FEI Horizon Calculator

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Inputs

Observation Height	h= inches feet miles millimeters meters kilometers
Object Distance	o= inches feet miles millimeters meters kilometers as  tangent (level from observer) curve (great circle distance)
Earth Radius	R= inches feet miles millimeters meters kilometers ϕ= latitude°    Refraction( 0 %) *
Image Width	w= px
Horizontal FOV	fov= °

  

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Calculations

value	formula	in	ft	mi	mm	m	km
Horizon† *	d=sqrt(h(h+2×R))	181965	15163.7	2.872	4621905	4621.9	4.622
Surveyor Drop†	Dₛ=8"×o²	9800	816.7	0.155	248920	248.9	0.249
Drop†	D=sqrt(R²+o²)-R	9802	816.9	0.155	248978	249.0	0.249
Obscured† *	x=sqrt((o-d)²+R²)-R	8260	688.3	0.130	209795	209.8	0.210

value	formula	radians	degrees	DMS
Tilt ∠	t=o/R	0.008841	0.5065	0° 30' 23.5"
Dip ∠ *	a=atan(d/R)	0.000725	0.0416	0° 2' 29.6"
Angular Size	α=2*atan(h/o/2)	0.000030	0.0017	0° 0' 6.1"

value	formula	pixels
Sagitta, horizon centered	w*(H*cos(a)-(Z*cos(fov/2)*sin(a))/(2*Z*sin(fov/2))	0.30
Sagitta, camera level	w*d/R*tan(fov/4)/2	0.30

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NOTES (v0.0.6):
Calculations assume equal elevation terrain, clear line of sight, sane input values.