Primitive Archer
Main Discussion Area => Bows => Topic started by: Del the cat on December 14, 2014, 09:08:49 am
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Sometimes you just gotta do the test, all the theory and pontificating in the world won't make you right if it ain't so!
After some discussion on another thread I couldn't get a consensus on what was a good test.
So I made two symmetrical bows, straight tapers 40" long (plus 1" for nocks) tapering from 3" wide to nothing and the other from 1.5" wide to nothing.
I drew 'em on the tiller rig to 20" and 22" draw whilst videoing 'em with the camera position fixed on a tripod.
One thing that showed up is it's surprisingly hard to get 'em sawn out perfectly and mounted dead straight.
The result did rather shock me, the curves we near as dammit identical (within the positional/sawing errors I've just mentioned).
The pics shown are the 20" draw as I felt this was a more realistic draw. The 22" draw is very much the same result... damn near identical.
There have been plenty of learned papers written on this sort of thing, and as a kid I spent hours pondering if the centre width mattered as long as it tapered to a point, after all regardless of the grip width it would always be half that width at half that length... did it sort of automatically regulate itself?
Anyhow it only took me 40 years to do the test ::)
Del
PS. Anyone who want's to say "I told you so!" be my guest :laugh:... but seeing is believing :)
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Interesting tests Del. Did you happen to check and compare the perspective weights when drawn?
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I am wondering what your analysis of the test is. As a rule I am not in the "pyramid with no thickness taper" camp as a practical matter, but I am curious about the physics of it all.
They both appear to be a tad round in the handle. I would have expected the wider one to be less so.
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Never tried a pyramid. I've read that you don't actually do any thickness tapering, just pick a dimension for draw weight and let it ride all the way to the tips. Is that right? Then maybe all you add is the grip lamination for thickness there, cut it out, and you're done? Seems simple enough. Would this work for any kind of wood?
George
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Didn't this just prove what we already knew?
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Didn't this just prove what we already knew?
I don't profess to be able to speak for "We" !
Maybe you already knew it... I didn't... I didn't spend the time doing it on a whim.
I fact I've just re-done it setting up more carefully to get better pics so that I can be confident in the result.
I'm a great believer in the empirical but will allow others to draw their own conclusions.
Del
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Interesting tests Del. Did you happen to check and compare the perspective weights when drawn?
Yeah, the wide one was much heavier (presumably twice the weight).
They are too light to weigh accurately.
Del
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I am wondering what your analysis of the test is. As a rule I am not in the "pyramid with no thickness taper" camp as a practical matter, but I am curious about the physics of it all.
They both appear to be a tad round in the handle. I would have expected the wider one to be less so.
I've just re-done the test with a more careful set up. All it shows is that the skinny one has one limb stiffer than the other. It's difficult to cut a thin limb V accurately on the band saw. I think it's pretty conclusive that the grip width has little if any effect on the curve in a straight "taper to a point" design. It does effect the draw weight tho'.
There is no 'handle' as such and in the re done shots I actually support the centre on an off cut of arrow shaft.
they look pretty much arc of a circle to me (try holding a CD up to it). I've added another ipc with a circle centred on the draw point of the string...
In the re- done shots the draw length is half the bow limb length.
Mind... of course we all knew this ::) ;)
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Thanks, Del, for showing us this. Now I know.
George
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Nothing wrong with challenging the status quo, if nothing else to prove to yourself what you think is right, not everything you read or see on the internet is true, thanks for doing the test now try it with a stiff handle >:D
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Thanks Del, you saved me from sawing up my last piece of plastic(I can't spell polycarbonate) >:D
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Nice simple test Del. Thanks for taking the time to share it with us. 8)
Glad you posted the second set of photos, much clearer to see just how near identical and nice the bends are.
While I didnt see it spelled out (which aint to say it wudnt spelled out ::)), and not sure if it matters or not, but I am assuming these are the same thickness, is that right?
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thanks Del,very nice test,,I really made things more clear for me about the tiller,, I appreciate your time and effort,, B
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Nice simple test Del. Thanks for taking the time to share it with us. 8)
Glad you posted the second set of photos, much clearer to see just how near identical and nice the bends are.
