How to cut a board so that it can be bent spherically?

[Whazupp]

TL;DR Summary

In bathroom remodelling, curved surfaces are made by serrating polystyrene (XPS) board and bending it. But there are no instructions on how to make the cuts to get the board to curve spherically. Is it possible somehow?

Example of normal application:

What i'd like to achieve:

More information:

Wedi board serration either straight or angled depending on radii wanted.

It's also possible to serrate outwards to achieve radii less than 200mm (example from ThermaSheet)

Any ideas on how to do this?

 

[TeethWhitener]

Interesting problem. Maybe consider cutting a triangular patterned serration, kind of like a geodesic dome:
https://en.wikipedia.org/wiki/Geodesic_polyhedron

 

[Whazupp]

That's seems like a great idea! I need to test in practice if the vertices get too weak when 3 or more cuts intersect. Thanks for the tip!

 

[Baluncore]

It will not be possible on only one side of the sheet, without cutting wedges from the sheet and then stitching them together, like a soccer ball made from pentagons and hexagons.

If you can cut V'ee slots, close together on both sides of the sheet, then you can shrink the peripheral area to approximate a spherical surface.

If you cannot bend a sheet of paper to the surface you want, then it cannot be solved with V.ee slots on one side only, so you will need to compress surface area with slots on both sides, a bit like a concertina.

 

[Tom.G]

https://en.wikipedia.org/wiki/Gore_(segment)

(above found with:
http://www.google.com/search?&q=gores+on+a+sphere)

Cheers,
Tom

 

[berkeman]

Paging @phinds to see if he has any ideas...

 

[phinds]

I don't think you'll find ANY technique that would allow spherical bending due to the compression that would occur. Compression in only one direction can be achieved with wood by steaming it for a long time and then bending it but spherical requires bending in, effectively, multiple directions so the compression could not be accommodated. Try it with a piece of paper. The wrinkles you get are the compression I'm talking about and the wood just won't compress like that.

 

[DaveC426913]

The OP's plan cannot be done the way s/he hopes. Though that doesn't mean it cannot be done.

As phinds points out, even with the most forgiving material - paper - you simply cannot make a curve in 2 dimensions, no matter how many crimps you make.

(Consider what would happen at the pole: you'd have to have 100% crimp to get 0% surface).

Depending on the application, there may be other ways of achieving the effect.
What radius is required?
What angle must it subtend? (OP's diagram suggests 90 degrees)
What stresses will the shape be subjected to? (How strong need it be?)

 

[Baluncore]

(Consider what would happen at the pole: you'd have to have 100% crimp to get 0% surface).

But to make a hemisphere you only have to reduce the equatorial periphery to 63.662% of the flat sheet.
That can be done by cutting adjacent 'V' slots like \//\ on front and back to allow shrinkage.

 

[Rive]

Well, if it's the spherical surface what's needed and not the solution for the serrated grooves, then maybe 3D printing?

 

[hutchphd]

This is exactly the map projection problem and has a rich and venerated history: How do you make a good flat map of the Earth without distorting local stuff?

\

 

[DaveC426913]

This is exactly the map projection problem and has a rich and venerated history: How do you make a good flat map of the Earth without distorting local stuff?

Ehh... The OP appears only to be looking for a spherical shape. There's no concern for how that represents or distorts anything on the surface.

Sure it's loosely related field, but the OP's issue is really just "how can I make a spherical surface" and frankly, starting with a flat surface is by no means a requirement.

Heck, if the OP simply found a hard plastic ball of the right radius, he could cut it down and have a perfect surface with zero seams. (Not likely in practicality, but you see my point.)

 

[hutchphd]

From the OP:

In bathroom remodelling, curved surfaces are made by serrating polystyrene (XPS) board and bending it. But there are no instructions on how to make the cuts to get the board to curve spherically. Is it possible somehow?

So I do not know what you are talking about!
If he has a big thermal press there is no problem. If he starts with a big ball he's pretty much there..

 

[Baluncore]

So I do not know what you are talking about!

