Can anyone help with this please?

I want to make a hollow wooden ball from segments cut from flexible board. The board will only curve in one direction – ie. You can’t make a dish with it.

What shape should the pieces be?

I’m looking for a formula with variables: (R) for the radius of the sphere, (N) for the number of segments, (W) the width of a segment, (L) for the distance from one end of the segment. So that I can plug in N and R and get the width at each value of L.

If I then mark a straight line on the flat board and mark off all the half widths at intervals I can cut N of these shapes, bend them and fasten the edges to make a sphere(oid). I want the joints to lie on the surface of the sphere.

I think the center line of the curved segment is elliptical (but I'm not sure) so I possibly need to calculate the length of curve of an ellipse from one of it's vertices.