While I didnt see it spelled out (which aint to say it wudnt spelled out ::)), and not sure if it matters or not, but I am assuming these are the same thickness, is that right?
Yeah, cut out from the same sheet of plastic. (about 1/8" thick)
Del
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To me this both makes sense and is utterly counterintuitive. I think we all owe a debt of gratitude to Del for clearly illustrating the principle.
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Thank you Del, I have al;ways wanted to do that. Tim Baker always told me they would bend the same but it didn't make sense to me. Cool test! I am curious as to the handshock.
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OK, I DO want to say "I told you so!" And you, and you, and you for years. If you can find my posts on "pyramid" bows you will find I have literally been saying this for many years and having it fall on deaf ears. Not only here but on the leatherwall too.
I have made only "pyramid" bows for a dozen years because they take less time to make and shoot as well as the best other designs.
OF COURSE, the design is not mine and not new. I came across it in Archery, the Technical Side a long time ago.
Thanks Del for posting the tests. I still urge everyone to try the test. You can make a single "limb" tapered to a point and make it out of plywood if you want or thin hickory or whatever. Clamp the big end in a vice and flex the pointy end. Doing it yourself will make a true believer out of you.
This one was about five years ago.
Jim
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Thanks Del. Hard to argue against the results. I have been told for years that this would be the results. Didn't disbelieve it so much as question what difference it makes (pyramid vs parallel) in the final analysis. Most efficient design? Greatest cast? This test has got me to thinking about things for sure. Thanks for doing it.
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This is a headscratcher for me, but I am thinking the uniform thickness and compression/tension properties of the plastic material lend a different result than would be had using yew, osage, vine maple, hazel, etc, with some crown on the back. I could be full of beans though. My late father used to tell me, "You're all wet, mister." He was always right.
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Thank you, Del.
My conclusion from your test is that for a given homogenous material and thickness and constant thickness and shaped as a pyramid, the bending profile will be the same regardless of thickness.
Also, though wood is not a homogenous material, a given species shares similar physical/strength characteristics and, therefore, a given wood species will exhibit similar results.
Have tension/compression stresses along the length of such a limb profile ( & other typical profiles) been measured?
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This is a headscratcher for me, but I am thinking the uniform thickness and compression/tension properties of the plastic material lend a different result than would be had using yew, osage, vine maple, hazel, etc, with some crown on the back. I could be full of beans though. My late father used to tell me, "You're all wet, mister." He was always right.
It is an assumption to think that the compression and tension properties are uniform/equal in the plastic used.
With wood the tension strength is something like 3 times greater than the compression strength in most cases. But the stretch and compression are about the same--1 percent--before failure. We're flying blind for the most part, but whatever the strengths are, their ratio remains the same from end to end.
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This is a headscratcher for me, but I am thinking the uniform thickness and compression/tension properties of the plastic material lend a different result than would be had using yew, osage, vine maple, hazel, etc, with some crown on the back. I could be full of beans though. My late father used to tell me, "You're all wet, mister." He was always right.
Nope - just the same as wood, steel, pasta.....
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Thank you, Del.
My conclusion from your test is that for a given homogenous material and thickness and constant thickness and shaped as a pyramid, the bending profile will be the same regardless of thickness.
Also, though wood is not a homogenous material, a given species shares similar physical/strength characteristics and, therefore, a given wood species will exhibit similar results.
Have tension/compression stresses along the length of such a limb profile ( & other typical profiles) been measured?
Nope - thickness determines bend.
Bending profile will be the same IF and only when the thickness is constant.
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I recently had an order for 'holmguaard style' re-enactment bows. I had ten to make.
I first roughed out a pyramid bow from an already thicknessed piece of ash.
Roughed out a pyramid taper.
Then further narrower the outers to give them the holmguaard outer limb look.
Over to the belt sander and a few seconds on the working limb to make it thinner than the outers.
Bingo perfectly tillered bow that took an hour tops.
The real beauty of a pyramid is that tiller is SO easy to read that it allows you to stress the wood evenly. Wood that has been stressed evenly with no stiff/weak spots returns faster. So we get back to what Hickmann said in Archery - The Technical Side.
