Actually I mostly used your formula, you are not accounting for changing feet to miles in your calculations. The actually formula uses the Pythagorean theorem to deduce the proper drop. The globe doesn't just drop by 8 inch per each mile. It drops 8 inch in a mile and then the next mile is dropped an additional 8 inch from the 8 inch dropped position since it's a curve. You are misinterpreting 8 inch/mile for just squaring 8. You need to use triangles to proper gauge the distance. I was hoping the distances would be good approximations, but the effect is greater then I thought.

Check out this website which explains the math a lot simpler and better then I could

https://dizzib.github.io/earth/curve-calc/?d0=28&h0=194&unit=imperial

It actually heavily depends on the eye level. I entice you to play around. You won't see a lighthouse 28 miles away that is 194 feet high while at sea level. But be on a platform or a ship, lets say 100 ft above sea level and that lighthouse is visible weather permitting.