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	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	78	6.5	0.001	1989	2.0	0.002

value	formula	radians	degrees	DMS
Tilt ∠	t=o/R	0.001516	0.0868	0° 5' 12.6"
Dip ∠ *	a=atan(d/R)	0.000725	0.0416	0° 2' 29.6"
Angular Size	α=2*atan(h/o/2)	0.000174	0.0099	0° 0' 35.8"

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.