Scaling Hull Plate Flexibility to Analyze Tortured Plastic Build Method

I intend to build 30ft catamaran hulls using a Cylinder Mold / KSS method. After building the hull shell halves on the mold, the keel line is stitch and glued and the hull shell is bent/tortured into a compound shape. I am aware Kelsall used darts or cut fingers along the keel and didn't lay the inner skin on the core below the waterline to help get a 3-D rocker shape. I would like to have a fairly good idea of how much I can bend my hull skins before they buckle or give me a wavy, unfair shape if I don't cut fingers in it... or where to and spacing of fingers/darts.. solid glass skins here btw.

I want to build a 1/4 scale hull with a shell that has 'scaled' mechanical properties. The knee jerk method would be to scale the hull by a 1/4 in all directions including skin thickness... eg. a 0.2" thick solid laminate becomes 0.05" thick for the model. BUT bending stress (MC/I) has the pesky 4th power on inertia. So the bending stress will not scale by 1/4 if the skin is 1/4 thick on the model. The modeled stress will actually be significantly greater (16 times?). Tensile stress, divided by area, has the same issue to a lessor degree. If force is scaled by 1/4, it would over-stress the model by 4 times as area reduces by a factor of 16 not 4.

SO, How do you scale down a model to achieve similar mechanical properties to evaluate how the full scale hull will react to bending and tensile loads such as those applied when 'tortured' into a 3-D shape? Any advice is appreciated.
Thank You!
Zach

 

My tentative answer based on the document here below, especially the table page 8 :
If your model, including the thickness involved, is at scale 1/4, the module d’Young of the material used for the model should be at scale 1/4 the one used for the scale one. Then, applying forces at scale (1/4)^3 on your model, you will have geometrical deformation at scale 1/4 and, the adimensional strain being similar (deformation/geometry), the stress (if you are also able the measure them on the model) will be also at scale 1/4. Practically, that often means to use thermoplastic materials for such model in mechanical similitude but take care of the accuracy and stability of its module d’Young.
https://gisnt.org/pdf/analyse dimensionnelle et lois de similitude.pdf

 

It won't work if you scale directly. The shear, tensile, compressive, and bending strengths remain the same; they don't scale.

 

Thanks Dolfiman! That's exactly what I was looking for. I wouldn't have thought to scale the modulus of elasticity, but that makes perfect sense.

 

When you scale a model, the surface increases by the square, but the volume by the cube. The stress, or pressure on the surface, therefore increases by the square. Young's modulus assumes a linear behaviour between certain limits. The yield point is critical for a design, not just the slope of the line.

 

Pay close attention to Gonzo. While he tends to overgeneralize, here, he nails it. The materials do not scale.

For this reason, when scaling, in general, ( a shoutout to Gonzo!), the materials would be different. Now, I understand how this blows up your plan to learn cylinder moulding before you build, but it is a terrible idea. Gonzo did not go so far as to say it. I have building experience, I will.

If you want to learn to work with foam core, a better plan is to build a section of the hull or a section of something that could go into the build. The 1/4 scale idea is also bad for another reason. It is too big and will drive cost, but to little benefit at 7.5 feet long.

Strip planking is the best way to scale because you can change the strip dimensions to get them to cooperate with the bending properties of that material. Plus it is cheap. You can plane down materials and no need to glass any foam. But you need to really pin down the purpose of the model.

Your fears of crushing the foam are well founded and intuition correct. It will fail.

 

Why do you want to make it complicated when it doesn't need to be? Buy some 1/8 ply (the cheap stuff, doesn't need to be waterproof) or melamined HDF and some battens. Torture the ply/hdf in the hull shape you want, stabilize any darts with a layer of glass with epoxy. Smooth any joints and holes with some filler and thoroughly wax or shrinkwrap the thing. You can now lay fiberglass over this quick and cheap male mold.

 

Do you have the Gougeon book? Those guys have done a number of tortured ply multihulls and there is a very good chapter in their book. They were all single skin ply mind you, not multi skin like cylinder molded. I have not read the book for years but i believe they would make a model out of the thin birch ply that is used in model making and had figured out what thickness would scale to the okoume they would use on the full size hull.