Primitive Archer
Main Discussion Area => Bows => Topic started by: Aussie Yeoman on September 07, 2024, 02:14:35 am
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This week a friend and I made a pair of bows on the basis of some mathematical modelling.
I modelled a pyramid bow using non-published, aggregated/averaged data from some white oak. I used a working strain that should theoretically have induced about an inch and a half of set. Between a friend and I we made two - one 50 lb at 26 inches and the other 40 lb at 26 inches.
I haven't made exhaustive measurements, but the early indicators are that the final dimensions (thickness) are within 1 mm of the projected data generated by VirtualBow. You can see from the photos that we didn't get the finished bows to match the projections exactly, but they're pretty close. And the average set of two limbs is 40 mm - just slightly over 1.5 inches. As predicted.
You can see we didn't quite match the projected tiller shape exactly, but it's pretty close.
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Fascinating work. What are the limbs dimensions?
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Here they are!
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Thanks that's perfect. If you had made them 11 to 15 % less in draw weight what does your calculations say you should predict for set? Per mine, 11 to 15% less the ideal range for no set for white oak.
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I modelled a pyramid bow using non-published, aggregated/averaged data from some white oak. I used a working strain that should theoretically have induced about an inch and a half of set.
Aussie,
deliberately designing to 1-1/2" of set and coming in at 40mm is great. I wished some of mine came in that close. Guess it is all in the test data. Have you considered or tried a simple bend test to obtain a working strain?
@sleek
you should give it a try
https://www.virtualbow.org/
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Do you have any pics of the bow unbraced, that show where the set occurred? 40mm is a good result in my books too, from an oak board stave.
I find oak can take a lot of set, unless it's very dry or heat tempered.
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Do you have any pics of the bow unbraced, that show where the set occurred? 40mm is a good result in my books too, from an oak board stave.
I find oak can take a lot of set, unless it's very dry or heat tempered.
Hamish, I think he could have designed for any amout of set he preferred.
Not to sidtrack the design part of this thread, but should one prefer more or less set with any particular kind of wood? ie do white oak bows work out the best with a moderate ampunt of set (40mm)?
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Thanks that's perfect. If you had made them 11 to 15 % less in draw weight what does your calculations say you should predict for set? Per mine, 11 to 15% less the ideal range for no set for white oak.
Sorry Sleek I don't quite follow - is your objective to get less set or to have a lower draw weight? The thickness of the 40 lb and 50 lb bows is pretty much identical - the difference between them is the width. 40 lb is 80% of 50 lb, so the lower draw weight bow is 80% of the width.
deliberately designing to 1-1/2" of set and coming in at 40mm is great. I wished some of mine came in that close. Guess it is all in the test data. Have you considered or tried a simple bend test to obtain a working strain?
Yeah I've done heaps of bend tests. And I got a copy of al the bend test data that Tim Baker did decades ago for TBB1. The working strain is what I used to calculate the dimensions of these bows. In this case, the working strain is about 0.75%.
I've done a few different bend test styles - simple cantilever, simple supported beam, three point cantilever... But the one I want to try is a four-point bend test. This spreads the load evenly between the two inner supports, and so better simulates a bow's limb in that part of the test sample.
Do you have any pics of the bow unbraced, that show where the set occurred? 40mm is a good result in my books too, from an oak board stave.
I find oak can take a lot of set, unless it's very dry or heat tempered.
Stand by and I'll take some pictures.
I have never tried heat treating, but I may for this 50 lb job to see what happens. I'll have to brush up on my HT knowledge.
Not to sidtrack the design part of this thread, but should one prefer more or less set with any particular kind of wood? ie do white oak bows work out the best with a moderate ampunt of set (40mm)?
I'm not sure on that one. I haven't done the testing. Designing these bows to have this level of set is what allowed me to get 1 lb per mm or width at this length without an outrageous amount of set.
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I tried to take photos of the set, which turned out to be a challenge. Most of the set comes from the inner third of the limb.