I haven't made a true pyramid in years but this thread has reawakened the urge!
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Cheers guys.
I may just run up a quick 2" parallel strip of polycarbonate just for comparison to complete the test.
Whadda mean obsessive? ::)
Del
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It will bend too much at the center. >:D
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It will bend too much at the center. >:D
Ah yes, but it's the quality of the bend... ;)
Del
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OK, I DO want to say "I told you so!" And you, and you, and you for years. If you can find my posts on "pyramid" bows you will find I have literally been saying this for many years and having it fall on deaf ears. Not only here but on the leatherwall too.
I have made only "pyramid" bows for a dozen years because they take less time to make and shoot as well as the best other designs.
OF COURSE, the design is not mine and not new. I came across it in Archery, the Technical Side a long time ago.
Thanks Del for posting the tests. I still urge everyone to try the test. You can make a single "limb" tapered to a point and make it out of plywood if you want or thin hickory or whatever. Clamp the big end in a vice and flex the pointy end. Doing it yourself will make a true believer out of you.
This one was about five years ago.
Jim
I dont doubt that the design works, but for me personally, there is more to building bows than doing it quickly. I build bows that are aesthetically pleasing and for me the pyramid design is not. I like to see the thickness taper in the limbs, beauty is in the eye of the beholder!
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Misslemaster, please modify your post to show where my quote ends. I do not want to be known as making bows for esthetic reasons--though the pyramid bow is much nicer looking in front or back view than a flat bow, in my opinion.
Thanks
Jim Davis
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What surprises me is how they both bend so much in the handle.
Thanks, Del. Jawge
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Whether it is a building a bow or a scheme, a pyramid is ugly. >:D
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To me this both makes sense and is utterly counterintuitive. I think we all owe a debt of gratitude to Del for clearly illustrating the principle.
Kinda +1.
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OK, I DO want to say "I told you so!" And you, and you, and you for years. If you can find my posts on "pyramid" bows you will find I have literally been saying this for many years and having it fall on deaf ears. Not only here but on the leatherwall too.
I believed you, Jim! I believed Baker when he said it, too, and it surprises me that so many experienced guys didn't.
I think the confusion often comes in because A. not every piece of wood can be made into a pyramid bow, and B. One does have to tweak them for practical reasons, such as the fact that the tips don't taper right to popints and need that 1/4" or whatever, and you do have to come down from fades.
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I think the confusion often comes in because A. not every piece of wood can be made into a pyramid bow, and B. One does have to tweak them for practical reasons, such as the fact that the tips don't taper right to popints and need that 1/4" or whatever, and you do have to come down from fades.
Absolutely right.
Pat M, that's why I dislike the term "pyramid" for this design. I think Tim Baker may be the origin of that word usage. The bows are much closer to an Eiffel Tower shape than a squat pyramid. I'd like a better term, though triangle doesn't quite do it either.
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What surprises me is how they both bend so much in the handle.
Thanks, Del. Jawge
In Del's experiment, the whole test piece is limb, from tip to tip. With a stiff handle in there, the limbs start, and start bending, at the outer end of the fades. From there on, they will look like Del's test limbs.
Jim
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Yes, Jim, but I would have thought the wider inner portions would have bent less. Not sure I see that. Jawge
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What surprises me is how they both bend so much in the handle.
Thanks, Del. Jawge
I think this is both a function of ACTUALLY bending (slightly) in the handle, and (with actual bows that have fades) it APPEARING to bend more in the handle, because the transition from fade to limb thickness is rather sudden for a pyramid bow.
Knoll: I did this same test myself years ago (never posted, ADHD prevents me from taking pictures and then getting around to putting them up) but with thin pine slats, oak scantlings, and some 1/4" thick belly lams that hadn't worked out. With wood of uniform dimensions, the result is almost exactly the same. TINY differences, not big ones. With crowned staves, any amount of crown, to me THAT seems to make a difference, at least enough to require some care in tillering.
