Celestial navigation explained - page 5

Traditional method : lines of position (LOPs) and intercepts

circles and lines of position

This method was invented in 1875 by the admiral Marcq de Saint-Hilaire (some other sources say Y. Villarcau and A. de Magnac). The true line of position A, tangent to the circle of position, can be merged into the line of position B because the estimated position e is close to the true position O.
On the line of position B, the intercept is the difference between the true (observed) altitude and the calculated altitude:


Practically, the procedure is as follow:

  1. find the estimated position with an accuracy of 50 nautical miles (in order to get a fix with 1 nautical mile maximum error due to the method itself);
  2. observe with the sextant a star altitude Hs at the time C (GMT);
  3. correct the sextant altitude Hs with the instrumental error, the dip of the apparent horizon, the terrestrial refraction, the astronomic refraction, the parallax, the semi-diameter of the star (if needed) to get Ho (observed altitude);
  4. compute the azimuth of the star using the estimated position and the data's of the Nautical Almanac at the time C;
  5. compute the calculated altitude Hc;
  6. compute the intercept ITC = Ho - Hc;
  7. plot the line of bearing (azimuth of the star) from the estimated position;
  8. plot the line of position perpendicular to the line of bearing, at a distance ITC from the estimated position, away if Hc > Ho;
  9. start over again the steps 2-8, at least once, to get the drawing below:


O is the observer true (astronomic) position.


Note: ITC is used in this text as foreshortening for InTerCept and is not an abbreviation. Don't confuse the intercept ITC with ITP - the Intercept Terminal Point.
ITP is the point through which the circle of position passes. The LOP is tangent to the circle of position at this point.

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