Bows by the numbers - modelling a bow before cutting timber

[Aussie Yeoman]

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.

[Zugul]

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! 

[willie]

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

[sleek]

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! 

[Hamish]

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.

[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]

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?

[willie]

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

[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.

[Selfbowman]

Y’all must be scratching your head or that’s a stupid question. 🤠🤠