So we are arguing over decimal places. I say 1666.666, you say 1667.1539. ft... Your math is just using 8.00233872 inches instead of 8 inchesI am well aware of numbers being squared for use in various formulae but you are quite ignoring what I have been saying. Any unit multiplied by that same unit, results in that unit². A clear example is the one you just gave 32ft/s². How do you think it became s²? Because the time unit s was multiplied by the time unit s. In many equations units get multiplied and divided, and that effects what the resulting units will be.
A number squared with or without a unit does result in a larger number but once units are involved, the units get squared. Units play a huge role in math, physics, chemistry, etc., because that is precisely how one comes up with things like ft/s or ft/s². Formulae express certain information and relationships symbolically; it's how scientists know what information is being stated and how the result applies.
That has nothing to do with what we at discussing.
0.31574886 miles or 1667.1539808 ft. You'll notice that agrees exactly with the diagram you gave, the very one that gives the trig functions for figuring it out.
Use your way for 2000 miles, 3000 miles, and 3959 miles.
Do you really want to quibble over such discrepancies? I mean, really? A half a foot difference over 50 miles. Seriously?
In actual fact, your math shows more of a curve than mine. It only reinforces the fact that some things that are visible to us, over a flat surface, should actually be even FURTHER beyond the curve of the earth. They should be even further beyond our ability to see them.
If you extend the distance to 2000 miles, 3000 miles and 3959 miles, the drop would be even greater using your method. So, let's use your math, to build a car engine and mine to dig a post hole...It's only a matter of accuracy to within 1/2 foot over 50 miles.
I'm sorry but if you still want to say my math doesn't work, you're not going to hurt may feelings.....