Stretch spiral cut sheet to form helical shape

I’m trying to simulate a shape similar to (but not the same as!) the attached picture of a chimney cowl.


Basically I’m aiming to cut spiral lines in a flat surface and then press or pull the centre along the Z axis to form the helix type shape.

My current rather poor attempt is attached. I’m well out of my depth here - the surface is not cut and doesn’t follow the lines, the top doesn’t rotate, etc.

Any help or pointers would be great…

Stretch spiral (12.2 KB)

Here’s a quicky possible solution:

Stretch spiral (20.6 KB)

Substituting an ellipse for the rectangle makes it look prettier I think:


Thanks for that Birk - it looks very similar to the chimney cowl. However I’m at fault for not describing my objective very well.

I want to simulate taking a sheet of material with arc lines cut in it spiraling out from the centre.
Then I will press the centre in the Z axis to form a dome like structure. As the centre is displaced it will rotate slightly and all the spiral strips will distort.

I’ve now found a better picture of the sort of end result - however it’s not my intention to make paper hats!