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Making Templates for a Sunburst by P. Michael Henderson

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General Discussion

The templates need to be very accurate if the sunburst pieces are to fit together. About the only way to make the templates accurately is to make use of trigonometry.  While many people’s eye’s glaze over at the mention of mathematics, stick with me a bit longer and let me see if I can make sense of it for you.  I’ve tried to use tables for everything so all you have to do is look things up in the table. (an Excel spreadsheet is available at the end of this article.) 

A circle consist of 360 degrees.  If we’re going to have 16 pieces in a sunburst, each wedge will be 22 1/2 degrees.  Now into the trigonometry.

Trigonometry deals with angles and especially with triangles.  Here you see a wedge shaped triangle, with one angle indicated as “a”, and the sides labeled 1, 2, and 3. For our situation, the angle “a” is 22 1/2 degrees.

The way we’re going to make this template is - we’re going to know the length of side 1.  If we could find the length of side 2, we can measure/mark that and then draw side 3.  There’s a way to calculate the length of side 2, and it’s by the using the tangent of angle “a”.   The tangent of angle “a” is defined as the length of side 2, divided by the length of side 1.  Since we know the angle “a” (which is 22 1/2 degrees), we can get the tangent of it.  And since we know the length of side 1, we can calculate the length of side 2.  Let me do an example.

The tangent of 22 1/2 degrees is 0.414214. I’m going to use a length of 22 inches for side 1. So we know from the definition of the tangent

Tangent = length of side 2/length of side 1

or

Length of side 2 = tangent * length of side 1

Let’s substitute what we know into the equation:

Length of side 2 = 0.414214 * 22

Length of side 2 = 9.112698

Or a little less than 9 1/8 inches (9.125 inches), since we have to work
in fractions with our rulers.

Now that we’ve done the trigonometry, let’s look at the actual marking
and cutting.

Since I set up the tables in the spreadsheet as 24 inches, 22 inches, 20 inches, and 18 inches, I’m going to use 22 inches because it’s the longest one that fits the material I have.

At the other end of the ruler, I’m going to mark the 22 inch location
with the striking knife.

Now, mark a line upward from this 22 inch mark using the combination square.

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