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Old 03-23-2013, 06:50 PM   #517 (permalink)
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Originally Posted by sgtlethargic View Post
Why are there no comments on the Excel graphs?

After digging around for a mathematical solution to the posted equation by Mathematica, I came across a description of what is meant by "sin^m" listed above.

The math form below shows another way of handing the "sin^m", which is not solvable by normal means.

So now we had a way of properly solving the shape of a Tear Drop, and an excerpt is shown below. Here are the equations for X and Y:


Increment = 0.1 (number of desired steps in shape)
A10 = cell A10
$C$7 = 1.925 (constant) used to create a shape with a 2.5:1 length/width ratio
$F$8 = M (constant)

And here is what the spreadsheet data looks like....

To solve for a shape where Y is positive, vary T from 0 to PI. To solve for a shape where Y is negative, vary T from PI to 2PI. In this case I am only interested in solving for Y in the positive state, so T is varied from 0 to PI.

Here is the original graph presented by SGT.

I'm not sure about the Y-axis units for this graph, as they do not give output of 2.5:1 for length/width.

The graph below however does indeed maintain AeroHead's 2.5:1 length/width ratio however. We have "two units" in the X-axis (-1 to +1) and one-half of the 0.8 units of width (0.4 units) shown. 2.0/0.8 = 2.5:1

SGT, thanks for posting your original graph of this shape, as it gave me the incentive to dig deeper for those who are math challenged, like myself.

Hope this helps, Jim.
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Last edited by 3-Wheeler; 03-24-2013 at 01:35 PM..
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