What is the Rate of Perceived Horizon Curvature Change with Altitude?

[Baluncore]

As the elevator car rises, the line between surface and atmosphere as I perceive it begins to appear curved; the higher I go, the more curved I perceive it to be. So... at what rate does that perceived curve change and what calculation(s) do I need to measure that perceived curve?

You are asking for the curvature, which is usually defined as the reciprocal of the radius.

The radius of the horizon circle, measured as an angle, y, away from the south-pole of the projection, will be: y = arcsin( R / ( R + x ) ); where R is the radius of the Earth and x is your height above the Earth's surface.

You can solve that for the rate of change by finding the derivative y' .