Easier to show is where the stress is distributed throughout the limb - more stress = more set at that location. I could fiddle with the design more to distribute the stress throughout the limb more evenly, but the layout of this bow is super simple, and the tillering almost takes care of itself. So it has its trade-offs.
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Looks like you have a couple of nice bows there. And they appear to match the modeling to within a good tolerance.
I have a few questions:
You state that the thickness is within 1 mm of the design dimensions. Does this mean you tillered to get the desired weight at the desired draw and then measured the thickness for comparison to the model?
Are the computed cross sections and actual bows rectangular at all points on the bow, or does the modeling accommodate non-rectangular cross sections?
Have you taken draw curves to check against the model?
Why did you make 2 sets of string grooves?
How do the bows shoot?
Does your Virtualbow compute the set, or did you calculate that separately? (my copy of Virtualbow does not do set)
Do you have any setup for, or intention to measure the dynamic properties of the bows for comparison to the model?
By the way, I also think a 4 point bend test setup should be best for characterizing wood. The other test methods mentioned preferentially test a single location, which is bound to add uncertainty to the results. A 4 point test should average over more wood. It should also fail at the weakest spot in the tested section. If you have a test setup please post a picture some time.
Dave
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Yeah I've done heaps of bend tests. ..I've done a few different bend test styles - simple cantilever, simple supported beam, three point cantilever... But the one I want to try is a four-point bend test. This spreads the load evenly between the two inner supports, and so better simulates a bow's limb in that part of the test sample.
I have done conventional 3 and 4 point testing in the past but for a future bow I am considering a simply tapered minibow made from a ripping off the plank in question, putting a string on it and drawing until it retains set, and then "reverse" modeling it in virtual bow.
The working strain is what I used to calculate the dimensions of these bows. In this case, the working strain is about 0.75%.
that works good for a few of the local white woods here. maybe 70% for less set. thanks
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Reducing set is the goal, not getting a lower draw weight. I'm asking g what the program would show had you built the bows to the same dimension but with lower draw weight.
Thanks that's perfect. If you had made them 11 to 15 % less in draw weight what does your calculations say you should predict for set? Per mine, 11 to 15% less the ideal range for no set for white oak.
Sorry Sleek I don't quite follow - is your objective to get less set or to have a lower draw weight? The thickness of the 40 lb and 50 lb bows is pretty much identical - the difference between them is the width. 40 lb is 80% of 50 lb, so the lower draw weight bow is 80% of the width.
deliberately designing to 1-1/2" of set and coming in at 40mm is great. I wished some of mine came in that close. Guess it is all in the test data. Have you considered or tried a simple bend test to obtain a working strain?
Yeah I've done heaps of bend tests. And I got a copy of al the bend test data that Tim Baker did decades ago for TBB1. The working strain is what I used to calculate the dimensions of these bows. In this case, the working strain is about 0.75%.
I've done a few different bend test styles - simple cantilever, simple supported beam, three point cantilever... But the one I want to try is a four-point bend test. This spreads the load evenly between the two inner supports, and so better simulates a bow's limb in that part of the test sample.
Do you have any pics of the bow unbraced, that show where the set occurred? 40mm is a good result in my books too, from an oak board stave.
I find oak can take a lot of set, unless it's very dry or heat tempered.
Stand by and I'll take some pictures.
I have never tried heat treating, but I may for this 50 lb job to see what happens. I'll have to brush up on my HT knowledge.
Not to sidtrack the design part of this thread, but should one prefer more or less set with any particular kind of wood? ie do white oak bows work out the best with a moderate ampunt of set (40mm)?
I'm not sure on that one. I haven't done the testing. Designing these bows to have this level of set is what allowed me to get 1 lb per mm or width at this length without an outrageous amount of set.
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I have a few questions:
You state that the thickness is within 1 mm of the design dimensions. Does this mean you tillered to get the desired weight at the desired draw and then measured the thickness for comparison to the model?
