Labels  Values  formula  
R, radius of Earth (miles)  3963  
D, distance from observer (miles)  60  
α, angle to observer (radians)  0.015140045  D / R  
A  3962.545807  R ∙ cos(α)  
B  59.99770782  R ∙ sin(α)  
C  0.454192687  R  A  
E  59.99942695  sqrt(B²+C²)  
F  29.99971347  E / 2  
G  3962.88645  sqrt(R²F²)  
H  0.113549798  R  G  
H in feet  599.5429355  H x 5280 ft/mi  
Calculate the height of the effective barrier between observer and object under observation, created by the  
curvature of the Earth, as a function of the distance between observer and object under observation.  
I.e., calculate the maximum height difference between a straight line and a curve which follows the curvature  
of the Earth.  


The fundamental deficiency in this approach is the assumption that Earth has no atmosphere.  
In the real world, the Earth's atmosphere acts as a lens, which refracts light. Depending  
on atmospheric conditions, it is often possible for things beneath the horizon to appear at  
the horizon, or even above the horizon. Here are a couple of very good web pages on this topic:  
http://wwwrohan.sdsu.edu/~aty/explain/atmos_refr/horizon.html  
http://wwwrohan.sdsu.edu/~aty/explain/atmos_refr/altitudes.html 
Dave Burton
30 April, 2016