Approximating a sphere

[Dabeer]

I've been scratch-building a sphere for the start tank for the J2 engine for my 1:72 Saturn V, and while I'm familiar with the patterns that spheres can unfold to, I'm having trouble getting the size right. When approximating a sphere (or other complex curve), what's the best way to measure to get the size to appear to be correct? I've identified 4 possibilities:

1. Inside. Make the edges of the panels match the true radius. The part fits entirely inside the true sphere.

2. Outside. Make the center of the panels match the true radius. The part fits entirely outside the true sphere.

3. Average. Average the edges and middle of the panels to equal the true radius. The true sphere crosses each panel twice, so at the edges the part is outside the true sphre, and at the middles the part is inside the true sphere. The feels like the right way to go, but when I tried it, the part seemed to be too large to fit its place on the model.

4. Circumference. Divide the true circumference by the number of panels and make the width of the panels match the result. This seems to result in a smaller part, entirely within the true sphere.

Or am I over thinking this, as usual?

[zubie]

I've looked at at your post several times now and in the end, I suspect using the internal radius may make more sense, but I have a feeling that really isn't the problem you are having. I suspect the real problem is the inevitable error at the seam itself. If you slice a sheet and then re-attach along the same cut, there will be a very small but existing width to it. Not exactly a gap, but there will be infinitesimal discontinuities that don't allow the sheets to reconnect like a jigsaw. Add a curve to this, and the paper will inevitably be stretched on the the outside (picture slicing corrugated cardboard on one side only then folding slightly along the cut to see what I mean). It can be corrected with sanding, but at 1/72, this is not a very big sphere. True that for cardstock this error is not particularly big (unless you are doing a particularly small subject), but it will be cumulative with consequent seams.

So the sphere presents an interesting example because you can't make a true sphere from a flat sheet of paper without introducing some distortion or only making an approximation. Leaving distortion aside (softening and rounding paper), the typical approximation is either with rings or ogival petals. The more sections of each, the closer to a sphere you will get, but in either case, the more sections means more seams and each with its cumulative error. Rings will give you the least error for rising cross-sections (latitude circs), but will introduce errors in the rise (longitude circ). Petals will do a better job on the rise, but do a worse job on the rising cross section (and I also find them a bit of a pain at the narrow tip end, but that might just be me). A mix of each might yield interesting results, but I think you will have to work out what gives the best result at this scale. (for an example of a mix and match idea see pattern I suggested for an ogive cap for a loco on ogive shape thread.

The inevitable stretch of the outside over the inside suggest to me the inside circumference is probably the closest to what you want, but I'm sure that when you put it together it will end up ever so slightly bigger. How much will probably depend on several factors from the glue you use to the weight of stock, how sharp your cutting tool was, etc. Just looked at pics of the start tank and noticed a quite visible raised equatorial seam and what looks like endcaps, so probably a great place to hide the slight errors in the parts.

[Dabeer]

Thanks for giving this a look, and some thought. If nothing else, you led me to a petal construction technique that might alleviate much of the frustration I have with that type of pattern :D

I think you might be right, though - errors in construction, extra glue, paper thickness, etc are all more likely to expand the final size than contract it, and so starting with the smallest measurement might be more likely to give me the most satisfying result. And, of course, working at this scale, or this size, errors can accumulate and be significant rather quickly.