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))	132448893	11037407.8	2090.418	3364201891	3364201.9	3364.202
Surveyor Drop†	Dₛ=8"×o²	288	24.0	0.005	7315	7.3	0.007
Drop†	D=sqrt(R²+o²)-R	288	24.0	0.005	7317	7.3	0.007
Obscured† *	x=sqrt((o-d)²+R²)-R	n/a	n/a	n/a	n/a	n/a	n/a

value	formula	radians	degrees	DMS
Tilt ∠	t=o/R	0.001516	0.0868	0° 5' 12.6"
Dip ∠ *	a=atan(d/R)	0.485809	27.8348	27° 50' 5.3"
Angular Size	α=2*atan(h/o/2)	3.095269	177.3458	177° 20' 45"

value	formula	pixels
Sagitta, horizon centered	w*(H*cos(a)-(Z*cos(fov/2)*sin(a))/(2*Z*sin(fov/2))	195.83
Sagitta, camera level	w*d/R*tan(fov/4)/2	221.46

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