How to repeat a hanging chain

Hi, I created a model that creates s hanging chain.

The points inside the curve don’t get load, so the top remains straight.

I want to create the transition from square to arch in the fixed height. I did it manually by making a chain, duplicating the line, reducing the size of the curve containing the points that will not get load, adjusting the load until the vault hits the same height, I repeat this until the rectangle becomes completely vaulty.

In the end I want to mirror the transition and create a lofted surface.

I want to know if there is a way I can create the desired outcome without creating the line one by one manually.

Here’s the grasshopper model! (10.2 KB)

I’m not sure how to control the final height of the chains to be identical. I tried by distributing the same total load to each chain, and the resultant heights appear to increase linearly.

dividing varying the amount of load applied to each point by the power of the number of points gives this

i found that power of approx 3.14 (pi!) looks fairly close to equal height.

My exploration is a bit of a mess. you’ll see the red groups affect the height. I’ve used a meshloft from Chromodoris because it’s fast, but not necessary.

Maybe you could use another goal to control the height? What properties does your final form need? (24.6 KB)

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