There is a scale issue in play which is typically overlooked by the popular literature; the best way to anchor a toy boat in a pond is with an elastic line and relatively huge anchor... the best way to anchor a large ship is with large heavy chain and a relatively small anchor. Our boats all lie on a spectrum between.Fantastic visual explanation. One question that may or may not be simple. Smaller boats dont usually carry all chain so what in your opinion is the correct "range" for the chain length in combo with the rode? Is there a magic number/ratio of chain to rode or is it insignificant? If it is insignificant then should we consider all rode and loose the chain? I was under the impression that the chain does add considerable holding power provided of course that the scope is correct. Perhaps my assumption is unfounded.
As to the ratio of chain to rope, the chain nearest the boat does practically nothing with regard to catenary, so there's not much theoretical point in exceeding about 75% chain in terms of the deployed rode even if you expect to benefit from the catenary effect.
However, per your last: the catenary from chain doesn't really do much, especially in typical depths, until you're talking about much larger vessels than most here are concerned with. The only thing that really matters is scope.