Dave
I just want to point this out.. Thats exactly how folks should be doing it, you reduce the thickness of the bow to reach your draw length, not to reduce the draw weight. Too many people think wrong when tillering and that's what leads to set very often. The bows over all width is what makes the bows draw weight. I'm sure you knew this already, but felt it's important enough to highlight and not let it be glossed over.
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So, what I did was cut the bow's limbs out just oversize (in thickness, anyway) and then tillered as normal, seeking out the target draw force while keeping to the projected tiller shape as much as I could. The limbs ended up being just slightly thinner than the calculated dimensions.
The computed sections are all rectangular. The real bows have limbs that are ever so slightly rounded around the corners, and the handle more generously so. Especially in the handle, I figured the change in deflection was small enough to disregard.
I've not yet shot mine, nor have I measured F/D curves. A project for a different weekend. But I love data so it's something I should do. :D
The two sets of nocks at each end are for the bowstring and the stringer. My stringer is just a long length of paracord with a loop at each end.
The version of VirtualBow I have doesn't calculate/project set. I just fiddled with the design so the model had a working stress that I knew should theoretically produce that much set. I think your spreadsheet is probably the most advanced of all of us who have such programs in modelling bows. Actually Alan Case's SuperTiller might do it too... But mine definitely doesn't and neither does VirtualBow.
Do you have any setup for, or intention to measure the dynamic properties of the bows for comparison to the model?
I'm not sure I can. Could you elaborate?
A dedicated 4PBT setup is something that's been percolating in my mind for a few years now. When I build one I will definitely share.
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Indeed. When I teach my classes I tell students that the width determines the draw weight, and the thickness determines the draw length.
I have a few questions:
You state that the thickness is within 1 mm of the design dimensions. Does this mean you tillered to get the desired weight at the desired draw and then measured the thickness for comparison to the model?
Dave
I just want to point this out.. Thats exactly how folks should be doing it, you reduce the thickness of the bow to reach your draw length, not to reduce the draw weight. Too many people think wrong when tillering and that's what leads to set very often. The bows over all width is what makes the bows draw weight. I'm sure you knew this already, but felt it's important enough to highlight and not let it be glossed over.
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Reducing set is the goal, not getting a lower draw weight. I'm asking g what the program would show had you built the bows to the same dimension but with lower draw weight.
Ah yes, I'm picking up what you're putting down now. Unfortnately the bulk of my bend test data is currently on a dead laptop, and I've not yet been able to rescue the data.
I can't remember if theres a linear or exponential relationship between working strain and set. Woodbear might know off the top of his head. Reducing the working strain by making the limbs thinner would definitely reduce set. However you'd have to make the limbs wider to bring the draw weight back up again.
You'd know this already of course but I'm pointing this out for the benefit of digital archaeologists who will excavate the internet hundreds or even scores of years from now.
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I just want to point this out.. Thats exactly how folks should be doing it, you reduce the thickness of the bow to reach your draw length, not to reduce the draw weight. Too many people think wrong when tillering and that's what leads to set very often. The bows over all width is what makes the bows draw weight. I'm sure you knew this already, but felt it's important enough to highlight and not let it be glossed over.
Wait wait wait... So after nearly 4 years of me being on this forum pretty much daily I learn this TODAY??? I mean, I know the wider the limbs, the thinner they have get to accomodate for a certain draw length, but I have never thought about it in that way! It all makes so much more sense now! (A)
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does the modeling accommodate non-rectangular cross sections?
Hi Dave,
Stefans Virtualbow app only accomadates retangular sections, but lets you easily design multi lamination bows with different materiels ("Traditional" cored "glass" Bows). I think one could approximate a non-retangular crossection by creating layers with differing stiffnesses, the MOE of a layer being proportional to the desired width in the crossection
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Absolutely! Glad you saw the thread then! Yes, the verbiage that describes tillering is very wrong and leads to incorrect conclusions when people say things like, "tillering the bow down" implying a drop in weight, when what they are actually doing is decreasing the bows bend radius allowing for a longer draw. It's a key element in bow making and why I say that most folks tiller a bow wrong, and as a side note, often make their bows to narrow and or short, due to being over poundage for the bows dimensions.
