3D model in 3DXML format available here :

http://www.3dvia.com/models/FDB6F2F3C5D7E9FB/log-spirale-3d-xml-file

This proposal is based on the shape of a snail shell.

But how to design it in 3D ?

Simply put :

1-make a flat (logarythmic) spiral

2-project on a cone

3-make a circle slip on this curve with a regular adjustment of the radius.

I don’t know how other guys do but my method to get a clean result is do the design 3 times

First try :

-I made a large model (over 2 meters) because I thought computation would be easier. Wrong : took me few hours to get nowhere.

Second shot :

-Close to the final model but the geometry was too complex to be computed as one solid. And I was not happy with the square shape grid. Garbage !

Finally:

-Sweep on center curve with reference to vertical surface. Angle Law driven.

-every 60 degrees, clockwise, counterclock wise

-manual closing (purple curves)

-trim and split

-parallel on surface +-.75mm

-close contour with line, project line on external skin

-split skin on closed contour, thickness 1.5mm

-boolean add on bodies.

-2 more turns for the top

-finish with a sphere.

 (special thanks to J.F.Rameau)

B.