I don't think you understand the geometry. Where are you getting "3.6 degree decline" from? That degree of decline is going to depend on other variables. You are mashing up different concepts from trigonometry, algebra, and geometry in a nonsensical manner. Post the math. 1) The earth is an oblate spheroid, but is close enough to a sphere. 2) Cutting a sphere through the midpoint gives you a circle. 3) You measure viewing distance by using a right triangle and solving for a leg of that triangle. 4) The hypotenuse is the radius of the circle + the height above ground, whether that's 5 feet or 6.8 miles 5) Leg 1 of the right triangle is the radius of the circle (which takes you to the point on the circle at the maximum possible viewable distance). 6) You can then use the Pythagorean Theorem to calculate the viewable distance that extends from the hypotenuse above the circle to the most distant point on the circle that is viewable. >I would be interested to hear your explanation about the ship sinking past the horizon and then being re-viewable by zooming in from the same viewpoint. This is bullshit. If someone was actually able to do this, it was probably because the seas calmed down from 6 foot waves to 1 foot waves, and/or the ship dumped ballast, not because "zooming in" magically made the ship observable.