George, like I mentioned above, when this was discussed in depth on Paleoplanet a few years ago, I realized that both my pyramids and many I was seeing made, weren't really arc of the circle, exactly. It was more parabolic, bending less off the fades, and less at the tips, almost like tangents to the arc.
I also have a hypothesis, that with a pyramid bow, there is an exact right bow length for each draw length, because the string angle exerts pressure at different angles thoughout the draw. It seems to me there must be an optimum spot/angle/drawlength to stop, and that we should be designing the bows (length, primarily, to accomodate this.
Somebody on pg 2 wondered if tests have been done to see if limb strain is consistent all along the limb. The answer is yes. The nature of the bend itself shows engineers that the strain is consistent. Same thickness, bend to same arc= consistent strain, (but more pressure, as leverage applied to any one spot is greater the closer you get to the handle.
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The wider inner limb/would be handle area/does resist bending relative to what a thinner limb would. It is just resisting a stronger leverage effect than the limbs further out deal with-the same reason we can make tiny limb tips and they remain fairly stiff-there is so little leverage at that point.
If anything I am a little surprised that there is a such a clean correlation between width and final bending, it is neat that a straight line taper matches up with the changing leverage at a 1:1 ratio.
SOM
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The wider inner limb/would be handle area/does resist bending relative to what a thinner limb would. It is just resisting a stronger leverage effect than the limbs further out deal with-the same reason we can make tiny limb tips and they remain fairly stiff-there is so little leverage at that point.
If anything I am a little surprised that there is a such a clean correlation between width and final bending, it is neat that a straight line taper matches up with the changing leverage at a 1:1 ratio.
SOM
Yeah, that's what I love about bows... all the high school fancy physics analyses beams for small defelections and analysis of bows makes loads of assumptions.
Nothing is linear, the angles change, string deflection vs tip deflection isn't linear... yet at the end of the day the FD curve turns out remarkably linear! ;D
The empirical always trumps the maths!
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Del, if you took a flat straight board and bended it into a hoop attaching the too ends it should form a perfect circle. What would happen if you attached too pyramid bows together at the tips? Assuning the spot of gue on the tip of each bow could actually hold it. What would happen if you took 1 pyramid bow and bent it so the tips would attach to each other?
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The wider inner limb/would be handle area/does resist bending relative to what a thinner limb would. It is just resisting a stronger leverage effect than the limbs further out deal with-the same reason we can make tiny limb tips and they remain fairly stiff-there is so little leverage at that point.
If anything I am a little surprised that there is a such a clean correlation between width and final bending, it is neat that a straight line taper matches up with the changing leverage at a 1:1 ratio.
SOM
Yeah, that's what I love about bows... all the high school fancy physics analyses beams for small defelections and analysis of bows makes loads of assumptions.
Nothing is linear, the angles change, string deflection vs tip deflection isn't linear... yet at the end of the day the FD curve turns out remarkably linear! ;D
The empirical always trumps the maths!
Del, a friend of mine who has a doctorate in physics laughs about this all the time. He refers to it as Edisonian vs Nuetronian. Same as trial and error vs science. Trial and error most always wins.
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Del, if you took a flat straight board and bended it into a hoop attaching the too ends it should form a perfect circle. What would happen if you attached too pyramid bows together at the tips? Assuning the spot of gue on the tip of each bow could actually hold it. What would happen if you took 1 pyramid bow and bent it so the tips would attach to each other?
Good Q,
But of course there is no longer a string pulling twards the centre of the circle. My guess is, with two pyramids you'd get an oval, maybe like a pair of lips :-* :laugh:
I have the two pyramids so I s'pose I could try it...
But I still have a stinking sinus cold... so it's prob' just thought experiments for me. (Maybe a stiff drink too)
Del
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OK tried it...
The big prob is attaching the tips, didn't really work at one end where I tried to tie 'em together, so I held the other end by hand...
I think you can see it's an ellipse.
Anything else you'd like me to do before I get my dinner? ;)
Del
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What if you bend one pyramid bow right around and join it at the tips? Have your dinner first!
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What if you bend one pyramid bow right around and join it at the tips? Have your dinner first!
