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Topic Archives => Build Alongs => Topic started by: bvalentine002 on March 07, 2006, 10:52:00 AM
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I want to pose a trignonmety question to help design bows.
When building a pyramid style long bow, what is the optimum rate of width taper that will place equal stress across the entire limb thus delivering low individual stress points and a circular tiller? Is there a mathematical formula for calculating this?
Obviously there are a lot of variables so I propose the following assumptions:
1. The limb material is equally stiff (no weak spots), flat (no crown or reflex/deflex), dense (no soft spots), and thick (no taper from fade to tip). This would most likely apply to board-bows or glass laminated bows with non-tapering cores laminations.
2. I am not concerned about compression or tension failures. I am just interested to know what the width taper would have to be to avoid thickness tapering.
3. An example rate of width taper would be something like 1.5" of taper over 30" of limb length or .05" per inch. Thus, a limb that has 20" of working length (like a kids bow) would need to have 1" of total taper and a 40" working limb (like a long ELB) would need to have 2" of total taper.
If a taper can be found, it should be easy to build the starting dimension of a pyramid limb by applying the taper to the working limb length and adding the desired tip width. Using the above example, a 30 working limb with 1/2" tips should be 2" wide at the fades.
-Brett
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Brett, maybe you covered this in your assumptions, but I think at some point you'd have to take wood type into account, perhaps develop a wood specific formula.
The acceptable ratio is likely to be very different depending on the wood used, such as osage/ipe vs. red-oak/cherry, etc.
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The only true pyramid bow I made is hickory backed red oak. 66" long, symetrical, 4" handle area, 2 1/4" at the fades and tapering to 3/8" tips...so 66-4=62 divided by 2 = 31" long limbs going from 2 1/4" to 3/8".
I think the wood the bow is made of will have a big affect on this formula also. Pat
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The true pyramid bows I've made have been around 2-3/4" at the fades, tapering to 3/8" tips, 64" ntn, 8" handle/fade area. Anything under that starting width and you have to thickness taper to get the circular tiller and avoid the inner limbs doing all or the majority of the work.
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Brett, Thats really a very good question, I have made a lot of pyramid bows and have given a lot of thought to how I could figure the optimum thickness tasper. I have a weight formula I use that might help, lets assume that all dense woods will end at 3/8 tips and all medium dense woods will end at 1/2" tips. Now in reality I don't favor a circular tiller, I prefer an elyptical tiller and stiff tips. But just for the sake of a formula we will go with circular tiller. If you are making your bows between 62" and 68" long and you are sure the mc of the wood is below 8% you can safely figure that 16oz of wood will give you a 50# bow and that you should add 1oz of wood for every 5# of draw weight at 28". This may mean starting your fades at 1 1/4" or it may mean starting them at 2 1/2". Obviously the thickness of the woods determines how much a piece of wood can bend and the width determines how much it will bend in relation to other parts of the limb. I will usually start off with a pyramid shape and thin modify it a bit by side tillering. seems when I am done the mass weight of the bow almost always comes out very close to what I listed above regardles of the wood species, from poplar to ipe. Steve
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It seems to me that an even levevl of stress across the full length of the limb is mathematical and doesn't depend on the material.
The optimal ratio may be too narrow for certain wood (cherry), or wider than necessary for others (osage). Thus the actual taper can be modified.
I'm not that concerned about hitting a weight either. Assuming we can come up with an optimal taper, varying the thickness (stack height)should be the best way to chcange weight.
Keep 'em coming...
Brett
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To a point, Brett, I agree... however, w/r/t the thickness assumption that you just stated for changing the weight -- I'm not sure. At least as far as I see it, a wood such as osage would have to be made much thinner to hit weight with that assumption, whereas a wood like cherry would have to be proportionally thicker to hit that same weight (all else being held as constant, that is), and therein lies part of the problem, again as far as my own experience with cherry (and of course this is only for example, I am not hanging you on wood or word choice) being that thick, it would cause serious problems on the belly, most likley resulting in failure, and that failure most likely beginning with severe crysalling.
