It's been a couple of days and I'm still waiting on Pcdefenders to get back with some answers.
In the meantime I thought I'd have a crack at answering one his questions. " So if you are correct and the frigate is travelling over a curve as you seem to be inferring then why do we not see the curve looking left to right across the horizon?"
Because this horizon is a circle around you, when you stand in the middle of that circle there is no curve left to right.
You can verify this by looking two ships on the horizon that are the same distance away from you, relative to your position on the earth these ships will be exactly the same elevation.
But here's where it gets interesting, say you're looking at 3 ships on the horizon over a 90 degree arc, ship A is to your left, ship B is 90 degrees to the right of A, and C is right in the middle.
Say that you're a shortarse and your height of eye is 1.7m, this will give you a visual horizon of about 5km depending on conditions.
You'll need to somewhere with a reasonably unobstructed view of the horizon. Out at sea is usually pretty good (water seeks level, right?

).
You can now draw a Right angle triangle from you to ships A and B, sides are 5km and the hypotenuse is near enough 7km.
This imaginary hypotenuse is completely level relative to you (you could even set up some gadget involving levels and lasers to observe this) but you'll notice that ship C and a bit of the ocean are sitting further out from the hypotenuse because the horizon is a circle.
Ship C is still only 5km from you, but the hypotenuse from A to B is only 3.5km, making it appear like C could be further away. It would be hard to make out with the naked eye as the angle change looking at an object 3.5 km to 5km would be very small. (Tiny fraction of a degree)
This is not a difference in elevation for the vessels, just different points on the circumference of a circle relative to you.