Now you just teasin' this poor ol' kitty :( ;)
Del
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It's the only way left I could think of bending it ;) ;)
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If anything I am a little surprised that there is a such a clean correlation between width and final bending, it is neat that a straight line taper matches up with the changing leverage at a 1:1 ratio.
Actually it is not a straight line taper but the curve is quite close to one. According to TBB4 page 117, the breakdown of stress ratios are from handle to tip at 5 even intervals 30% 27% 22% 15% 6%. The "pyramid" should be a little fatter than a triangle.
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scp said:
Actually it is not a straight line taper but the curve is quite close to one. According to TBB4 page 117, the breakdown of stress ratios are from handle to tip at 5 even intervals 30% 27% 22% 15% 6%. The "pyramid" should be a little fatter than a triangle.
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I remember those numbers being corellated to % of energy storage in each 1/5th of an evenly STRAINED longbow. Even on a pyramid, I could believe that the energy storage broke down like this, but the strain would be consistent.
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I've built one , it was out of an oak floor board .
I did it just to see how it worked , went from 2" at the fades to about 3/8" at the tips straight taper and set a stop up on the bandsaw to keep the thickness the same and stopped at the fades to keep a stiff handle .
Didn't take an hour total to start putting arrows through it , I left the grooves on the bottom of the board to show folks that it is a floor board ( growth rings run vertical and grain runs horizontal and it was pretty clean exept for one spot where the grain has a wave in it ).
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Yes, Jim, but I would have thought the wider inner portions would have bent less. Not sure I see that. Jawge
Jawge, maybe it's easier to think of just one limb with the wide part clamped. The limb could be as long as you want as long as the ratio of length to width is maintained. The wide end would always bend as much as the rest of the limb, because the leverage at any point has the same relation to the width at that point.
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I have enjoyed reading this whole, insane thread and the fact is , it doesn't matter, either your bow works or it doesn't. The fun and the pain is in the making, too much D*** thinking.
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If anything I am a little surprised that there is a such a clean correlation between width and final bending, it is neat that a straight line taper matches up with the changing leverage at a 1:1 ratio.
Actually it is not a straight line taper but the curve is quite close to one. According to TBB4 page 117, the breakdown of stress ratios are from handle to tip at 5 even intervals 30% 27% 22% 15% 6%. The "pyramid" should be a little fatter than a triangle.
SCD, you are quoting a writer who is not an engineer, as far as I know. Klopsteag and Hickman were engineers. Machinery's Handbook was written by engineers. Those sources say that if the thickness is uniform, both geometry and physics dictate that the sides should be straight.
Taking into account the need for nocks, the limb stops tapering when the width of the nock is reached.
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For giggles, I set a 2x4 across two saw horses, then laid a 4x4 ft sheet of plexiglass diagonally across it. I used duct tape wrapping over the "tips" and connected it with some 1/4 inch rope.
When I gave it a pull, whatdya know, the "tiller" looked good.
Now I imagine if you made a diamond shape, such that the angle of the bow limbs was described by an obtuse angle (reater than 90 degrees), you would still get that same tiller effect. So then, comes the question....at what point does the angle become so acute that the effect is lost? Is it even possible to get to such an acute angle that it would behave differently?
Or is this akin to "squaring the circle"?
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SCP, you are quoting a writer who is not an engineer, as far as I know. Klopsteag and Hickman were engineers. Machinery's Handbook was written by engineers. Those sources say that if the thickness is uniform, both geometry and physics dictate that the sides should be straight.
The engineer who did the calculation is named in the book.
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SCP, you are quoting a writer who is not an engineer, as far as I know. Klopsteag and Hickman were engineers. Machinery's Handbook was written by engineers. Those sources say that if the thickness is uniform, both geometry and physics dictate that the sides should be straight.
The engineer who did the calculation is named in the book.
I knew something had to be wrong. There are two somethings wrong. First on the page cited, engineer David Dewey is talking about a "D-longbow," not a "pyramid" bow. Second, I found no mention pages 117,118 to leaving the sides wider than a straight line.
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I knew something had to be wrong. There are two somethings wrong. First on the page cited, engineer David Dewey is talking about a "D-longbow," not a "pyramid" bow. Second, I found no mention pages 117,118 to leaving the sides wider than a straight line.