I just want to point this out.. Thats exactly how folks should be doing it, you reduce the thickness of the bow to reach your draw length, not to reduce the draw weight. Too many people think wrong when tillering and that's what leads to set very often. The bows over all width is what makes the bows draw weight. I'm sure you knew this already, but felt it's important enough to highlight and not let it be glossed over.
Wait wait wait... So after nearly 4 years of me being on this forum pretty much daily I learn this TODAY??? I mean, I know the wider the limbs, the thinner they have get to accomodate for a certain draw length, but I have never thought about it in that way! It all makes so much more sense now! (A)
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Set in the limbs looks pretty good. Simplicity and effectiveness, and speed of manufacture vs perfection there is always a trade off. I agree you could tweak the design so it doesn't take as much set up near the fades, but that defeats the purpose of your experiment. I would be really happy with your results, and I'm sure any student in your bow building class would be too.
I have made bows from the charts in Elmer's Target Archery, which were mathematically designed, too. They have a similar distribution of set, ie slightly more set near the fades than I would find ideal. Nonetheless they are very good bows, and still have relatively low set overall, shoot really well.
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Thanks for the answers to satisfy my curiosity.
I agree that cutting the thickness 1mm or 2mm over the design dimensions and carefully thinning to achieve the desired draw at weight is the appropriate cautious way to approach making a bow “by the numbers”. Try as I might to cut that 1-2mm (1/16”) over thickness, there is always some place a wiggle with the band saw (or hatchet) makes the cut much closer than intended.
In order to predict set mathematically, one needs to have bend test data that measures both set and total sample deflection vs applied force. I am glad to hear that the work put in digitizing Tim Bakers bend tests has proved useful. I am curious what version of the table you have. I have a copy with the values, but cannot find the version with the excel formulas that calculated the values. As I recall the “working strain” values are defined as the point where the sample has taken a set of about 8% of deflection.
To elaborate on what I mean by the dynamic properties of the bow:
My program and Super tiller both calculate the “static” forces and shape of the bow “paused” at full draw. The best part of Virtualbow is making the dynamic modeling of the bow accessible in a usable software package. By dynamic, I mean modeling what happens when the arrow is released. Virtualbow shows a fascinating evolution of the shape of the limbs and distribution of the released energy among the various components of the bow and arrow during (and after) the acceleration stroke. The problem is, it is still very theoretical, and needs comparison to real bows to validate and/or correct the model. There are a number of assumptions & estimates; like perfect instantaneous release, damping factors for wood and string, string modulus, string mass, and center serving mass, that go into the model. Some of these are measurable, and some need modeling results to refine the assumptions and input to the model.
While measuring the movement of all the moving sections of the bow & arrow is a daunting task, the most basic dynamic test is to measure the energy delivered to the arrow compared to the energy expended drawing the bow. If you have access to a chronograph, measuring the speed of a range of arrow weights, from say 8 to 16 grains per pound, would allow computation of the kinetic energy delivered to the arrow a function of arrow mass. Combined with computing the energy represented by the area “under” the draw curve, this allows computation of the efficiency of the bow as function of arrow mass. The efficiency vs arrow mass can be compared to the efficiency predicted by the model. Armed with this info one could adjust some of the inputs to the program to better match reality. If we can get close to predicting arrow speed, I will be more inclined to believe the dynamic results as relates to those “fascinating” shapes & vibrations predicted for the bow limb in the acceleration stroke.
Dave
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Thanks for the answers to satisfy my curiosity.
I agree that cutting the thickness 1mm or 2mm over the design dimensions and carefully thinning to achieve the desired draw at weight is the appropriate cautious way to approach making a bow “by the numbers”. Try as I might to cut that 1-2mm (1/16”) over thickness, there is always some place a wiggle with the band saw (or hatchet) makes the cut much closer than intended.
