Board Bow Schematics

[BryBow]

What is the mathematical formula for determining the thickness of a board to attain a desired pull weight if ripping on a table or band saw before gluing on the riser and tillering?

[Ifrit617]

There isn't one.

Jon

[Grasshopper Mouse]

Yeah, pretty much the same answer you got on TradGang: there are no schematics for making self bows.
Every piece of wood is different and you have to work with what the wood tells you.

Guy

[JackCrafty]

At first I wasn't going to try to answer his one because you guys did a good job of answering already.  I almost clicked on the next topic within a few seconds...

But the more I thought about this one, the more interesting it became.  Would it be possible to create a mathematical formula for the shape of a bow?  Just input wood type, poundage, and draw length and out pops a set of pre-tillered dimensions?  And why isn't there a formula?  Are we too dumb to come up with one, even one for the sake of argument?

Well, I'll put one out there.  It works with any type of wood.  It assumes that the poundage is small enough that you can glue a riser onto the wood for a handle and not look silly.  So, here it is.

2" wide x 1" thick x 68" long.  Glue on a riser and a backing, taking into account any curvature in the side profile, and let dry.  Begin tillering.

[BryBow]

It's true that you can just tiller a bow till your sweet little pea brain hearts content. I do it all the time now. Thanks for your great thought processes and kind answers.

[bubby]

Lots of variables to consider, design, wood type length, getting a mathematical equation to do this with a wood bow kinda takes the fun out of it, be almost like building a glass bow

[Aussie Yeoman]

There are actually formulae for calculating selfbow dimensions. There are a few bowyers who have sunk hundreds of hours into creating spreadsheets that will give very precise measurements for bows of desired proportions and various statistics.

Nagler, Hickman et al championed the idea of using formulae for making bows.

There are lots of naysayers about who will say that doing such takes away from the heart and soul of wood bowyery. But through the use of such devises and stratagems, Nagler reported he was able to use gnarled, twisted character staves that other bowyers passed over for being too difficult.

Now, I could send you my spreadsheet for making bows, but that'd be cheating. Instead, I will post this link to a long and unfinished series of posts on how to figure it out yourself:

http://ozbow.net/phpBB3/viewtopic.php?f=34&t=5450

With what I've included there, it will be possible to figure out how to mathematically calculate dimensions for a pyramid bow of whatever dimensions you require.

Dave

[BryBow]

Well... That's what I'm talking about. I thank you for your reply Aussie. I hope more forum participants will take advantage of your link.

[PEARL DRUMS]

Self bows and board bows are totally different critters. If you apply these formulas to a board you will not get the same results unless they tested boards of all different grain orientations separately. 1/4 sawn doesn't compare to rift sawn doesn't compare to flat sawn.

[JackCrafty]

Interesting link.  Lots of work went into the answers.

The explanations try to show how math can be be used to create bows with a rectangular cross section and a basically pyramid design.  This is fine if that's what you are looking for.  But you still have to build the bows and fine tune everything.  The dimensions may end up being significantly different.  Bows with trapped/rounded bellies or backs are not discussed, as far as I can tell.  And as Pearl Drums mentioned, the way the wood is cut will affect the strength and bending characteristics.

If you want to get in the ballpark of the dimensions before you start, so you can save yourself some time, then developing formulas may help.  As for me, I can rough out a bow in about the same time as it would for me to crunch the numbers and check my answers.  And then I still have to rough it out and get it floor tillered before I can start the real tillering.

I can see how this might help someone in the beginning of a professional bow making start-up.  After a while, though, the shapes will come naturally as you gain more experience.  Professional bowyers keep track of their final measurements and keep them in a book or something.  This book is usually well guarded because it contains the "secret recipes" that help a bowyer make a living.

Not many bowyers are willing to hand over their recipe book.  That's why this question may not get a direct answer.

[BOWMAN53]

ive made two hickory board bows with the same dimensions and ended up with different thickness, not a huge diference but a difference just the same. not to mention that even after the bow is made and it can lose weight after being shot in, and the humidity affects bows alot too. so even you did hit your target weight, it can change. i dont think there ever will be an exact formula, just a rough estimations to get you close. theres just too many variables to account for.

[Aussie Yeoman]

Like I said earlier in this thread, the processes in the link I posted were just the beginning.

The next stage after that is to apply the same principles to different bow shapes in order to get different tiller shapes, such as ELBs, regular elliptically tillered longbows, Mollegabet, paddle, and everything else. It has just been a matter of time in writing it all out.

The next stage after that is to demonstrate how to calculate a shifted neutral plane, and the effect of different cross sections. In this way, it is possible to take into account different cross sections, such as a trapped or crowned back, flat vs rounded vs trapped belly and so on. Again: I did say the link I posted was not complete.

When I make a bow with this method, I usually do a bend test on a sample of wood from the same board I will make the bow from. In this way I know the properties of the piece of wood I will be using quite accurately. But that being said, it is possible to use previous test results, make it a little oversize, then dial it in. I did this recently a number of times and made full draw longbows consistently in under three hours.

By using these methods, it is possible to learn things about bow design in a very short time that may otherwise take a very long time indeed to learn. Such as a bow with consistent thickness should not in fact taper in straight lines, but be ever so slightly bulged near the flares, and ever so slightly concave near the tips.

I used to make by handle risers obscenely thick in an effort to make them stiff. After starting with calculating dimensions, I learned I was wasting wood, and found I could get away with a much thinner handle and still achieve sufficient stiffness.

It also means that unconventional or even unknown (as in 'I have no idea what this piece of wood it but it has nice grain) woods can be dependably turned into reliable bows.

I know people don't like this method of bowyery. But you know what? We're all bowyers together. I used to get all in a frazzle when glass bowyers would call their bows 'traditional'. Now I just accept that they have chosen to make the bows they make, and I have chosen to make the bows I make. They make very nice looking bows, and I do what I can.

[bubby]

I guess if your an engineer or love mathematical equations that's the way to go, just gives me a friggin headache , bub

[Ifrit617]

I guess if your an engineer or love mathematical equations that's the way to go, just gives me a friggin headache , bub

LOL +1 I despise math.

Jon