testing scaled down models

I have been posting questions off and on relating to things I do in achery involving bows and arrows. Studying the movement of the limbs in slow motion is one of the tools we can use for developing limb designs.

 I have been getting a bunch of things ready for a testing lab I am trying to build at home. One of the problems we deal with in testing is the ability to compare apples to apples and oranges to oranges. Because of this building all the test samples with known variables is the only real way to accomplish this. 

 My question is, would a scaled down bow say 1/4 scale give accurate data? The expense and time involved in the construction has prevented studies like this from ever really taking place. With scaled down versions the cost and time involved would make it a lot more feasable. I can see where 200 samples built might be neccessary. 

The bows would also be tested for performance and efficiency and not just photographed.

No. You would run into material characteristics that do not scale linearly - e.g., 1/8 inch of aluminum does not have the proportional flex or strength of the full half inch; ditto for plastics, wood, fiberglass, composites… You would have to establish a whole long list of factors to make such testing useful, which means 3X the testing before you get meaningful results from mini-bow #1.

But don’t feel bad. Even the Wright Brothers took years to understand this. (They championed thick wing sections, which performed better at scale. Thin wing sections are actually superior at full size, but they kept “proving” the opposite well into the 1930s until full-scale testing disproved their contentions.)


Aerodynamics can work; mechanical properties of materials, not so much.

Has anyone tried to develop a computer model of material, thickness, length, curvature? Not going to be easy, but nastier problems have been modeled.

Wood is close to the absolute last material I would trust to scale down in any predictable manner.

Probably, the DOD has some pretty intense nuclear simulations including (from what I’ve been told) the material characteristics of the casing – either of the bomb or the reactor depending on the exact simulation.

They take a while to compute, though. (Understatement)

Thats kind of what I was thinking as I have no way to scale them down molecularly.

   I have a pet theory I would like to prove or disprove, I wonder if this could accurately be expressed in a model.

  My theory involves outer limb mass where the limbs are moving the fastest at the tips. Most attribute the added speed from lighter tips to their ability to accelerate faster. I feel like that is part of the answer but I also feel they have less momentum going at the end of the stroke and the arrow is better able to slow it down sucking out the energy. If this proves out to be true it would justify further experiments on optimizing limb thickess tapers to allow the limb to unfurl rather than just snap back.

I would be using carbon fiber or fiberglass, wood would only be used as a spacer in the core.

You are basically talking about the light bat/heavy bat argument from baseball. You might be able to find some useful inferences from the more rigid studies on that.

It’s possible that high-end modeling tools could also answer some of these questions, but you’d need access to such a workstation and a skilled user.

Kind of the opposite from the baseball model. With a bow any left over momentum would be described as lost energy, the arrow was not able to control the bow limbs enough to sap out the energy. Instead od snapping to a stop when the limbs slam home the inner limbs have not yet quit moving.

You might be able to build and study scale models, by making the necessary compensating adjustments in either the physical models, or in the mathematical analyses of your results. This assumes that you somehow have some a priori knowledge of what adjustments you need to make.

In 1957, the U. S. Army Corps of Engineers built a working scale model of the entire San Francisco Bay. From Wikipedia: