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Generating flat pattern from equation


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I've been tasked to generate flat patterns for a pipe liner that consists of a main line and a small line (lateral) sticking out of the top. I'm unable to unwrap my 3D model with tools in SolidWorks 2016 due to the nature of the compound surfaces. I came up with some equation driven curves to define what the curve looks like when a smaller diameter cylinder intersects a larger diameter cylinder. The flat pattern is composed of 3 pieces, the main and two patterns that make up the rest of the lateral. These pieces will be sown together.

The circumference of the lateral is going to be divided in 4 sections; for the two lateral patterns and the two lateral arms on the main pattern.

The problem that I am seeing is as follows:

The quarter circumference lengths are not equal to what I expected. Each quarter length is suppose to be 3.14" for a lateral diameter of 4". However, in the flat pattern they are 2.83". This leads me to believe that my equation for the curve for the main pattern is incorrect. I can't see where I have made a mistake. I start at x1 = 0 and I end at x2 = 6.42 (the "distance" it takes to travel circumferentially starting at the beginning of the curve and ending where the lateral seam makes contact with the main line). I believe my equation for the curve is correct. I've include a snapshot of my derivation.

I also included my SolidWorks sketch as well as some pictures of the model. The generating sketch is in Sketch1 (the other sketches are there to separate the patterns for printing).

After thought: What I think I might do is increase the diameter of the lateral slightly to "force" the quarter section lengths of the circumference to be correct i.e. going from 4" to 4.45" made my quarter lengths to be 3.15", what it is suppose to be if I had a 4" diameter lateral.



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