In order to predict set mathematically, one needs to have bend test data that measures both set and total sample deflection vs applied force. I am glad to hear that the work put in digitizing Tim Bakers bend tests has proved useful. I am curious what version of the table you have. I have a copy with the values, but cannot find the version with the excel formulas that calculated the values. As I recall the “working strain” values are defined as the point where the sample has taken a set of about 8% of deflection.
To elaborate on what I mean by the dynamic properties of the bow:
My program and Super tiller both calculate the “static” forces and shape of the bow “paused” at full draw. The best part of Virtualbow is making the dynamic modeling of the bow accessible in a usable software package. By dynamic, I mean modeling what happens when the arrow is released. Virtualbow shows a fascinating evolution of the shape of the limbs and distribution of the released energy among the various components of the bow and arrow during (and after) the acceleration stroke. The problem is, it is still very theoretical, and needs comparison to real bows to validate and/or correct the model. There are a number of assumptions & estimates; like perfect instantaneous release, damping factors for wood and string, string modulus, string mass, and center serving mass, that go into the model. Some of these are measurable, and some need modeling results to refine the assumptions and input to the model.
While measuring the movement of all the moving sections of the bow & arrow is a daunting task, the most basic dynamic test is to measure the energy delivered to the arrow compared to the energy expended drawing the bow. If you have access to a chronograph, measuring the speed of a range of arrow weights, from say 8 to 16 grains per pound, would allow computation of the kinetic energy delivered to the arrow a function of arrow mass. Combined with computing the energy represented by the area “under” the draw curve, this allows computation of the efficiency of the bow as function of arrow mass. The efficiency vs arrow mass can be compared to the efficiency predicted by the model. Armed with this info one could adjust some of the inputs to the program to better match reality. If we can get close to predicting arrow speed, I will be more inclined to believe the dynamic results as relates to those “fascinating” shapes & vibrations predicted for the bow limb in the acceleration stroke.
Dave
Dave, again i say, i am absolutely excited to see you on here. Is virtual bow one of your programs? Regardless, id love your input on and help with, getting a very simple formula and theory ive got proofed and on a spreadsheet, if you can. Or, just another deep thinking math guy like yourself to bounce ideas off of. I dont know what time zone you live in, but id like to give you my umber if we can chat?
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and some need modeling results to refine the assumptions and input to the model....
Stefan, the developer of Virtualbow mentioned the need for feedback a while back....
Hello everyone,
I'm the author of that program, willie has pointed me to this thread. I'm glad some of you like it and find it useful. Keep in mind that it's not yet finished by far. It's more of a starting point. That's also why I'm always interested in suggestions and feedback.
and additionally
http://www.primitivearcher.com/smf/index.php/topic,65115.msg916720.html#msg916720
Perhaps more recent info at
https://www.reddit.com/r/VirtualBow/
or
https://github.com/bow-simulation/virtualbow/issues
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Virtualbow is not my program, but I like it, have used it and exchanged email with and given some feedback to the author, Stefan.
He has stated the need for validation, and invited feedback on how the program matches real world measurements. This is part of the reason for my encouragement of measurements of the arrow speed, for a bow of known dimensions and material. Providing such feedback is not as easy as it sounds, as one really needs all the details to enable adequate modeling the bow, including string material # of strands, etc. etc. Even measuring the arrow speed is fraught with uncertainty, as there seems to be a significant difference in an Olympic archer's release, a hunter's release and a flight shooter's release.
Sleek,
I sent you a PM with contact info.
Dave
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Question for smart guys! Can you compute the ideal arrow mass or weight for a flight arrow shot from a fifty pound bow given the force draw on the bow? I have found that to light an arrow dies fast and to heavy always falls short in flight situations. I’m sure mass placement in the arrow is as important as mass placement in the bow.
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Y’all must be scratching your head or that’s a stupid question. 🤠🤠