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how to create a spiral hemisphere with the same distance

Hello everyone,

I would like to create a spiral hemisphere with opposing spirals as shown in the picture. However, the special requirement is that the distance between the two spirals or between the revolutions should always be the same. 
When I create a spiral with the Helix tool, the distance on the planar plane is always the same. As soon as I project it onto the hemisphere, it is logically no longer always the same. (as can be seen in the picture).

Is there a feature or a workaround that I don't know that can solve this?



https://cad.onshape.com/documents/45dba9a13797ddb80d90e967/w/448939e33b89713aacf14704/e/9090cba823a3cded292c81c8

Thanks for any help.

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