SB-12 – VOR/VOR VOR/NDB NDB/NDB Navigation for Aviation

Description:

Calculate an aircraft's current geographical latitude and longitude (sometimes also called a fix) from the known positions of two VOR stations, two NDB stations, or mixed VOR and NDB stations, and either the VOR station's magnetic declination, or for an NDB, the local magnetic declination, preferably at the aircraft's current position, plus either the aircraft's magnetic radial FROM the VOR station, or the relative ADF bearing measured clockwise from the aircraft's nose, and the magnetic heading of the aircraft at the time of that ADF reading.

Disclaimer:

This program is designed for experimental navigation calculations over distances and at altitudes typical of general aviation (GA). It uses an approximate planar model of the Earth's surface, with corrections for the convergence of meridians towards the poles, rather than full spherical or ellipsoidal geometry.

This approximation introduces systematic position errors that can become substantial over long distances. The magnitude of these errors depends on the geographical configuration and generally increases with distance. Consequently, the program is not suitable for the extended navigation distances typical of high-altitude airline operations.

Operating conditions:

• The calculator must use 2nd Deg mode, not 2nd Rad or 2nd Grad. The initialization function 2nd E' enforces 2nd Deg mode.
• Southern latitudes and western longitudes are negative. Station coordinates use DDDMM.mmmmm; bearings, headings and declinations use decimal degrees (DDD.ddddddd).
• Magnetic declination is positive east and negative west. For a VOR, use the station's magnetic declination; for an NDB, use the local magnetic declination, preferably at the aircraft's position.
• For each VOR, enter its magnetic radial FROM the station, not merely the OBS course selected on the receiver (unless the CDI is centered with a FROM indication).
• For each NDB, enter the relative ADF bearing measured clockwise from the aircraft's nose, and record the aircraft's magnetic heading at the time of that ADF reading. For a VOR, the corresponding stored aircraft heading must be zero.
• The two observations should refer to approximately the same aircraft position. The program treats both VOR radials and NDB bearings as infinite, undirected lines; the 180° difference between a VOR radial FROM a station and an ADF bearing TO an NDB does not affect the line intersection.
• The (folded) acute intersection angle must be at least 5°. Obtuse and acute intersection angles are equivalent here; folding is based on sin(α)=sin(180°-α). The program rejects intersections of nearly parallel lines because of excessive error amplification.
• Before first use, press 2nd E' to initialize the program.

Usage:

To initialize for a new pair of navigation stations, press 2nd E'. Enter the geographical coordinates and magnetic declination of both navigation stations, followed by the appropriate VOR radial or ADF relative bearing for each station. Either station may be a VOR or an NDB:

VOR observations: No aircraft heading is needed. After initialization, the heading registers are zero; leave them at zero for any station that is a VOR. The program adds that VOR's station declination to the magnetic radial to obtain its true radial.

NDB/ADF observations: The ADF gives a bearing relative to the aircraft's nose, not a geographical bearing. The program converts the relative bearing to an absolute true bearing by adding the aircraft's magnetic heading at the moment of the ADF reading and then the local magnetic declination. Enter the magnetic heading and invoke the appropriate heading-storage subroutine:

Thus, in a VOR/NDB combination, store the magnetic heading only for the NDB; leave the VOR's heading register at zero. For two NDBs, use SBR ( and SBR ) separately if the aircraft's heading changed between ADF readings, or SBR EE if the same heading applies to both.

D or 2nd D' do not store the aircraft's heading automatically. D and 2nd D' versus SBR (, SBR ) and SBR EE are mutually independent.

Do not enter an already converted absolute magnetic bearing as though it were a relative ADF bearing while a nonzero heading is stored.

Press E to calculate the aircraft's position. If the geometry is acceptable, the aircraft's latitude appears on the display (x), and its longitude is placed in the test register t, both in DDDMM.mmmmm format. After calculation, A, B, C, 2nd A', 2nd B' and 2nd C' retrieve their stored values instead of accepting new ones; D and 2nd D' always accept new readings (in order to allow for quick successive fixes).

For another fix using the same pair of stations, enter new radials or ADF readings with D and 2nd D', update the magnetic heading for each NDB as necessary, and press E again. To change station coordinates or declinations, press 2nd E' and re-enter all data; initialization clears registers 01–29, including the stored headings.

Intersection quality: After pressing E, use SBR = to display the acute intersection angle (0–90°) in x and the error margin amplification factor in t. The error margin amplification factor indicates how the geometry magnifies bearing errors; it is not an absolute position-error estimate. This subroutine also works after a rejected calculation.

If the (folded) acute intersection angle is less than 5°, the program rejects the fix and stops with a blinking "9.9999999 99" in the display (x), instead of producing position coordinates (and register t is set to zero). SBR = can still be used after that to examine the intersection geometry.

Function keys:

Subroutines:

Output:

Distances in registers 21 and 22 are signed because the program intersects complete lines rather than directional rays. A negative value places the aircraft on the opposite side of the station from the direction used in the calculation. In particular, negative distances are normal for NDB bearings, which point TO the beacon.

Registers 23 and 24 provide a second calculation of the intersection coordinates, starting from station 2; they are available for cross-checking only. The normal displayed fix uses registers 07 and 08. The true directions in registers 11 and 12 are used directly in trigonometric calculations and are not normalized to 0–360°.

After SBR =, x and t show the intersection angle and error margin amplification factor instead of latitude and longitude; the stored coordinates in registers 07 and 08 remain available. Or simply press E again.

Good to know:

The program does not interrupt ongoing calculations. Its functions and subroutines do not use CLR or = internally, so ongoing arithmetic operations are not prematurely cleared or evaluated.

Registers used:

Glossary: