Del's Pyramid Taper Test!

[DC]

It's the only way left I could think of bending it

[scp]

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.

Actually it is not a straight line taper but the curve is quite close to one. According to TBB4 page 117, the breakdown of stress ratios are from handle to tip at 5 even intervals 30% 27% 22% 15% 6%. The "pyramid" should be a little fatter than a triangle.

[Springbuck]

scp said:

Actually it is not a straight line taper but the curve is quite close to one. According to TBB4 page 117, the breakdown of stress ratios are from handle to tip at 5 even intervals 30% 27% 22% 15% 6%. The "pyramid" should be a little fatter than a triangle.
[/quote]

I remember those numbers being corellated to % of energy storage in each 1/5th of an evenly STRAINED longbow.  Even on a pyramid, I could believe that the energy storage broke down like this, but the strain would be consistent.

[Poggins]

I've built one , it was out of an oak floor board .
I did it just to see how it worked , went from 2" at the fades to about 3/8" at the tips straight taper and set a stop up on the bandsaw to keep the thickness the same and stopped at the fades to keep a stiff handle .
Didn't take an hour total to start putting arrows through it , I left the grooves on the bottom of the board to show folks that it is a floor board ( growth rings run vertical and grain runs horizontal and it was pretty clean exept for one spot where the grain has a wave in it ).

[Jim Davis]

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

Jawge, maybe it's easier to think of just one limb with the wide part clamped. The limb could be as long as you want as long as the ratio of length to width is maintained. The wide end would always bend as much as the rest of the limb, because the leverage at any point has the same relation to the width at that point.

[duke3192]

I have enjoyed reading this whole, insane thread and the fact is , it doesn't matter, either your bow works or it doesn't. The fun and the pain is in the making, too much D*** thinking.

[Jim Davis]

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.

Actually it is not a straight line taper but the curve is quite close to one. According to TBB4 page 117, the breakdown of stress ratios are from handle to tip at 5 even intervals 30% 27% 22% 15% 6%. The "pyramid" should be a little fatter than a triangle.

SCD, you are  quoting a writer who is not an engineer, as  far as I know. Klopsteag and Hickman were engineers. Machinery's Handbook was written by engineers. Those sources say that if the thickness is uniform, both geometry and physics dictate that the sides should be straight.

Taking into account the need for nocks, the limb stops tapering when the width of the nock is reached.

[JW_Halverson]

For giggles, I set a 2x4 across two saw horses, then laid a 4x4 ft sheet of plexiglass diagonally across it.  I used duct tape wrapping over the "tips" and connected it with some 1/4 inch rope. 

When I gave it a pull, whatdya know, the "tiller" looked good. 

Now I imagine if you made a diamond shape, such that the angle of the bow limbs was described by an obtuse angle (reater than 90 degrees), you would still get that same tiller effect.  So then, comes the question....at what point does the angle become so acute that the effect is lost?  Is it even possible to get to such an acute angle that it would behave differently? 

Or is this akin to "squaring the circle"?

[scp]

SCP, you are  quoting a writer who is not an engineer, as  far as I know. Klopsteag and Hickman were engineers. Machinery's Handbook was written by engineers. Those sources say that if the thickness is uniform, both geometry and physics dictate that the sides should be straight.

The engineer who did the calculation is named in the book.

[Jim Davis]

SCP, you are  quoting a writer who is not an engineer, as  far as I know. Klopsteag and Hickman were engineers. Machinery's Handbook was written by engineers. Those sources say that if the thickness is uniform, both geometry and physics dictate that the sides should be straight.

The engineer who did the calculation is named in the book.

I knew something had to be wrong. There are two somethings wrong. First on the page cited, engineer David Dewey is talking about a "D-longbow," not a "pyramid" bow. Second, I found no mention pages 117,118 to leaving the sides wider than a straight line.

[scp]

I knew something had to be wrong. There are two somethings wrong. First on the page cited, engineer David Dewey is talking about a "D-longbow," not a "pyramid" bow. Second, I found no mention pages 117,118 to leaving the sides wider than a straight line.

I'm talking about the proper way to taper a well made bow. Either through thickness as in a "D-longbow" or through width as in a "pyramid bow".  We usually combine the two tapers. What makes you think a straight triangle with even thickness would make a better bow?

[Jim Davis]

It has not been the purpose of Del's thread or my contributions to compare designs or promote a design as the best. But, Klopsteg and Hickman, among others, point out that every inch of a triangular limb of uniform thickness is able to contribute equally to the storage of energy. This is not true of a bow that tapers in thickness because there is one best thickness for any particular degree of curvature. In a bow of tapering thickness, thicker sections have to bend less, therefore they store less energy.

Why ask me? None of the research is mine. Why not read the original material?

[scp]

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.

Actually it is not a straight line taper but the curve is quite close to one. According to TBB4 page 117, the breakdown of stress ratios are from handle to tip at 5 even intervals 30% 27% 22% 15% 6%. The "pyramid" should be a little fatter than a triangle.

Even though it is not 1:1 ratio, the ratios are not random.
30% -3 27% -5 22% -7 15% -9 6%
It sure describes a nice curve often found in nature.

[son of massey]

I didn't think the breakdown would be random, and I can rationalize the results from an 'amount of material resisting bending/physics' point of view. It is just neat to me it works out that way. I don't think it is hard to imagine a universe wherein the leverage effect would be some odd ratio to material strength, in which case a curved outline would match up better. Its just a neat thing that a relatively straight line fits the bill.

SOM

[mikekeswick]

Thickness determines bend, width determines weight.
Done.
 
Now lets go make bows!!!!