Bows by the numbers - modelling a bow before cutting timber

[Aussie Yeoman]

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.

[sleek]

Fascinating work. What are the limbs dimensions?

[Aussie Yeoman]

Here they are!

[sleek]

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.

[willie]

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/

[Hamish]

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.

[willie]

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)?

[Aussie Yeoman]

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.

[Aussie Yeoman]

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.

[Woodbear]

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

[willie]

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

[sleek]

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.

[sleek]

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.

[Aussie Yeoman]

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. 

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.

[Aussie Yeoman]

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.