Folding surface/facade with consistent width of panel/surface?

Hi,

I worked with grasshopper a lot a couple years ago and am just now coming back to it and having trouble getting my head in the right mindset to create a solution for my intention.

I am creating a changing surface/facade to cover an existing form created from a radial grid. (not nearly a final form but just so you can get the idea)

All I want to make is a surface that folds back and forth over my form along the radiuses of the circular grid. I have found a few examples online, though no script that was really helpful or effective. I know it isn't a very difficult task, and I've been able to do it by dividing the surface along radiuses, offsetting and lofting and adjusting seams, all manually.

(tested at two different angle sizes)

HOWEVER, I can only come up with how to do this and maintain the angle all the way around the form, and not the panel width! Since they are wrapping around radially, if the panel width is maintained, then the angle will be more acute towards the center of the radial grid and more obtuse the further out it is. 

Here is the scope of the fold essentially (from one side of the form to the other).

How do I maintain a consistent length and let the angle be based off of that length and its position on the grid?

Thank you so much, I'd really appreciate any ideas!