You start with a thick flat sheet. You cut the surface(s) where it needs to shrink then bend it to close the cut. Repeat the process until the external surface is an approximation, close behind the final surface you require. You then plaster the approximation to remove the surface errors. For a sphere you could finish with a concave arc profile scraper, like the one you might use to finish a cylinder.

Working out where to cut becomes a tiling problem. Minimise parameters such as the thickness of the plaster, the number and the length of cuts.

By cutting part way through the slab, you maintain a level surface and do not need to stitch or glue both sides of a gaping wound. Soccer balls and the gores on maps require more stitching.

 

[hutchphd]

As I recall Buckminster Fuller did a "geodesic" projection of the globe. I think it was a dodecahedron and he called the Dymaxion Globe.
Same thing, only soccer ball is a truncated icosahedron.

 

[Shane Kennedy]

Summary:: In bathroom remodelling, curved surfaces are made by serrating polystyrene (XPS) board and bending it. But there are no instructions on how to make the cuts to get the board to curve spherically. Is it possible somehow?

Example of normal application:

View attachment 293789

What i'd like to achieve:

View attachment 293792

More information:

Wedi board serration either straight or angled depending on radii wanted.

View attachment 293791

It's also possible to serrate outwards to achieve radii less than 200mm (example from ThermaSheet)
View attachment 293790

Any ideas on how to do this?

I don't think you'll find ANY technique that would allow spherical bending due to the compression that would occur. Compression in only one direction can be achieved with wood by steaming it for a long time and then bending it but spherical requires bending in, effectively, multiple directions so the compression could not be accommodated. Try it with a piece of paper. The wrinkles you get are the compression I'm talking about and the wood just won't compress like that.

Take a geodesic dome and attach the parts to each other, on the flat. http://www.domerama.com/software/geodesic-software/

 

[phinds]

Take a geodesic dome and attach the parts to each other, on the flat.

Which has absolutely nothing to do with bending a sheet of wood.

OOPS ... he DID say "cutting" not "bending", so ... right on.

EDIT: Hm ... I think originally, he DID say "bending", not cutting.

 

[hutchphd]

As mentioned previously

As I recall Buckminster Fuller did a "geodesic" projection of the globe. I think it was a dodecahedron and he called the Dymaxion Globe.
Same thing, only soccer ball is a truncated icosahedron.

Of course each facet of the dome is flat and so only in the limit is it really a sphere. This is all very well trodden territory.

 

[Anachronist]

I cannot tell if you want to tile a concave or convex spherical surface.

Either way, you won't be able to do this with square tiles, if that's what you intend. You can lay square tiles into a concave sphere but you'll end up with odd-shaped gaps.

An easy sphere approximation would be an icosahedron (made of equliateral triangles) and then you can use plaster to smooth it out.

Or, take a quarter of a geodesic hemisphere and unwrap it to a flat surface, then trace the triangles on cardboard, but it out, and fold to shape. I could do the cutout in CAD software, with difficulty.

Another option is to take a quarter hemisphere made from styrofoam (you can get foam balls at Michael's or other art supply stores), and fit bits of cardboard tiles to it, cutting tiles to shape as needed to get them to fit while you glue the tiles together. Once the glue dries, remove the foam mold.

 

[Jodo]

In steel fabrication a technique called the orange peel method is used to cap off pressure piping.
The sphere in DaveC's post above gives a good visual of the cuts needed. Cut the sphere in half at the equator then cut all lines up to the top pole. Now lay the cut out flat.
It wouldn't be pretty and there definitely would be a minimum radius one could achieve.
I would try it

 

[Anachronist]

Summary:: In bathroom remodelling, curved surfaces are made by serrating polystyrene (XPS) board and bending it. But there are no instructions on how to make the cuts to get the board to curve spherically. Is it possible somehow?

It depends on how close to a sphere you want to get. An icosahedron can be unfolded into a flat sheet. If you include some extra triangles in the spaces available, you can include overlapping facets that can be glued together. An icosahedron doesn't have an equator, but there are plenty of similar shapes that do.

That's more of an "origami" solution, though. It seems like you want to be able to score a sheet into a doubly curved surface. I don't see a good way to do this without folds and cuts, however.