Scaling plywood

ok well if you can achieve in a model you will certainly find it easier in full size as the lines are longer and easier
It is a bit like flare in topsides of a metal boat, the longer the easier
The problem with sheet ply in compound, is that it is hard to hold into place whi;e you get things figured and glues
probs better to double dia the ply in strips

 

Similar sheet goods (1/8" BS-1088 Okoume compared to 1/2" BS-1088 Okoume, for example) will bend the same at scale, though the effort will increase as will the radius you can get before this break. As a rule, if you double the thickness, you can expect a 60% - 65% reduction (species plus sheet construction dependant and I've seen much higher, say a 75% decrease) in the radius potential, on the thicker sheet before failure. Improvements can be made with moisture content and/or heat, plus continuous restraint during the drying process (leaving it on the mold), but then again, this isn't comparing apples to apples anymore.

Simply put, most designers I know, have come up with a clever design and built a reasonable scale model, to check out building methods, material flow, etc., just to find the full size prototype, just doesn't want to conform the way the model did. It's part of the learning process and though math is helpful as is software, but there's not a lot of options to learning about reality. Eventually you'll get to a point, where you can look at a shape and say 3/8" will make that bend, but good luck with 1/2", mostly because you've broken enough 1/2" to know. If you'd like to take this further, rip some 6" wide edges off a sheet of 1/2" and 1/4" plywood and test their minimum radius potential. If the 1/4" yields at say 12", you'd think 24" will do for 1/2", but the reality thing will show you 30" is really pushing it, maybe something like 34" is more realistic.

 

A scale thickness will more accurately represent the weight of the end product but not its rigidity or strength.

If your scale is actually 1/4 then both volume, and therefore weight, will vary together.

But strength varies with cross section, not volume, so the scaled down panel will be proportionally stronger and more rigid that the full sized one.

In Gerr's Elements of Boat Strength you see this in a comment he makes about using thicker plywood for bulkheads because the thinner ply his scantling rules may actually indicate practically results in somewhat bendy panels that can be difficult to work with.

The scale model would otherwise have a scale bend too, as you're asking about.

Flip what Par wrote around: to have similar bending characteristics for a scale bend you'd need thinner than scale stock. Exactly how thin is not something I pretend to know how to tell you; but, consider: when people designing one sheet or two sheet canoes test their hull shape with card stock they are really testing to see if the form is fully developed or not, and have to rely on experience with actual panels if the full size boat can be bent as much as their model is.

 

Anatol, in order for complex bending or deformation to scale in a similar manner, L, W, and T all have to scale by the same proportion. This is the only way to keep the stresses in congruent arbitrary cubic elements the same on all 6 faces. (Proportional is good enough, but the same is easier)

If you were forming a plate by taping the edges down to a frame, with no forces applied except to the edges, then the securing force per inch will scale likewise. This gets you similitude. All of the stresses are the same at congruent locations.

One minor note. The panel will weight 1/8th as much. The perimeter is 1/2 as much. 1/2 the force times 1/2 the distance is 1/4. So this model panel will distort differently under it's own weight. You need to build it in a 1/2 g environment for complete similitude. Or you can monkey with the modulus of elasticity and density of the materials to get gravity to shape up.

Edit. For regular developable surfaces using isotropic materials, it is not as important to scale thickness this way as long as all the applied forces are perpendicular to the plate's face. But plywood is a long way from isotropic, so not a bad idea even then. And I've been known to push and pull on the ends a bit, too.

 

Scaling

For the scale model, with all dimensions scaled, the bending of developable surfaces will behave similarly (will acquire proper scaled shape on fitting to frames, etc.) between the model and the full size prototype, PROVIDED the elastic modulus for the full size and scaled materials are the SAME. This is assuming you are bending sheets in the elastic range for the material. If plastic deformations occur, then there is a more complicated problem.

For example, a steel boat, stitch and weld, with 0.25 plate thickness, and the same hull model 5:1 with 0.050 plate thickness, will produce hulls of identical shapes, because the elastic modulus for the thick or thin plates are the same values.

As stated by others here, plywood would tend to have its elastic properties variable with thickness, manufacturing method, and wood source. Of course forces are vastly different to get the sheet bent to the frames, but that is not what you were asking.

