Celestial navigation explained - page 7


Errors... and how to live with them

The reason why the 3 LOPs don't intersect as a point but as a triangle is the observations errors.

The observations errors are:

  • systematic error
  • random errors

The systematic error is the algebraic sum of the uncorrected index error of the sextant and the observer personal error. If not equal to zero, a personal error shows the observer inclination to always overestimate or underestimate the stars altitudes of a definite value.

The random errors depend on the observer experience and the observation conditions (bad horizon, rolling ship, abnormal atmospheric refraction, ...).

If you are really experienced (and lucky) and there are no random errors, then the systematic error can be eliminated by taking the cocked hat centre as True Position ONLY IF the observations azimuths are spread over more than 180°.

 

If the observations azimuths are not spread over 180°, the True Position is NOT the Cocked Hat Centre.

 

In this second case, to say that the True Position is the cocked hat centre, you need to correct 2 LOPs by moving them backwards and 1 LOP by moving it forward.
This is impossible because the systematic error is a constant of the same sign.

We have here an 'outside' fix: the True Position is outside the cocked hat.
Knowing his own personal error (inclination to always overestimate or underestimate the stars altitudes of a definite value) is the only way to find the True Position.

If there are random errors (and there will be, no matter how good observer you are), then the situation is even worse...

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