Creating spiral with constant slope on tapered cone

Hello all--

I am creating a structure that is basically a tapered cone and would like to create a ramp with a constant slope along the height of the cone. I have tried many things, but am albeit not very proficient and have come to the end of my ability. My most recent effort is shown below; I begin with a central line and create a series of circles from division points along the line from which circles are created at varying radii, rotate the circles and evaluate length to get a spiralling series of points which are then interpolated to form a line. The obvious problem here is that the circles are evenly spaced in the z vector and as the cone decreases in radius the slope of the spiral must increase.

It's totally possible that this is the worst way possible to go about it, but I can't figure it out. Any help would be greatly appreciated.

Many thanks--

Grasshopper trainee

Replies to This Discussion

Permalink Reply by Laurent DELRIEU on April 21, 2014 at 5:07pm

I think you must search for loxodrome équation on cone
You can find on my page équation for a sphere

Permalink Reply by Dane Carlson on April 21, 2014 at 6:27pm

Laurent--

Thank you for your reply... I've looked through the script and really have no idea how to apply the spiral to a shape other than a sphere. Is it possible to include a shape input somewhere than the spiral lines would be inscribed on? Thanks very much for your thoughts.

Permalink Reply by Laurent DELRIEU on April 21, 2014 at 6:28pm

Hélix is also a good start. See ISO SCREW there is a definition with helix you will have to modify the radius because it is no more constant. I hâve just an iphone so i can't help you more :(

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