8 inches per mile

This is the rate of the earth's curvature.

I don't think I've ever seen it expressed this way before.

I haven't seen that one either. Here's another way of looking at it.

For an observer on the ground with eye level at h = 5 ft 7 in (1.70 m), the horizon is at a distance of 2.9 miles (4.7 km).

I would have thought it was much farther.

With these simple mathematical tools one could pretty easily calculate the circumference of the earth, from watching a sailing ship of known height disappear over the horizon.