This is a cycloid in a circle - I don't know how to model that![br][br]Thanks to Zbynek Konecny for his technical assistance and to Tim Brzezinski for his ideas about cycloids.[br]
Here's a link to some cycloid info: https://proofwiki.org/wiki/Length_of_Arc_of_Cycloid[br][br]And Tim's cycloid investigation: https://www.geogebra.org/m/fVPsKXfk[br][br]Algebra will have to wait!