Earth curvature calculation spreadsheet  
Labels  Values  formula  
R, radius of Earth (miles)  3963  
D, distance from observer (miles)  18.7  
α, angle to observer (radians)  0.004718647  D / R  
A  3962.955881  R ∙ cos(α)  
B  18.69993061  R ∙ sin(α)  
C  0.044119272  R  A  
E  18.69998265  sqrt(B²+C²)  
F  9.349991326  E / 2  
G  3962.98897  sqrt(R²F²)  
H  0.011029833  R  G  
H in feet  58.2375203  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://aty.sdsu.edu/~aty/explain/atmos_refr/horizon.html  
http://aty.sdsu.edu/~aty/explain/atmos_refr/altitudes.html  


Note: the previous version of this spreadsheet (using 60 miles as the distance) is here:  
http://www.sealevel.info/Earth_curvature_calculation_spreadsheet_v1.htm  
This is an exported Excel spreadsheet. You can load it directly into  
Microsoft Excel 2003 or later, or another compatible spreadsheet  
program, such as Kingsoft WPS Office "Spreadsheets" (but not  
OpenOffice), to view (or change) the formulae & values. 
Dave Burton
30 April, 2016
(minor updates 3 November, 2017)