Stupid question

[DC]

We need an Isaac Asimov. There's a test for you all

[KS51]

I've just some rough calculation assuming the string forms a 90 degree angle on the fingers and pulls on the tips at 90 degrees.
That would give the string tension and thus force on each tip of about 0.7 times the draw weight.
So for a 40# bow there would be 28# on each tip.
Now this doesn't even start to look at the leverage onto the siyah....
Del
(I still reserve the right to be wrong  )

Del has this correct by my reckoning.  The 40# is the horizontal leg of the triangle and the string is the hypotenus [spl?]  So, you divide 40# by .717 to get ~57#  and half of this comes from each string going away from the arrow so you get ~28.5# at the tip (This is also the Shearing force at the nock).  If the string is at a 90deg angle with the tip, then the stress going down the siyah (which is effectively straight) is based on the moment within the siyah which increases the further down the limb you go so M = F x L.  Then, the bending stress (V) is based on the moment and the section modulus ( S ) and V = M / S  or combined V = F x L / S.  Now, you also have the shearing stress (U) from the shearing force U = Fs /A.  Finally the maximum stress is the combination of the bending stress and the shearing stress ( based on Mohrs Circle)  stress max = (V^2 + U^2)^ .5  ( this is read "the square root of the sum of the squares").

For glued on siyahs you would want your glues bond strength at least 4 times as strong as the max stress to account for the shock load aspect.

Side note : section modulus is very specific to shape.  For rectangular sections, S = width x height^2 / 6

Ken

[Ballasted_Bowyer]

wow +1

I understand about that kind of math but not how to do it. Would love to see you write an article for Primitive Archer working over the forces at work in the launching of an arrow from a primitive bow (no shelf please and not cut near center.) Article should be as plain spoken as the math allows and replete with illustrations. Or maybe write a follow up to Klopsteg's "Archery, the Technical Side."

If you mean after the string is released And the arrow begins to move and accelerates around the handle, that is beyond me. Engineering dynamics involves vector calculus. I can say that the energy is not released along a straight line and there is a lot of movement in directions other than what does a hunter or warrior any good.

[Pappy]

WOW +2.  I use to be pretty good at math but gave it up when I started building bows.
 Pappy

[upstatenybowyer]

Wow +3. The buck stops for me somewhere around 11th grade. LOL. Lots of props to you math guys though. 

[Hawkdancer]

What happened to "primitive"??  If I get my draw weight/length, and the bow doesn't break, and the arrow flies true, the world is right!  And perhaps, there is meat tonight !  Hmm" Apple smoked venison!  I think someone is overthinking the process here, on the other hand, I am mathematically challenged and don't have a clue what has been said in that field.  Good theory, though.
Hawkdancer

[loon]

hang 2 weights from a string, you'll be pulling their weights added together. so the siyah is feeling the equivalent of it having a loop put on it and being pulled 20#. or I think it does... since they're at an angle it may be different? just need 2 scales to test it. tie a string to a scale that's tied to something, the other end somewhere else solid. pull on it on the center as if it was a bow with another scale. that or make a bowstring with a scale in between it (ie tied to a loop going on the bow's notch, and the hook tied to the rest of the string), and pull it with another scale.

but maybe it'll be more than that when the bow is released and then reaches brace

[Johnny K]

So... Just for fun, I grabbed a pencil and paper... This is what I came up with:)

I believe that when testing each limb separately, the only way to correctly simulate the internal forces acting on the wood fibers in that limb is to pull the tip in the exact same direction (at the same angle to the bow) as it would be pulled with when normally drawn with a regular length bow-string, and this is nearly impossible to keep track of by hand. On the first page there is a quick break-down of the applicable forces, and on the second an apparatus that I am of the opinion would be required to correctly test individual limbs by subjecting them to the same force they would undergo if the bow was normally drawn. Note that this device will only work on bows with non-bending handles.

Oh, and of course: I am not by any means an expert, there may be serious errors, I just took twenty minutes and put down some scribbles...

Enjoy!

[Ballasted_Bowyer]

The testing tool suggested is definitely on the right track. I would suggest being careful how the clamp is used because the wood could bruise or the jig could flex and give a false reading. It seems the key on the clamp would be to keep forces per unit area (stress) on the test piece similar to that experienced under duress from the bow hand. Perhaps a pair of rubber coated pegs an inch in diameter set up as a fulcrum and balance pin would make a good clamp.