Gaussian curvature

[Nojjan]

I understand that if the Gaussian curvature of a surface is 0 it can be bent from a flat sheet. I am wondering, does it have to be 0 or how much is too much to work, consider that a sheet of plywood may work but not a sheet of aluminum? Is the curvature in the attached picture too much?

Thanks and best regards

[lazeyjack]

thats a simple curve, no compound, you can pull it into a circle if you want

[diagram]

Nojjan,
What are you trying to accomplish? Sounds like you are looking for a developable surface. Rhino will do this - Nautilus too.

[Nojjan]

It is sort of the developable surface that I am after. To explain it better, how much "non-developable" can a surface be with it still being developable? The only measurement of this that I have come across is Gaussian curvature and that is why I am asking for a quantified value of how much "wrong" is acceptable.

[diagram]

I think there is some tolerance but it depends on the material. For example, you can force plywood to a certain degree - plate aluminum.... doubt it. There is a paper on conic development that uses ruling lines - if I remember correctly. I have it somewhere but, will not be near my storage area for some time. Steve Holister who wrote the Nautilus Program - New Wave Systems could probably shed some light on this for you. In Rhino - if I remember correctly - the unroll surface command is based on the conic development and you can use this to test your panel. You might want to call them or go to their message board. Use to be you could call them personally but, I don't think that is the case now. If I get a chance to get to my storage area I'll look for that paper - it is brief - sorry I can't supply immediately. In general though I would think it depends on the material - and probably not too forgiving - in practice anyway. Good luck.

[CDBarry]

There is an article on developable surfaces on this site in the articles section.

The limits of how much a material can be forced depend on the material and the type of curvature, since curvature induces stress in the material, so it's not a simple question.

Obviously metal can be forced into double curvature, most ships and many boats are double curved - it requires either force or heat, so if you apply enough force you can do it. However, metals are ductile, so they take more abuse than plywood.

Warping, (negative curvature) especially, induces shear stress and compression stress, so the panel has to be supported properly by other structural members to avoid buckling, and warp in plywood has to be low enough not to exceed the limits for rolling shear failure, or else you will get premature delamination. You can calculate the induced stress in the material by standard engineering methods, and then compare iot with failure criteria.

[diagram]

CDBarry,
Great reply and certainly more succinct than mine. I am not sure if Nojjan's question is more related to the actual materials or his computer modeling.

[Nojjan]

I guess I am clear enough in the question, sorry. I am looking for someone who has built a design with surfaces of Gaussian curvature not equal to 0 but still managed to use flat panels.

I came up with this question since I use lofted surfaces in Solidworks for the hull shape (I find the parametric modeling very appealing) and when I analyse them with Rhino I get some areas that are not perfectly single curved.

Thanks for the input guys, I will read the suggested article.

[Gilbert]

I have an custom autocad lisp routine that will give me ruling lines for developable areas between two 3d curves. I know that the area is developable if it gives me ruling lines. I am using Autocad 12. The supposed ruling lines that the program itself generates are a joke. I don't know if the newer releases are any better.
The only other softwares I have that claim to tell you if a surface is developable are a Rhino demo and freeship. And while they are pretty good, I find that they at times give me results that I do not find very trustworthy.
That is, they sometimes tell me an area is not developable when I know for a fact that it is. I don't know why there should be confusion like this, but I suspect that the software tries more than one method to determine if a surface is developable and if the results don't agree completely you are not given a definite answer. If these softwares would give you an option to select the method you would like to use to determine developability and then give you the results from that method you could use the results of the method you judge most trustworthy.
Another question that you need an answer to if you are using plywood for instance is "well, ok, this is developable, but will the thickness of plywood I want to use bend to that tight a curve?"
Gaussian curvature is a great tool for helping to shape your model but I don't know that it is very much help in determining developability.

[diagram]

Nojjan,
I made a model (note jpegs) perhaps some of my issues with this will help. The hull was done in Nautilus. After discussing this with Steve Hollister that I wanted to build out of plywood or aluminum (warping the panel was never an option in my mind) - it beame apparent that blue was the color I needed to achieve for developability(Green in Rhino). This took me quite awhile - manipulating the nurb surface. Nautilus has very nice functions to maipulate nurb surfaces points can be on the surface added or subtracted as desired. The bottom panel with straight sections forward became very stressed - warped - colors went from yellow to green to red and mixtures there in as the panel moved forward to the stem. As I strove for "blue" I found that my sections needed convexity in the forward portion. Sta0-4+. Once I figured this out my time to build a model dropped dramatically and the Unroll function in Rhino worked without protest. I cut scale panels of the boat as a test and it worked out very well. As to full size I cannot comment, unfortunately.
And, on the practical side I restored a 1959 Riva 'Super Tritone'. We called Riva and asked them their opinion. We had noticed that a staight edge showed no concavity or convexity in the forward sections. They informed us that .5 inch(12mm) Bruynzeel would work fine. It did NOT and we ended up cold molding the forward section in 4 layers of Occume 1/8" and scarfing in the Bruynzeel from about station 4 aft. Sections are straight forward - everything nice and snug against the frames. This was before I was into 3d modeling and helped when I did this project. So, this long winded diatribe may or may not help. Below jpegs. includes sta.2 - GL

[Dutcher]

Nojjan,

I recently build a boat from aluminium sheet metal witch i designed in rhino.
I imported the surfaces into Acad where i nested them.
The plates where cut with a cnc plasmacutter.

When i flattened the bottomplates rhino said the flattened area is 0,03% bigger wich (i think) means the surface isn't 100% developable.

But when i build the boat i noticed that the plates fitted well without much forcing.

So i think that if you stay under 0,05% it won't cause you to much trouble with most materials.

I hope you can do anything with this info

[otseg]

I have tortured plywood 40 years. When I was at Gougeons in the 70's Meade made a guage that he used to measure all of our various tortured plywood hulls (Multi Hull Amas). With quite alot of transverse curve he found that you could get about 3" in the longitudinal direction.

Often when skining a framework you can torture the plywood to a non developable surface without cold molding. The key is that the panel is trimmed to net size as much as possible before nailing it down. Wetting the ply with hot water helps quite alot.