Spiral Design Help Needed

I am an artist working on a large installation. I know very little about math but found that there are some posters that have commented on equalizing the space between spiral loops.

I have a hanging, 9 foot in diameter, flat horizontal spiral element. In my maquette (3d model) I have hung my mock-up components. I am decreasing the length of the hanging components as I move around the spiral. This decrease in length is consistent from one component to the next. As I move around the spiral the space between the loops is increasing. The bottom loops are close and as I move up the spiral the loops are further apart. Is this normal mathematically???

My question: how do I adjust my measurements so that I keep the spacing, between the loops consistent as I move up the spiral? Maybe a visual image would help, I am trying to create the effect of a tornado movement - the spiraling upward movement. I am happy to post a photo of the maquette.

Thank you for any help!!

An image or two would help. Are you using Rhino and/or Grasshopper, or are you just looking for general help with geometry?

Hi David,

Thank you. I am not using a program; would not know the first thing about how to program it! Everything I do is by hand. I have made a paper and string model before moving into my finished elements and wire attached to my aluminum spiral.

Here are several photos of the maquette. I have also included a photograph of two the other parts to the finished sculpture; the spiral piece will be added to these other two pieces, one is a circle and the other a vee.

I hope the photos give you a sense of what I am encountering and how AI would like to correct it. As I climb, in height, I have only shortened the string by one inch. And you can see what a jump I am getting in distance. The model is scaled down from my final piece.

Thank you for any help you can provide!

This forum is about using Rhino which is CAD software and Grasshopper which provides visual programming of Rhino.

It looks like the spacing of the strings is constant along the spiral, which means the angle from the center to adjacent strings increases as the spiral grows. To keep a constant spacing between loops of the spiral (constant pitch) the increment each string is shorter than its neighbor needs to be inversely proportional to the distance of each string from the center. The further a string is to the center the less it should be shortened relative to the string next to it.

This is a type of design for which Rhino with Grasshopper is very good tool to use in designing. It does take time to learn how to use Rhino with Grasshopper, probably much more than you may have available to complete your installation.

Thank you, David. I apologize for taking time in this thread that pertains to the specific programs. I am uncertain as how to contact someone who understands the type of mathematical equation I need to solve my issue and upon my search, saw this forum. I will give your suggestion a try.

Thank you and my best,

Hi Rebecca,
I’ll be available to help you if you like so.
Send me a private message.

Hi Ricardo,
Thank you! I am uncertain as to how this forum works. What additional information would you need?

For anyone interested in drawing a constant pitch spiral, an easy way to construct it is to do a cylindrical projection of a helix onto a cone:

@Rebecca2, the advantage of learning to use Rhino and it’s associated programming tool Grasshopper is that you can create visualizations without having to tie all those knots, then easily adjust parameters to see the effect of changes. E.g.:


But, as @davidcockey says, learning these tools takes time and effort. If you haven’t used them before then the programming for these visualizations probably looks daunting:

But if you like to experiment with ideas and have a (perhaps as yet undiscovered) aptitude for it then using Grasshopper can be really rewarding.


What is a method to create a cylindrical projection without using Grasshopper?

Hi David,

Draw a line from one end of the helix to the matching end of its axis. Sweep that using the helix as the rail and taking the road-like option. Create the intersection of the swept surface and the cone.