I'm sorry but your earth model necessitates a geometric horizon of no more than 1.22 times the square root of the observers height in feet. That is plenty accurate enough for local measurements. Guess what, horizon isn't geometric. It's an apparent location. Your model requires a geometric horizon.
What on Earth are you talking about? Nothing physical is measured in units of feet to the square root. Topography can go up or down by tens of thousands of feet. The only topography-free feature on Earth is the sea. And the atmosphere refracts, so the visible horizon is a bit below the geometric horizon.
I'm sorry but your earth model necessitates a geometric horizon of no more than 1.22 times the square root of the observers height in feet. That is plenty accurate enough for local measurements. Guess what, horizon isn't geometric. It's an apparent location. Your model requires a geometric horizon.
What on Earth are you talking about? Nothing physical is measured in units of feet to the square root. Topography can go up or down by tens of thousands of feet. The only topography-free feature on Earth is the sea. And the atmosphere refracts, so the visible horizon is a bit below the geometric horizon.
Start again with a coherent problem description.