Not based on fact, but thoughts only. So... let's get it tried, then true? I have a lot of black cherry boards that I've been itching to make into bows... we'll see. But first let's get some good ideas on what an appropriate ratio(s) would be. Hey, I'm game! (just don't shoot me!)
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If I remember correctly TBB #2 recommended a 4:1 ratio for a try pyramid bow. Not sure how you figure the length though...
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Tim,
I see your point. The thickness of the wood would change the distance from the center of the lamination. This increases the amount of compression that the outer-most layer of the belly is under. Thus, as the thickness increases, the weight would too, but the compressive forces would be so great that they would crush the wood.
I think what we may be finding through this discussion is that there some woods that cannot be made into pyramid bows with equal limb thickness. Maybe we should reframe this for Glass-Lam bows and stronger wood.
Rangeball,
I'm not sure I understand the 4:1 ratio? Are you talking about width to thickness ratio? I have heard 4:1 when deciding how thick to make the backing and belly wood (such as a belly that is 4x as thick as the backing).
-Brett
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Brett, I think any bow can be made a pyramid provided it starts wide enough and is long enough. If I recall correctly the one discussed in TBB #2 was over 3" at the fades.
The ratio I was referencing was width at fades to tip width, if I remember correctly. I may be completely lost though :)
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oops, actually it's ME that has misunderstood, in that I thought the question pertained to selfbows/backed/unbacked board bows. Different story, I am sure, for glass. Sorry.
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"When building a pyramid style long bow, what is the optimum rate of width taper that will place equal stress across the entire limb thus delivering low individual stress points and a circular tiller? Is there a mathematical formula for calculating this?"
"When building a pyramid style long bow, what is the optimum rate of width taper that will place equal stress across the entire limb thus delivering low individual stress points and a circular tiller? Is there a mathematical formula for calculating this?"
If this is the only goal then a triangular limb of any starting width will yield perfect circular tiller every times if same thickness from limb from grip to tip. Draw weight would be determined by limb width. Thickness by the elasticity of the wood and the length of the bow.
But this is not the best design for a couple of reasons. Such a bow is evenly strained from grip to tip, so takes equal set grip to tip. Near-grip set yields exaggerated string follow, so tiller should be elliptical. Bend near the tips shortens the bow at full draw, increasing stack, lowering energy storage. So outer limbs should be relatively stiff. Tim Baker
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Originally posted by tim baker:
then a triangular limb of any starting width will yield perfect circular tiller every times if same thickness from limb from grip to tip.
Tim, I have to disagree with you on that one. Think of the extremes: A 66" bow, 3/4" wide at the fades tapering to 3/8" tips will have ALL the work beign done in the inner quarter of the limbs. The forces the limb is under decrease as you travel out toward the tips. Simple leverage. Otherwise all the glass bows out there wouldn't need tapers - they're nearly all triangular limbs. The inner limbs need to be strengthened - either by making them thicker or wider. Thought I remembered you saying that before. ;)
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Jeremy: Perfectly truangular limbs, straight sides aiming at a point, will yield evenly strained, arc-of-a-circle tiller if even thickness. Is that the point of disagreement?
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Jeremy,
Thanks for responding...you sait it almost exactly as I would have.
To help explain more...if you took the same 66" bow and made the fades 4" wide and the tips 3/8", all the work would be done at the tips (whip tillered) becuase the fades would be too stiff to bend.
I'll try to say it another way: I would like to know what the perfect width at the fades and tip are for a given limb length in order to evenly distribute stress along the entire limb.
My goal in knowing is to avoid points of stress along a limb, thus avoiding set and compression failures in those areas.
Come On...any engineers out there?
-Brett
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One way to think of it is like this any wood that is the same thickness and bending the same amount will be under identical strain regardless of width, if wood is slightly thinner and still bending the same it is not under the same stress, Thickness determines how far wood can bend, width determines how far it will bend, and lots of other factors come in to make a decent bow, Steve
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Jeremy, Assuming uniform limb thickness and triangular fron view, the bow could be any width at the fades, 1" to 10" and stress along the length of the limb will be equal at all points, with circular tiller resulting. That's if the straight sides are aiming at a point at the nocks. This is straigh out of the engineering text books. It's against all intuition, but true. If the sidea are aiming at 3/8" instead of a point then the outer limbs will be a bit stiffer, the midlimb and grip bending slightly more. Tim
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Tim, assuming one wanted a bow in the pyramid style with even limb thickness, to avoid near grip set could they simply leave the limb out full width for a few inches or so then start the taper?