I'm talking about the proper way to taper a well made bow. Either through thickness as in a "D-longbow" or through width as in a "pyramid bow". We usually combine the two tapers. What makes you think a straight triangle with even thickness would make a better bow?
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It has not been the purpose of Del's thread or my contributions to compare designs or promote a design as the best. But, Klopsteg and Hickman, among others, point out that every inch of a triangular limb of uniform thickness is able to contribute equally to the storage of energy. This is not true of a bow that tapers in thickness because there is one best thickness for any particular degree of curvature. In a bow of tapering thickness, thicker sections have to bend less, therefore they store less energy.
Why ask me? None of the research is mine. Why not read the original material?
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If anything I am a little surprised that there is a such a clean correlation between width and final bending, it is neat that a straight line taper matches up with the changing leverage at a 1:1 ratio.
Actually it is not a straight line taper but the curve is quite close to one. According to TBB4 page 117, the breakdown of stress ratios are from handle to tip at 5 even intervals 30% 27% 22% 15% 6%. The "pyramid" should be a little fatter than a triangle.
Even though it is not 1:1 ratio, the ratios are not random.
30% -3 27% -5 22% -7 15% -9 6%
It sure describes a nice curve often found in nature.
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I didn't think the breakdown would be random, and I can rationalize the results from an 'amount of material resisting bending/physics' point of view. It is just neat to me it works out that way. I don't think it is hard to imagine a universe wherein the leverage effect would be some odd ratio to material strength, in which case a curved outline would match up better. Its just a neat thing that a relatively straight line fits the bill.
SOM
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Thickness determines bend, width determines weight.
Done.
>:D
Now lets go make bows!!!! ;)
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This is a cool thread, and one of the reasons I still lurk here. I hope to get making again soon, perhaps a pyramid/eiffel tower bow ;D
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I think this makes sense whether or not the taper is a straight line or slightly curved. I think the flaw comes in the practicality of it. I believe about all of the pyramid bows I see don't taper to a point but to a wider tip which means that the force on the limb is going to change. What we consider pyramid bows almost never act like a truly pyramid shaped limb and therefore are going to need some kind of taper to achieve that circular tiller. Considering that it isn't a truly pyramid shaped limb then that circular tiller is technically incorrect for the limb shape too for efficiency of mass distribution. Not sure how the tiller of an even thickness elongated trapezoid should be though. :P
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I think this makes sense whether or not the taper is a straight line or slightly curved. I think the flaw comes in the practicality of it. I believe about all of the pyramid bows I see don't taper to a point but to a wider tip which means that the force on the limb is going to change. What we consider pyramid bows almost never act like a truly pyramid shaped limb and therefore are going to need some kind of taper to achieve that circular tiller. Considering that it isn't a truly pyramid shaped limb then that circular tiller is technically incorrect for the limb shape too for efficiency of mass distribution. Not sure how the tiller of an even thickness elongated trapezoid should be though. :P
This was covered way back in the thread. If the triangle is drawn to a point the tiller will be circular, but since that leaves no room for nocks, you are correct that some taper somewhere is needed. I usually end up tapering the belly of the outer limb as needed.
BUT, it is possible to draw the side lines to the point but stop cutting along them where they converge to the desired tip width. The tips are parallel from that point. Then the whole limb bends but the tips bend a lot less, which is generally desirable to improve the string angle and return speed.
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There is a lot to be said for pyramid bows. I don't make them much anymore but I have to say I feel they are one of the most consistently good performing designs we have with self bows. They may not be the absolute fastest but they perform in the upper ranges and they are also durable, and low in handshock.
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Just out of interest I could get anything to stick polycarbonate to polycarbonate especially as the tips were so slim >:(.
So I stuck a sliver of rubber strapping edge on, onto the tip with CA and sawed a little notch into the rubber on the band saw! :laugh:
Del
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I found the passage in "Mechanics of Pre Industrial Technology" by Cotterell and Kamminga, on bows was helpful in understanding pyramid bows. I think the relevant pages can be seen online on Google books.