Question about how a pyramid bow works...

[toomanyknots]

Well I remember tim baker saying if you taper on the sides that has the same thickness to a point and then bend it, it will bend in a perfect circle. I am wondering about pyramid design, because I taper from 2 1/2" to 1/2" everytime, and no more. Works fine. Never have to tiller except if I screw up profiling the bow initially. My question is this:

- If I widened the entire pyramid profile, maybe by 1", so it went from 2/ 1/2" tapering to 1/2" to 3 1/2" tapering to 2 1/2", would this result in the same circular tiller when limbs are at a consistent thickness? It's seems to make sense that is would in my head currently, but I know there are alot smarter people on the forum who know alot more than me.

[Badger]

   I have gone round and round with Tim on this. I really couldn't say for sure either way but it does seem to work. Tecnicaly at any given length their is only one correct thickness regardless of draw weight. Adding width would be the way to add draw weight. Or if you made the bow longer you could make it thicker or shorter it would have to be thinner. All weight adjustments to be made from th sides. The big question mark has always been how do you find optimum thickness. The mass principle is an attempt at narrowing this down and started with the pyramid bow. Steve

[jwillis]

It should bend the same. Since the thickness is not changing, the change in width at each increment of length will determine the change in the bending strength at each increment along the limb. So, since the width is narrowing the same amount at each increment in length (a direct relationship), the resistance to bending also will change the same amount at each inch of length, giving it a circular side view full draw profile.

Steve, I think that is the challenging thing about the mass principle in application...knowing how to translate the predicted mass into the best combination of thickness and width for a resulting optimum combination...knowing how wide to start with and knowing when to stop narrowing after we get it bending correctly. I guess we need to have an idea what is the optimum strength-to-weight ratio for the material being used.
Jim

[George Tsoukalas]

Bows with a pyramid design should have a circular tiller. Near handle wood should do more than its share  If tillered elliptically more set will result. IMHO. Jawge

[Badger]

  Jim, actually is is a lot simpler that it might seem. Once you have a bow floor tillered it doesn't take that much more mass removal in thickness to hit desired weight so all you need to do is weight the bow once floor tillered and then adjust the width so mass is somewhat in line, allowing enough extra mass for some thickness trimming which is usally less than 2 ounces.

     Jawge I agree with you, circular tiller is the only correct tiller for a pyramid. Slight modifications to the pyramid shape can allow for slight mofications to the tiller shape. What has always confused me is how the pyramid can produce a circular tiller no matter what the starting width is. It does seem to work but I just haven't been able to get it in my head why. Steve

[jwillis]

Steve, thanks for explaining how to apply the principle!  Jim

[toomanyknots]

I screwed up the dimensions, I meant 2 1/2" tapering to 1/2" adding an inch making it 3 1/2" tapering to 1 1/2"

"The big question mark has always been how do you find optimum thickness."

ARG, I was just about to ask what thickness you think I should make this bow I'm dwelling on,...

" I have gone round and round with Tim on this. I really couldn't say for sure either way but it does seem to work"

Awesome steve. Pure awesome. You have made me very happy today. You have no idea. ... Just went out and got my monthly "play around with" red oak today. Found some ok pieces.Here is a plan for a bow, not a set in stone plan, just trying to figure a plan out:

Symmetrical

54" end to end, not counting siyahs. Actually 58", but 2" on each end will be taken up by siyahs.

9" non bending handle (probably just shouldn't ask, , you probably read my other thread)

Distance from top limb/bottom limb from handle: 22 1/2". Making working limb total 45"

Pyramid taper from 3 1/2" to 1 1/2" at end where siyah could connect.

Held at 6" reflexed and sinew backed.

Siyahs around 6" - 7"

Continuous thickness at ?

This is the only hole left in my plan. If I can't figure it out, I will most likely go with 2/8" I JUST made a bow with the same dimensions as above except the taper was 2 1/2" to 1/2". The thickness was 3/8". It pulled 45# at 26", but I pulled to 28" and did not weight it yet. I am just looking for 50 - 70, but mostly, just something shootable. I am scared of the sinew over powering the red oak, but if it brakes I will just take the sinew off and use it for glue. Maybe I will just do a layer or two at most. One layer to just protect the back. ?? Naw, I know red oak is a bad choice for sinew, but I don't have money to use anything else, and it just will eat at me if I don't try it once.