thinner limb more. So as long as it isn't over-worked, it's OK. This is like the bow Pathfinder was describing in his first reply post.

Comes back a lot to Steve's chapter in the book, where he said something like, "the mass principle is about making front view shape agree with side tiller shape."