Ships Over The Horizon, Globe vs. Flat Earth

All images below are generated with my Refraction Simulator, based on Fermat's principle, the Ciddor equation and the Ideal gas law, see Deriving Equations for Atmospheric Refraction. The images show how Globe and Flat Earth would appear in certain Refraction Conditions, as labeled in the images.




Image 2 shows what we see in good viewing conditions without mirages, when atmospheric refraction is so called standard refraction.

Image 1 and 5 show what we see in good viewing conditions with some inferior mirage. On the Globe model (1) the overall temperature gradient is standard −0.65°C/100 m. To produce the same observation on a flat earth (5), light has to bend upwards in a radius of about 7500 km. This requires that the air density is inverted, getting constantly denser with increasing altitude. This is not the case in reality. According to Calculating the Temperature Gradient (Destination PageDeriving Equations for Atmospheric Refraction) such an up-bending of light requires a temperature gradient of about −17°C/100 m. And because we can observe such a convex curved earth at any altitude, this gradient has to get even stronger with increasing altitude because the air pressure decreases with increasing altitude. This means the temperature would reach absolute zero = −273.15°C below 1700 m altitude, which is physically impossible.

Temperature gradients of −17°C/100 m are possible, but only in small layers directly above a hot surface, see Refraction above the Ground Layer (Destination PageRefraction Coefficient as a Function of Altitude). They produce inferior mirages. The hot air quickly raises up and gets replaced by cooler air, wich gets heated ect. This convection currents cause strong flickering. Above some meters the air is mixed well, becomes calm and approaches the standard temperature gradient of −0.0065..−0.013°C/m, which reduces only slightly up to 11 km altitude.

This is a fact. Aircraft speed measurements and calculations and altimeter calibrations are based on the model of the International Standard Atmosphere, see Fluggeschwindigkeiten, IAS, TAS, EAS, CAS, Mach and Barometric Formula.

Image 3 and 6: On normal refraction conditions (with or without mirage) the Flat Earth would always appear concave. It requires extreme refraction to get the same appearance on the Globe, see Strong Refraction Simulation and Reality for 2 Oil Platforms.

Image 4: Only on Zero refraction the Flat Earth appears flat. We never have exactly zero refraction in the atmosphere.

The observer height is 5 m. The magenta line shows eye level, the cyan line shows the geometric horizon. The ships are at 10 km, 20 km and 30 km distance. Zoom factor is 2500 mm (35 mm equivalent),

Refraction Simulation

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Created Tuesday, July 7, 2020
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Changed Saturday, October 7, 2023