Calculating Pyramid Bow Limb Width Taper

[FlyinCedar]

Ok...I have actually been thinkin of making a pyramid bow since reading about them in the traditional Bowyer's Bible.... Would someof you guys be willing to share your dimensions, including limb thickness and resulting draw weight? Also, the one shown in the Boyer's Bible tapers to a point, and has a wrap to hold the string, because it is too narrow for string grooves...were your done like this, or were the tips left wide enough for string grooves? Thanx...John

[bvalentine002]

Originally posted by tim baker:
Assuming uniform limb thickness and triangular fron view, the bow could be any width at the fades, 1" to 10" and stress along the length of the limb will be equal at all points, with circular tiller resulting. That's if the straight sides are aiming at a point at the nocks. This is straigh out of the engineering text books. It's against all intuition, but true. If the sidea are aiming at 3/8" instead of a point then the outer limbs will be a bit stiffer, the midlimb and grip bending slightly more. Tim

If you are right (and I'm not sure I believe you because this is not intuitive!!!       ), that is great news!

The next question...how can you get eliptical tiller from a pyramid bow?

-Brett

[Rangeball]

Originally posted by bvalentine002:
 

Originally posted by tim baker:
Assuming uniform limb thickness and triangular fron view, the bow could be any width at the fades, 1" to 10" and stress along the length of the limb will be equal at all points, with circular tiller resulting. That's if the straight sides are aiming at a point at the nocks. This is straigh out of the engineering text books. It's against all intuition, but true. If the sidea are aiming at 3/8" instead of a point then the outer limbs will be a bit stiffer, the midlimb and grip bending slightly more. Tim

If you are right (and I'm not sure I believe you because this is not intuitive!!!        ), that is great news!

The next question...how can you get eliptical tiller from a pyramid bow?

-Brett [/b]

Brett, I thought I was onto this with my question, which Tim quickly shot down  

I suspect it will have to do with belly tapering, thicker near fades and thinner toward tips with tips stiff.

I also suspect the response may be something like even width to mid-limb then taper to nocks and leave tips stiff, which is the common shape recommended on many sites such as Mickey and George's (among many many others).  Seems like this design is basically a modification of the pyramid style.

If one were to overbuild a pyramid a bit, I suspect they could avoid near grip set (with experimentation), but possibly at the risk of performance?

Tim, did the true pyramid bows outlined in TBB all suffer from near grip set?  If not how was this avoided and performance maintained?

[tim baker]

RedDwarf: You could say it's because the limb is narrower there, or that that area was not thick enough and without proper thickness taper to yield even strain along the limb. PS:  For a parallel-limb bow it's better to start narrowing to the nocks at about midlimb for most such designs, Narrowing farther out adds outer limb mass with no increased safety or reduced set.

FlyinCedar: Limb width will be determined by the wood used--poplar being very wide, ipe being very narrow. Thickness always determines itself during the tillering process--at identical thickness every stave would yield a different drawweight. So decide the length bow you want, the type wood to be used, then 'design' your bow. If of a mid-density wood like oak or maple, 66" long, 50lbs at 28" then 2.5" at the fades is about right, tapering as if to a point. You can aim to a point, then during that last 2" or so stay say 3/8" wide to leave room for side nocks, or continue almost to a point and tie or glue on a tiny back nock. I prefer one with a step in it to catch the string, so the string won't rest directly on the narrow tip wood.

Brett:  Good for you. A skeptic. That will save you from swallowing a lot of baloney. This is an easy thing to prove: buy a 1/4" wood slat at HomeDepot, cut it to pyramid shape, clamp the wide end, then pull on the pointed tip and watch perfect circular tiller result. This will be true if the slat in 1" wide of 1-foot wide. I learned of this in Archery The Technical Side. I wasn't so much skeptical, considering the source, as surprised. But after some thought it made sense: A point half way between point and base will feel half the leverage the base feels, so needs to be half the with to feel equal strain, etc. at any point along the limb. And this holds true for any width pyramid.

Per a few posts above, a pure pyramid is good, but not the best-performing design. The inner limb should be somewhat elliptical, to avoid near-grip set. Do this by slight thickening of a pyramid bow's near-grip wood, or letting the first one-forth or so of it's length be parallel, that portion tillered elliptically. Tim

[HACKSAW]

I think it is time we heard from O.L.
Hacksaw
Horace Worcester

[Rangeball]

Originally posted by HACKSAW:
I think it is time we heard from O.L.
Hacksaw
Horace Worcester

Why's that?

[bvalentine002]

Just to clarify: my understanding of an eliptical tiller is one in which the elipse would be up vertical (like a 0 ) and not like an egg laying on it's side (sorry, no better description!).

I remembere reading in TBB that the author made a hickory pyramid bow that shot as fast as almost any glass longbow. I lovevd the iddea because tillering the sides is much easier (and slower) than tillereing the belly.
Thanks, Guys!
Brett

[tim baker]

Brett: Elliptical tiller: Near grip wood barely bends, then bends progressively more severely as you move towards the tips. For stack reasons you don't want the outer limb to bend much though, unless it's an unusually long bow. But that's another story.

If it was in the TBBs about pyramid bows I likely wrote it, but have figured things out a little better since then, The fastest bows are longish, with relatively long, stiff, center sections and very narrow light outer limbs, strong elliptical tiller. My best such straight-stave bow, 54lb at 30.5", shot a 500-grain arrow at a witnessed speed of 192fps. Some of the witnesses were fiberglass guys, so you can imagine the evil pleasure we wood guys felt. Steve, Badger, was the shooter.

If you start out with uniform thickness along the limb you can't tiller from the side of course. Tillering from the side is a bad idea anyway, because you should lay out the front view of the bow before you start. That shape is an important part of the design process. Tim

[bvalentine002]

Stacking is a familiar experience for me! I'm 6'4" and I draw 31 - 31.5" (to low point of the grip). I just moved into the world of glass bow building. I have found that even with a 70" bow I'm approaching the stacking point. I'm using a reflexed form to help get around that...but that's another conversation all together.

Thank you all for your help!
-Brett

[Rangeball]

Tim, Steve, Anyone...  

Had a thought.

Would heat treating the belly help prevent near grip set on a pyramid bow?

[badger4x]

Range, heat treating seems to help reduce set most anywhere on the limb, heat treating can even reverse existing set, Steve

[Rangeball]

Interesting...  

I really like the looks of the pyramid design, and have even thought of building a heavier draw weight one, so when I do get set it may still give me the cast of a 50#er or so...

I have lots of bows in the thinking about them stage.  I need to put one into action, and this may be as good a place as any to start  

[NorthShoreLB]

I made one piramid style bow (kind of    ) and to me the advantage of the piramid style is that the fades are quite stiff, so no set there.

stiff out of the fades, makes the limbs of a longbow effectivly shorter, less limbs to move= more performance, without sacrifacing the stability of a longer bow.

that was my reasoning when I crafted mine,   71# @ 27"

Manny

[NorthShoreLB]

BTW,

I go with feel and sigth, no set mesuraments        

Manny