 

Hi PAR, just a grain of salt.
Good quality marine plywood have similar properties when they have the same weight. I always bought my plywoods with a balance, and checking the stiffness but I had the luck to have my plywood provider at 1 mile from the shop.
Sometimes (not always) it pays to double or triple the layers. You can get better shapes. For example with a 18 mm it's impossible to get a good shape on a 30-40 feet planning boat at the bow. It'll be too full, a common defect with plywood boats.
Worst you'll have to make an oversized structure to withstand the big bending efforts with lots of screws. Furthermore scarfs on a 12 or 18 mm plywood cut and glue operations are lengthy.
Let's take the same boat, 18 mm at the bottom with fine entries, 12 mm at the top sides with a nice flare at the bow locally 18 mm thick. With 18 and 12 mm plywoods you are going to suffer, or you have to redraw a boxy boat because of the material.
With 2x6mm and 3x6mm plywoods it's a breeze. Light structure-mold, identical to the structural calculations with minimal stringers. Just bronze grapes you can leave for the first layer (already epoxy "saturated" and finished on the inside face) to hold while glue sets on the already epoxy "saturated" structure. You need just a guy for cleaning immediately the fresh goo. I even used already glassed finished plywood on the inside face.
Scarfs are cut in minutes with a modified circular saw which is able to cut scarfs not only on straight line but also on soft curves. With a modest vacuum system (first mine was a 50 US$ used milking vacuum pump) the second and eventual third layers go fast and smooth, and scarfs are glued on place.
Joints are overlapped and thus you get a monocoque structure with no weak points. The interior structure is just bulkheads an a few stringers.
And as you buy 2 to 3 times the number of sheets so you can discuss the price, making it fairly similar to a 12 or 18 mm plywood.
For some designs, you can get shapes impossible to obtain with thick plywood and after calculating the cost (and time) the result is very close, even sometimes cheaper as the inside and structure are finished before layering the hull. I hate sanding in a crampy place, and having running and dripping epoxy on vertical or overhead surfaces. That takes pain, money and time. The lone remaining structural inside job are the composite chines, bulkheads and the engines bases.
All that needs a careful planning and a boat designed for that...Sure it's not worth to go in complications with a 20 feet sailboat, or a smal runaboat.

 

When you see the Gougeon scale using birch plywood to scale at 1/12 okoume 3 plies, it jumps to the eye (at least mine first time I saw it) that the ratio of the cubes is 125 and it's a constant taking care of the thickness and modulus differences for a 3 plies. Why cube? simply because the inertia (and rigidity potential) is the thickness at the cube, a section twice thicker is 2³ 8 times stiffer at equal modulus of the material. A 6mm okoume plywood is 8 times stiffer, or less bendable, than a 3 mm of the same wood, after you have other factors as the number of plies. On a 3 plies, the central core (fibre at 90°) is at the center, close to the "neutral fiber" and has less stresses that the outer plies. The stresses vary at the square of the distance from the neutral fiber.

birch 0.8³= 0.512 okoume 4³=64 64/0.512= 125 and so on for the 3 plies okoume 5 and 6 mm, the ratio 125 is the same for 3 plies plywood.
So you can interpolate that for a 3mm 3 plies okoume (3³=27) the good thickness for the 1/12 birch model is 27/125= 0.216 and the closest birch plywood is 0.6 mm (0.6³=0.216). I can say that works...I have made dozens of 1/12 models in 0.6 mm birch and it's rather accurate for a 3 mm okoume 3 equal plies.
The last birch 1.5mm is for a 6mm okoume 5 plies, a very different beast.
birch 1.5³= 3.375 okoume 5 plies 6³=216 ratio 64. And the ratio is rather accurate for extrapolating with precaution to 7.5mm 5 plies and 9 mm 7 plies in chine building.
It's the result of pure empiricism, clever experimentation and a pinch of luck.