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Rangeball: If perfectly uniform in thickness, and parallel in width for a few inches out of the grip, that would cause even more set near the grip, because that portion would be narrower than if the sides continued widening all the way to the fades. I hope this makes sense.
If the first few inches out of the grip is parallel then that portion must be a touch thicker, and have a whisper of thickness taper, just as if it was a typical bow design--after all, no part of a limb can know how the rest of the limb is shaped. A pure pyramid isn't a bad design, but performance will rise if tillered more elliptically, to reduce or eliminate near-grip set, the worst place to have set. Tim
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Tim
I have just built a couple of board bows with limbs that are parallel for 70% of their length and then taper evenly to the nocks.
These take their set about 2" into the parallel section (from the nock end). Am I correct in assuming that this is also due to the limb being narrower in that particular area than if the limb had continued to widen?
Could this be avoided by thickening the limb in that immediate area ie. limb thinner either side of the transition area?
Sorry for the slight side-track Brett
Red Dwarf
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Ok...I have actually been thinkin of making a pyramid bow since reading about them in the traditional Bowyer's Bible.... Would someof you guys be willing to share your dimensions, including limb thickness and resulting draw weight? Also, the one shown in the Boyer's Bible tapers to a point, and has a wrap to hold the string, because it is too narrow for string grooves...were your done like this, or were the tips left wide enough for string grooves? Thanx...John
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Originally posted by tim baker:
Assuming uniform limb thickness and triangular fron view, the bow could be any width at the fades, 1" to 10" and stress along the length of the limb will be equal at all points, with circular tiller resulting. That's if the straight sides are aiming at a point at the nocks. This is straigh out of the engineering text books. It's against all intuition, but true. If the sidea are aiming at 3/8" instead of a point then the outer limbs will be a bit stiffer, the midlimb and grip bending slightly more. Tim
If you are right (and I'm not sure I believe you because this is not intuitive!!! :knothead: ), that is great news!
The next question...how can you get eliptical tiller from a pyramid bow?
-Brett
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Originally posted by bvalentine002:
Originally posted by tim baker:
Assuming uniform limb thickness and triangular fron view, the bow could be any width at the fades, 1" to 10" and stress along the length of the limb will be equal at all points, with circular tiller resulting. That's if the straight sides are aiming at a point at the nocks. This is straigh out of the engineering text books. It's against all intuition, but true. If the sidea are aiming at 3/8" instead of a point then the outer limbs will be a bit stiffer, the midlimb and grip bending slightly more. Tim
If you are right (and I'm not sure I believe you because this is not intuitive!!! :knothead: ), that is great news!
The next question...how can you get eliptical tiller from a pyramid bow?
-Brett [/b]
Brett, I thought I was onto this with my question, which Tim quickly shot down :)
I suspect it will have to do with belly tapering, thicker near fades and thinner toward tips with tips stiff.
I also suspect the response may be something like even width to mid-limb then taper to nocks and leave tips stiff, which is the common shape recommended on many sites such as Mickey and George's (among many many others). Seems like this design is basically a modification of the pyramid style.
If one were to overbuild a pyramid a bit, I suspect they could avoid near grip set (with experimentation), but possibly at the risk of performance?
Tim, did the true pyramid bows outlined in TBB all suffer from near grip set? If not how was this avoided and performance maintained?
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RedDwarf: You could say it's because the limb is narrower there, or that that area was not thick enough and without proper thickness taper to yield even strain along the limb. PS: For a parallel-limb bow it's better to start narrowing to the nocks at about midlimb for most such designs, Narrowing farther out adds outer limb mass with no increased safety or reduced set.
