How to design and cut out the hollow spheres:
My costumes are usually based on hollow spheres made of cardboard panels taped together. The "lune" shaped cardboard panels are stuck together with sticky tape. The following section gives instruction on how to build such a ball in easy steps.
Calculating the panel or lune dimensions:
I use this formula to calculate the shape of each lune:
R = ∏ D (1/n + n/16)
This formula calculates the radius R of circle for each side of each lune. The sides are rather gently curved  so the value of R is usually quite large.
D is diameter of ball required for the costume  it is usually between 32 and 36 inches  note that you usually needit to go through a doorrway and that imits the size.
n is the number of panels or lunes to be used in the ball constructiion. (n is usually 12 or 16) Latterly I have prefered 16 panel (lune) spheres  16 panel balls require more work but the results are visually better.
The length of each panel (or lune) before neck and hip allowance "l" is ∏ D/2
And ∏ D/n Is the maximum width of each panel (or lune).
An example of a calculation: For a 36" 16 panel (lune) sphere.
R= 36 * ∏*(1/16+16/16) as ∏ = approx 3.1412
R = 120"
Thus to draw out the lune on a sheet of cardboard we now need to construct a compass with 120" radius  in the photo below I show how I do this using a length of 1x2 with a pencil inserted through one end with a screw point at the other.
The next step is to calculate the length of the panel. To do this, draw a line on a large sheet of cardboard of length l = ∏ D/2 = 56"
Draw arcs on both side of the line which intersect with both ends so that the overall shape of the panel is a lune as seen in the sketch below. Next , create a set back of half the width of a neck allowance (ca. 4") at one end and at the other for a body ca. 10" for a 20" entry hole  so that the panel should look like that in the picture shown below:
Getting the side curvature of the panels correct:
This is a typical improvised compass made from a length of 1"x2"with a screw at one end to make the point and a pencil inserted through the other end for drawing. This is used to describe an arc on a piece of cardboard which gives the curvature of the side of each panel. For a 32" ball the panel should have a side curvature of radius 104" the length of each panel is 50" and the maximum width 6.3".
But you need a neck hole of about 9"diameter  depending on your head size  thus reduce the length of the panel at one end by half the diameter of your head (don't forget to allow for your nose) say 4.5" and do the same thing at the other end of the panel for your body to go through my body fits through a hole of about 14 or 15" in diameter. The size depends on how big you are  thus reduce the other end of the panel by about 7.5" . Arm holes are about 8" from the neck hole and are elliptical with a 1 panel maximum width and 8" in length.

Trying out is as important as measuring. This bell shape formed the top of the spider abdomen.
Measuring for the spider (see costume ideas tab)  trial and error in measuring is important in getting the size right. This bell shape covered with black felt forms the top of the spider abdomen.
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