I smell that aviation birch plywood would be a good material to start with but you are limited to 2mm thick. Birch ply mimics faithfully the behavior of the 1/1 scale while bending and compounding plywood, because it has the same microscopic structure and same mode of failure. It's not the case for other materials which not have the same properties for compounding and bending as plywood. Metals are too thin, too much modulus and are ductile with a mode of failure totally different, so they will "foil can", warp but not break. Carboard is too rigid and isotropic with its random glued fibres which do not fail as plywood. I suspect that a lot of compounded canoes have to many cuts because the use of cardboard for the scale model. Just hot water and towels can make miracles while persuading a thin plywood...While cuts can help when there is too much material, this operation has the inconvenient to concentrate stresses, and to disrupt the continuity of the surface for bending.

Playing with the numbers we can interpolate that for a 1/4 the ratio will be 125/3 (1/12//1/4)=41.66 (simply linear because we are playing with bending linear curvatures on similar plywoods).
If the full scale is 6mm okoume 6³=216 216/42=5.14 the birch plywood for the scale is around 1.6-1.8mm birch (1.8³=5.832). I guess that 2mm would be fine for a 5 plies okoume.
For a 5mm okoume 5³=125 125/42=around 3 Cubic root of 3 gives a 1.5 mm birch as best approximation.
For a 4mm okoume 4³=64 64/42=1.524. The closest is a 1.2mm birch.
For a 3mm okoumé, 3³=27 27/42=0.643 the closest is 0.8mm birch, a bit thin. After you have to tickle like gluing a light sheet of japan paper outside...Or maybe 1 mm will work.

I would try a 42 ratio as first approximation for calculating the birch thickness for a 1/4 scale. That looks consistent. Experimentation will say if the cipher is the good one.
About strength do not worry you have plenty enough. If you want to know the true strength of the 1/1 structure you have to make the calculations (tedious but rather easy, any good book of NA will give you the method). But at scale strength is over abundant as pointed on another post.

 

For 1:4 model, to get fair curves from scaled down skins, and comparable weights, you are going to need to use 3 mm high density foam which you can epoxy on the outside, and maybe the inside with light glass fibres. This worked from me after much trial.

You can forget about trying to calculate equivalent skin strength in plywood at that scale, as you cant scale the constituent wood fibres.

 

No because the wood is an-isotropic and it does not scale it's cell size, grain distances, or as others have mentioned layers and glue. There is something to be learned from the scale model exercise but there is no assurance the full scale will behave the same. If you don't push the limits you might not be disappointed.

BTW I love the new name 'persuaded ply'! Who will trust a boat that has 'tortured' it's material before it even begins it's life? I would love to define the term with a safety factor on residual stress.

 

Prozac ply.

 

As if the name you use will change the reality.

You guys ever seen Frank Smoot's website?
He tried tortured, persuaded, prozac, xxxxx, yyyyyy, ply on a simple shape.
It failed fairly definitely because he did not want to follow some known limits, and tried a "new" technique to force the shape.

You might review what he had to say, what he actually did, and read between the lines.

About most everything else I have a good deal of respect for Frank and he has some interesting boats.

 

Of course.

But just to be serious-silly a moment more: an Aussie company should market some "Platyply" marine plywood.

 

The formula does not support your comment that the stresses vary at the square of the distance from the neutral axis

In bending,the tensile or compressive stress is defined by the equation
Sigma (stress) = M ( bending moment) times C ( the distance from the neutral axis to the point that you want to measure divided by I (the area moment of inertia)

For a given profile and bending moment, then the stress then varies linearly with the distance from the neutral axis

 

Dredging up ancient engineering knowledge, I is a fourth power component. So your equation may look linear, but I think you find that it is not.

Ix=b(h^3)/12 where b is the width and h in this case is thickness, I believe. It could be distance from the neutral axis, but I think that is accounted for in the division constant.

Through engineering who doo, looks like it is a function of the square of the thickness. But, I'm not am engineer so I could be talking out my backside.

 

While the equation for "I" is correct as you have stated, your comment was that the stress varied with the square of the distance from the neutral axis. "I", the area moment of inertia does not change in your example, and the stress is linear from the neutral axis to the outer fibre.

"h" is the thickness, height, but it is not the distance from the neutral axis. "c" in the equation that I provided above is the distance from the neutral axis to the point that you want to calculate the stresses.