Can making a bow wider lower the mass

[Badger]

My experience is also that narrow Ipe bows are better.

Steve
You must remember the Bamboo backed Ipe blank you sent me years ago.  It was extremely narrow at 7/8" with a very thick Bamboo backing, the bow was a nightmare to tiller out.  If I remember right I tillered it out as a flightbow, 25" or 26" draw.  You won the auction at paleo and when you tested the bow you said it was extremely fast.  I was wondering why that bow was so fast, I do have a theory.

      I rememeber the bow but not in detail, I am pretty sure it was r/d with a couple inches reflex. Ipe seems to hold up pretty well in narrow bows most of the time. I have seen some that chrsaled but not many. I think the flat belly you use so often is a huge key. I built a hickory backed lemonwood recently and was unhappy with how much reflex I lost. I am redoing it now about 1/2" wider and with a flat instead of rounded belly. I am curious how it will turn out.

[Bryce]

Fastest boo/ipe bow I've ever made was 1 1/8" or 1 1/16" wide. Pretty narrow. With an oval belly. Extremely fast!

[Marc St Louis]

No it was a straight limb bow maybe 64" long with about 4" of glued in reflex.  You were going to shoot at the flats but it broke on you before you were able to.  I still have pictures of that bow, here it is

[Buckeye Guy]

Steve
You know that I am just a backwoods country boy and have no clue how all this works out , and do mostly Hickory which just wants to be a bow no matter what we do to it, but when I get a hold of some of you alls beloved Hedge or BL they most always tell me that  they want to be 1&1/2"wide or usally more and very flat bellied .So I try to listen to them! That is all I can do , just listen for I have no other means of education to draw on unless you folks tell me that I have missed the boat and need to do otherwise.
Thanks for all you do
Have fun
Guy

[Arrowind]

well I'm reading and trying to follow.....I usually start wider but most of my bows are pretty wide by most standards...probably overbuilt. Mostly cause I'm worried I'll break them!  I'm starting to pay much closer attention to mass and it is definitely making a difference in performance.  Not sure about the relationship between wider and less mass but I have definitely seen a difference in trying to follow the mantra blackhawk mentioned..   wish I had something interesting to contribute...so I'll sit back and keep reading.

Love to read this stuff.   

[mikekeswick]

Yes just watch the set. Set tells you what is going on. One reason why I always trace the side profile of any bow i'm working on before bending it. I've found this much better than just doing it by memory.

[Marc St Louis]

One reason why I always trace the side profile of any bow i'm working on before bending it. I've found this much better than just doing it by memory.

The only time I do that is when I am teaching someone, to give them an idea of what to shoot for.  For myself I just start a bit wider then reduce the width to finished dimensions as I approach final tiller

[Slackbunny]

badger sorry I didnt explain propery and our messages overlapped

what I meant was that if you increase the width by 8mm then that is equilivent to increasing the depth by 1 mm ,in increasing limb strength.....I think you said that; if we add 25% to the width we only gain 25% draw weight, if we add 25% to the thickess we double draw weight. isnt this saying the same thing as 1:8?

  I see what you mean, thats just a standard engineering formula I believe, double the thickness 8 times as strong,

Yes it is is a standard formula. The principle is contained in the formula for the moment of inertia. For example the moment of inertia of a rectangular cross-section is: I=(b*h^3)/12, moment of inertia equals the base times the height cubed all divided by twelve.  So if you double b, you simply double "I", and if you double h you increase "I" by a factor of 8. "I" is a factor that is multiplied to the denominator of the stress equation. So if you double I you divide the stress that your specimen is feeling in half, and if you double h, you divide your stress by 8.

"I" is purely a geometrical value and remains the same for any material. It only changes when the shape of the specimen changes. "I" is different for each cross-section. But regardless of what your cross section is, that relationship of doubling the thickness will always give you 8 times the strength, and doubling the width will always give you double the strength. (At least for every shape I've looked at).

But the stress formulas that "I" is used in assume certain things. For example they assume a homogeneous material which wood is not. These equations do not account for things like grain or knots or growth rings. And they certainly don't account for crushed or stretched fibers. It is in these areas of uncertainty that the engineering stops and the craftsmanship begins.

[PatM]

It also doesn't account for reflexing from heat treating or even heat treating while kept straight. You can take a material of a given value and that all changes when you apply heat and/or reflex.
 Of course the 'new" material from that process will still follow the rule.

[Slackbunny]

It also doesn't account for reflexing from heat treating or even heat treating while kept straight. You can take a material of a given value and that all changes when you apply heat and/or reflex.
 Of course the 'new" material from that process will still follow the rule.

True, also variable moisture content can have a significant affect on a bow from day to day.

I do think that it would be possible to come up with a "General Equation of Bowyery" that would take into account all the major factors. You would need all the geometrical information which given the tapering thicknesses and widths of a bow would probably be an integral of some sort. Obviously the mass and mass distrubution would need to be accounted for as well. Then you would need factors that would account for grain orientation, and grain density. Knots could probably be dealt with similar to the way stress concentrations are in traditional mechanics. You would need a factor for moisture content, and you would need results of a bend test done on a standard sized scrap peice.  Backings would add an extra layer of complexity, and multilayer composites would be a nightmare.

It would be a mega complicated equation, and there would be a lot of room for error, but it would be cool. 

[Badger]

  Instead of formulas I think the idea is to develop work bench techniques based on formulas that are not neccesary to actually know. Wood is close enough in behavior to start off with averages just based on density and then as you build the bow and see how it behaves modify it based on experience.

[Slackbunny]

  Instead of formulas I think the idea is to develop work bench techniques based on formulas that are not neccesary to actually know. Wood is close enough in behavior to start off with averages just based on density and then as you build the bow and see how it behaves modify it based on experience.

I agree. But the engineer in me is always drawn to elegant equations. I just can't help it. Once I get started with the mathy stuff I find it hard to break away from it. Maybe I'm a nerd, but I just love math.

[Badger]

  Instead of formulas I think the idea is to develop work bench techniques based on formulas that are not neccesary to actually know. Wood is close enough in behavior to start off with averages just based on density and then as you build the bow and see how it behaves modify it based on experience.

I agree. But the engineer in me is always drawn to elegant equations. I just can't help it. Once I get started with the mathy stuff I find it hard to break away from it. Maybe I'm a nerd, but I just love math.

   I like working with people like you, I give you the problem and you give me back the math.

[Dan K]

Math is a fail safe path to truth, if done correctly, and helps the craftsmen to understand what they know to be true but not know why?  Thanks for contributing!