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Old 05-29-2018, 07:47 AM   #718 (permalink)
Tesla
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Parametric Teardrop Curves Equation

With the Tuna maybe it's to allow for eating on the run, say when it opens mouth and flares gills, maybe God might sign in and explain if we're lucky.

*** Edit Note for post 711 at top of page, there appears to be a risk with distorting the proportions of the template or other images overlaid, even when you only use the corners to adjust size, there seems to be some distortions which begin to accumulate, so the dimensions of images need to be checked sometimes. Luckily the template has height and length markers and the 80% tail length:height ratio should be 1.78 x 80% = 1.424 ***

The Parametric Teardrop first appeared back on post 501 and elaborated more over the next page particularly with post 517 where the equation is explained more clearly and more comments and posts later in the thread.
I decided to have another look at that one too, if you look at the image from post 501, you see it's basically a distortion of a circular form.



As the CoEfficients are adjusted the equation pushes the bulge to one side until it pushes past the arc and then an S-curve is formed.

Edit Note **** The details below may not be quite right as I have discovered a minor error in the spread sheet that affects tail ratio, this may not be so bad as it may be another potential adjustment to the equation for fine tuning, I need to play with it more, will come back for a definitive edit in future****

With the constraints of the template form, 2.5:1 Aspect, 1.78:1 Tail ratio and the maximum allowable angle of 22% at any point means that for anything close to the template parameters, it can only be in the S-curve range. I thought there was an inherent limit with the parameters that tail ratio can only get to 1.77, but as I looked into it I found an error in the spread sheet, not in the base equation but with the offset & scaling to conform with template presentation. After playing with it for a while I finally came to what I thought was a pretty good compromise, the curve below:



The small curve is how the equation plots in standard form, then I had to add scaling and offset factors to present it in the template form, overlay below.



To get the best fit to template I went to Aspect ratio of 2.68 and tail at 1.91:1, sounds way out but when you look at the overlay you see the fore body is extended and the excess at rear is after the 80% mark, that's part of the effect of the S-curve. Its hard to see but there is a slight bulge between the 20-50% mark and the maximum angle was 19.5 degrees at around the 75% mark on template and then tapers back a bit.
I still need to layout the table better and put in columns to compare directly with template angles, so more to come later.

Last edited by Tesla; 06-02-2018 at 08:50 AM.. Reason: Correct image and text
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