Chapter 20: Sight Reduction and Lines of Position

The Marcq Saint-Hilaire intercept method

Choose an assumed or dead-reckoning position. Compute Hc and Zn for the body at the time of observation using Pub 229 (for an assumed position with whole degrees of latitude and LHA), Pub 249 for selected stars, or a calculator. Compare Ho with Hc: the intercept a = Ho − Hc. If Ho is greater, the vessel is nearer the body's geographical position and the intercept is plotted toward the azimuth — 'Ho Mo To', Ho more, plot toward. Draw the LOP perpendicular to the azimuth at the end of the intercept.

• a = Ho − Hc, one minute of arc = one nautical mile
• Ho greater than Hc → toward the body; Ho less → away
• The LOP is perpendicular to Zn at the intercept point

Fixes and running fixes

Two or more LOPs from bodies whose azimuths differ by 60°–120° give a strong celestial fix; three-star fixes at twilight are the classic practice and their small triangle indicates quality. Sights taken at different times are advanced along the DR track like any running fix. A single body observed at widely separated times — the sun in the morning, at noon, and in the afternoon — gives a sun-run-sun fix.

Sources of error

Timing error shifts the LOP along the azimuth in longitude; altitude error shifts it perpendicular. Systematic error (a bad index correction, personal error, abnormal refraction) displaces all LOPs of a round in the same sense, producing a neat but wrong triangle offset from the truth — which is why a plausible small triangle is not proof of accuracy.