Del's Pyramid Taper Test!

[PatM]

Whether it is a building a bow or a scheme, a pyramid is ugly. 

[Springbuck]

To me this both makes sense and is utterly counterintuitive.  I think we all owe a debt of gratitude to Del for clearly illustrating the principle.

Kinda +1. 

[Springbuck]

OK, I DO want to say "I told you so!" And you, and you, and you for years.  If you can find my posts on "pyramid" bows you will find I have literally been saying this for many years and having it fall on deaf ears. Not only here but on the leatherwall too.

I believed you, Jim!  I believed Baker when he said it, too, and it surprises me that so many experienced guys didn't.

I think the confusion often comes in because A. not every piece of wood can be made into a pyramid bow, and B. One does have to tweak them for practical reasons, such as the fact that the tips don't taper right to popints and need that 1/4" or whatever, and you do have to come down from fades.

[Jim Davis]

...
I think the confusion often comes in because A. not every piece of wood can be made into a pyramid bow, and B. One does have to tweak them for practical reasons, such as the fact that the tips don't taper right to popints and need that 1/4" or whatever, and you do have to come down from fades.

Absolutely right.

Pat M, that's why I dislike the term "pyramid" for this design. I think Tim Baker may be the origin of that word usage. The  bows are much closer  to an Eiffel Tower shape than a squat pyramid. I'd like a better term, though triangle doesn't quite do it either.

[Jim Davis]

What surprises me is how they both bend so much in the handle.
Thanks, Del. Jawge

In Del's experiment, the whole test piece is limb, from tip to tip. With a stiff handle in there, the limbs start, and start  bending, at the outer end of the fades. From there on, they will look like Del's test limbs.

Jim

[George Tsoukalas]

Yes, Jim, but I would have thought the wider inner portions would have bent less. Not sure I see that. Jawge

[Springbuck]

What surprises me is how they both bend so much in the handle.
Thanks, Del. Jawge

I think this is both a function of ACTUALLY bending (slightly) in the handle, and (with actual bows that have fades) it APPEARING to bend more in the handle, because the transition from fade to limb thickness is rather sudden for a pyramid bow.

Knoll:  I did this same test myself years ago (never posted, ADHD prevents me from taking pictures and then getting around to putting them up) but with thin pine slats, oak scantlings, and some 1/4" thick belly lams that hadn't worked out.  With wood of uniform dimensions, the result is almost exactly the same.  TINY differences, not big ones.  With crowned staves, any amount of crown, to me THAT seems to make a difference, at least enough to require some care in tillering.

George, like I mentioned above, when this was discussed in depth on Paleoplanet a few years ago, I realized that both my pyramids and many I was seeing made, weren't really arc of the circle, exactly.  It was more parabolic, bending less off the fades, and less at the tips, almost like tangents to the arc.


I also have a hypothesis, that with a pyramid bow, there is an exact right bow length for each draw length, because the string angle exerts pressure at different angles thoughout the draw.  It seems to me there must be an optimum spot/angle/drawlength to stop, and that we should be designing the bows (length, primarily, to accomodate this.

Somebody on pg 2 wondered if tests have been done to see if limb strain is consistent all along the limb.  The answer is yes.  The nature of the bend itself shows engineers that the strain is consistent.  Same thickness, bend to same arc= consistent strain, (but more pressure, as leverage applied to any one spot is greater the closer you get to the handle.

[son of massey]

The wider inner limb/would be handle area/does resist bending relative to what a thinner limb would. It is just resisting a stronger leverage effect than the limbs further out deal with-the same reason we can make tiny limb tips and they remain fairly stiff-there is so little leverage at that point.

If anything I am a little surprised that there is a such a clean correlation between width and final bending, it is neat that a straight line taper matches up with the changing leverage at a 1:1 ratio.

SOM

[Del the cat]

The wider inner limb/would be handle area/does resist bending relative to what a thinner limb would. It is just resisting a stronger leverage effect than the limbs further out deal with-the same reason we can make tiny limb tips and they remain fairly stiff-there is so little leverage at that point.

If anything I am a little surprised that there is a such a clean correlation between width and final bending, it is neat that a straight line taper matches up with the changing leverage at a 1:1 ratio.

SOM

Yeah, that's what I love about bows... all the high school fancy physics analyses beams for small defelections and analysis of bows makes loads of assumptions.
Nothing is linear, the angles change, string deflection vs tip deflection isn't linear... yet at the end of the day the FD curve turns out remarkably linear!
The empirical always trumps the maths!

[Badger]

  Del, if you took a flat straight board and bended it into a hoop attaching the too ends it should form a perfect circle. What would happen if you attached too pyramid bows together at the tips?  Assuning the spot of gue on the tip of each bow could actually hold it. What would happen if you took 1 pyramid bow and bent it so the tips would attach to each other?

[Badger]

The wider inner limb/would be handle area/does resist bending relative to what a thinner limb would. It is just resisting a stronger leverage effect than the limbs further out deal with-the same reason we can make tiny limb tips and they remain fairly stiff-there is so little leverage at that point.

If anything I am a little surprised that there is a such a clean correlation between width and final bending, it is neat that a straight line taper matches up with the changing leverage at a 1:1 ratio.

SOM

Yeah, that's what I love about bows... all the high school fancy physics analyses beams for small defelections and analysis of bows makes loads of assumptions.
Nothing is linear, the angles change, string deflection vs tip deflection isn't linear... yet at the end of the day the FD curve turns out remarkably linear!
The empirical always trumps the maths!

  Del, a friend of mine who has a doctorate in physics laughs about this all the time. He refers to it as Edisonian vs Nuetronian. Same as trial and error vs science. Trial and error most always wins.

[Del the cat]

  Del, if you took a flat straight board and bended it into a hoop attaching the too ends it should form a perfect circle. What would happen if you attached too pyramid bows together at the tips?  Assuning the spot of gue on the tip of each bow could actually hold it. What would happen if you took 1 pyramid bow and bent it so the tips would attach to each other?

Good Q,
But of course there is no longer a string pulling twards the centre of the circle. My guess is, with two pyramids you'd get an oval, maybe like a pair of lips   
I have the two pyramids so I s'pose I could try it...
But I still have a stinking sinus cold... so it's prob' just thought experiments for me. (Maybe a stiff drink too)
Del

[Del the cat]

OK tried it...
The big prob is attaching the tips, didn't really work at one end where I tried to tie 'em together, so I held the other end by hand...
I think you can see it's an ellipse.
Anything else you'd like me to do before I get my dinner?
Del

[DC]

What if you bend one pyramid bow right around and join it at the tips? Have your dinner first!

[Del the cat]

What if you bend one pyramid bow right around and join it at the tips? Have your dinner first!

Now you just teasin' this poor ol' kitty  
Del