Developed unfolded shape of a spherical triangle

[marisse]

Dear All,

i am having a problem of drawing the unfolded elevation of a spherical triangle.

I want to cut a shape glass which later on i will gravity bend it to form a spherical triangle having a radius of 1123mm. The spherical triangle will form almost quarter of a hemi-sphere. Height of the spherical triangle measured from the top to the base is 1082mm.

Please help.

Thanks a lot.

Marisse

 

[hyposmurf]

Really I do not know how to do it .
But your question was done by the early topographer or catographers when they try to represent the map of the continents, the made a lot of trick to do it.

 

[berkshire]

Are you asking how to develop a pattern for a slice of a spere like an orange segment cut across the middle?
B.E.

 

[PeterCharles]

I don't think this shape can be unfolded in a true form. The closest I could get was a quarter of a hemisphere as a surface in SketchUp and unfolded in Pepakura "orange peel" fashion. I'd attached a picture but I can't in this forum.

I've made this before in real life but you need to deform the metal sheet. We pressed a 16 gauge flat sheet supported on the end of a tube around a metal sphere under a press on that occasion, then cut out the section we wanted.

 

[JStephen]

If you take a flat plate and shape it into a sphere (or other double-curved shapes), it requires that the plate be stretched or contracted in various places to form that shape. It can't be formed by simply bending a flat plate.

A similar problem arises in forming steel- as in water tower sections. There, the solution is partly trial and error.

In other words, there's not a simple solution.