Morris Dovey wrote:

Afterward I wondered if a catenary with that same 1/8" chord height
might apply more even pressure...



Take your choice, a catenary is a special case of a parabola where
only the weight of the cable, chain, rope, etc defines the curve.

x^2/a^2 + y^2/b^2 = 1 is the basic formula for a parabola. where the
values chosen for a & b define the curve.

Lew