The Obstructed Boat from Pensacola Beach

"If you can't see a ship's hull, it is just angular resolution or the camera - zoom will bring it back from the horizon."

Photograph ships whose hulls are hidden by the horizon from a beach, at several zoom levels, and with cameras of very different aperture sizes. Check whether the amount of obstruction changes. MCToon did this on 13 Feb 2023 at Pensacola Beach (30°19'4" N, 87°16'33" W) with a Nikon P1000: two cargo ships and a fishing boat, all with their entire hulls obstructed - only the cabins and superstructure visible.

From an eye height of about 1.5 m the horizon is about 4.4 km away (d = 3.57 × √h); a ship beyond that shows only what rises above the horizon line. The Rayleigh criterion (θ = 1.22 × λ / D) sets when detail blurs, not when objects disappear - like the bottom line of an eye-chart: unreadable, but still there. The P1000's 67.4 mm aperture (0.00057° at 550 nm) is 20× the iPhone 13 Pro Max's 3.36 mm (0.01144°) - and the amount of obstruction was exactly the same.

MCToon's 2023 Pensacola observation: zoom did not bring the boats back - the obstruction was unchanged at every zoom level. Unedited photos with EXIF data and an unedited video are published on his page. The aperture comparison (P1000 vs iPhone) was the follow-up test that kills the angular-resolution explanation.

Bottom-up obstruction is exactly what curvature predicts, and the flat model's two escape hatches for it - 'just zoom' and 'angular resolution' - both fail the tests. The same effect is why the horizon-dip clinometer works: the horizon is a line, and it is below your eyes.