Main Discussion Area > Bows
Bows by the numbers - modelling a bow before cutting timber
Woodbear:
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
sleek:
--- Quote from: Woodbear on September 10, 2024, 02:21:21 am ---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
--- End quote ---
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?
willie:
--- Quote from: Woodbear on September 10, 2024, 02:21:21 am ---and some need modeling results to refine the assumptions and input to the model....
--- End quote ---
Stefan, the developer of Virtualbow mentioned the need for feedback a while back....
--- Quote from: stfnp on February 26, 2019, 01:45:42 pm ---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.
--- End quote ---
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
Woodbear:
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
Selfbowman:
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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