FlyinCedar: Limb width will be determined by the wood used--poplar being very wide, ipe being very narrow. Thickness always determines itself during the tillering process--at identical thickness every stave would yield a different drawweight. So decide the length bow you want, the type wood to be used, then 'design' your bow. If of a mid-density wood like oak or maple, 66" long, 50lbs at 28" then 2.5" at the fades is about right, tapering as if to a point. You can aim to a point, then during that last 2" or so stay say 3/8" wide to leave room for side nocks, or continue almost to a point and tie or glue on a tiny back nock. I prefer one with a step in it to catch the string, so the string won't rest directly on the narrow tip wood.
Brett: Good for you. A skeptic. That will save you from swallowing a lot of baloney. This is an easy thing to prove: buy a 1/4" wood slat at HomeDepot, cut it to pyramid shape, clamp the wide end, then pull on the pointed tip and watch perfect circular tiller result. This will be true if the slat in 1" wide of 1-foot wide. I learned of this in Archery The Technical Side. I wasn't so much skeptical, considering the source, as surprised. But after some thought it made sense: A point half way between point and base will feel half the leverage the base feels, so needs to be half the with to feel equal strain, etc. at any point along the limb. And this holds true for any width pyramid.
Per a few posts above, a pure pyramid is good, but not the best-performing design. The inner limb should be somewhat elliptical, to avoid near-grip set. Do this by slight thickening of a pyramid bow's near-grip wood, or letting the first one-forth or so of it's length be parallel, that portion tillered elliptically. Tim
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I think it is time we heard from O.L.
Hacksaw
Horace Worcester
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Originally posted by HACKSAW:
I think it is time we heard from O.L.
Hacksaw
Horace Worcester
Why's that?
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Just to clarify: my understanding of an eliptical tiller is one in which the elipse would be up vertical (like a 0 ) and not like an egg laying on it's side (sorry, no better description!).
I remembere reading in TBB that the author made a hickory pyramid bow that shot as fast as almost any glass longbow. I lovevd the iddea because tillering the sides is much easier (and slower) than tillereing the belly.
Thanks, Guys!
Brett
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Brett: Elliptical tiller: Near grip wood barely bends, then bends progressively more severely as you move towards the tips. For stack reasons you don't want the outer limb to bend much though, unless it's an unusually long bow. But that's another story.
If it was in the TBBs about pyramid bows I likely wrote it, but have figured things out a little better since then, The fastest bows are longish, with relatively long, stiff, center sections and very narrow light outer limbs, strong elliptical tiller. My best such straight-stave bow, 54lb at 30.5", shot a 500-grain arrow at a witnessed speed of 192fps. Some of the witnesses were fiberglass guys, so you can imagine the evil pleasure we wood guys felt. Steve, Badger, was the shooter.
If you start out with uniform thickness along the limb you can't tiller from the side of course. Tillering from the side is a bad idea anyway, because you should lay out the front view of the bow before you start. That shape is an important part of the design process. Tim
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Stacking is a familiar experience for me! I'm 6'4" and I draw 31 - 31.5" (to low point of the grip). I just moved into the world of glass bow building. I have found that even with a 70" bow I'm approaching the stacking point. I'm using a reflexed form to help get around that...but that's another conversation all together.
Thank you all for your help!
-Brett
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Tim, Steve, Anyone... :)
Had a thought.
Would heat treating the belly help prevent near grip set on a pyramid bow?
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Range, heat treating seems to help reduce set most anywhere on the limb, heat treating can even reverse existing set, Steve
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Interesting... :)
I really like the looks of the pyramid design, and have even thought of building a heavier draw weight one, so when I do get set it may still give me the cast of a 50#er or so...
I have lots of bows in the thinking about them stage. I need to put one into action, and this may be as good a place as any to start :)
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I made one piramid style bow (kind of :bigsmyl: ) and to me the advantage of the piramid style is that the fades are quite stiff, so no set there.
stiff out of the fades, makes the limbs of a longbow effectivly shorter, less limbs to move= more performance, without sacrifacing the stability of a longer bow.
that was my reasoning when I crafted mine, 71# @ 27"
Manny
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BTW,
I go with feel and sigth, no set mesuraments :bigsmyl: :bigsmyl:
Manny