View Single Post
Old 03-23-2013, 06:50 PM   #517 (permalink)
3-Wheeler
Master EcoModder
 
3-Wheeler's Avatar
 
Join Date: Dec 2008
Location: Southern WI
Posts: 824

AlienMobile - '00 Honda Insight
Team Honda
90 day: 80.05 mpg (US)
Thanks: 94
Thanked 550 Times in 189 Posts
Quote:
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:

X=COS(A10)
Y=SIN(A10)*SIN((A10/2)^$F$8)/$C$7

Where:
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.
Attached Thumbnails
Click image for larger version

Name:	graph5.jpg
Views:	1199
Size:	22.3 KB
ID:	12730   Click image for larger version

Name:	graph4.jpg
Views:	1050
Size:	15.0 KB
ID:	12731   Click image for larger version

Name:	graph1.jpg
Views:	1209
Size:	62.5 KB
ID:	12732   Click image for larger version

Name:	graph2.jpg
Views:	1199
Size:	18.7 KB
ID:	12733   Click image for larger version

Name:	graph3.jpg
Views:	1176
Size:	21.0 KB
ID:	12734  


Last edited by 3-Wheeler; 03-24-2013 at 01:35 PM..
  Reply With Quote
The Following 3 Users Say Thank You to 3-Wheeler For This Useful Post:
aerohead (03-30-2013), KamperBob (04-02-2013), Tesla (09-23-2013)