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))	212489	17707.4	3.354	5397223	5397.2	5.397
Surveyor Drop†	Dₛ=8"×o²	487	40.6	0.008	12363	12.4	0.012
Drop†	D=sqrt(R²+o²)-R	487	40.6	0.008	12366	12.4	0.012
Obscured† *	x=sqrt((o-d)²+R²)-R	158	13.2	0.002	4018	4.0	0.004

value	formula	radians	degrees	DMS
Tilt ∠	t=o/R	0.001970	0.1129	0° 6' 46.4"
Dip ∠ *	a=atan(d/R)	0.000847	0.0485	0° 2' 54.7"
Angular Size	α=2*atan(h/o/2)	0.000182	0.0104	0° 0' 37.6"

value	formula	pixels
Sagitta, horizon centered	w*(H*cos(a)-(Z*cos(fov/2)*sin(a))/(2*Z*sin(fov/2))	0.36
Sagitta, camera level	w*d/R*tan(fov/4)/2	0.36

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