(48G) Light of Sight: Altitude

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(48G) Light of Sight: Altitude - Eddie W. Shore - 2026-05-01 07:29

The program calculates altitude required for an airplane to receive a signal from an airplane.

Inputs:
3:  height of the antenna in feet
2:  average height of the terrain between the airplane and antenna
1:  horizontal distance from airplane to antenna in nautical miles

Enter numbers only, no need to attach units.

Output:
1:  required height in feet, _ft unit object attached

Program LOSALT:
Code:
<< '1_nmi' * 3 ROLLD '1_ft' * '1_nmi'
CONVERT '3440_nmi' + SQ 3 ROLLD '1_ft'
* '1_nmi' CONVERT '3440_nmi' + SQ DUP
4 ROLL SWAP - √ 3 ROLL SWAP - SQ + √
'3440_nmi' - '1_ft' CONVERT >>


Example:
height of antenna:  426 ft
average terrain height:  846 ft
horizontal distance:  57 nautical mi

required altitude:  ≈1519.7282 ft

Note:  An average Earth radius is 3440 nautical miles is used.  Results will vary since Earth is a spheroid. 

Formulas Used:

R_ter: terrain height,  Rt = radius_Earth + R_ter
R_atn: antenna height,  Ra = radius_Earth + R_atn
D:  distance to antenna
R_alt: altitude
1 nmi ≈ 6076.1155 ft
R_alt = √(Ra^2 + (D - √(Ra^2 - Rt^2))^2) - radius_Earth


This is a partial adaption of the line of sight distance program of the HP 67.

Source:
Hewlett Packard. "Line of Sight Distance"  HP-67/HP-97 User's Library Solutions: Avigation.  Corvallis, OR.  Rev. E. April 1979.  pp. 18-22