Intercept method
The Intercept Method, or Marc St Hilaire method, is an astronomical navigation method of calculating an observers position on earth. The method gives the observer a position line on which the observer is situated. Usually the observer will take two sets of sights at an interval of approximately 3 hours and run-on the earlier position line to the time of the second observation to give a 'fix'.
Methodology
It is used for comparing the true zenith distance and calculated zenith distance of a heavenly object to find the intercept (position) on a position line. The line obtained is actually part of a small circle, as opposed to great circle, where any observer can stand and the heavenly object would have the same altitude in the sky. When plotting the small segment of this circle on a chart it is drawn as a straight line, the resulting tiny errors are too small to be significant.
An assumed position is used, this is usually a DR or Dead Reckoning position. This is worked out by applying the distance from the last known position either by log or by the estimated speed over time with the course steered. A sight is taken, that is the distance above the horizon of a heavenly object is measured with a sextant and the exact time noted in UTC. The sextant angle obtained is corrected for dip (the error caused by the observers height above the sea) and refraction to obtain the true altitude of the object above the horizon. This is then subtracted from 90° to obtain the angular distance from the position directly above, the zenith. This is referred to as the True Zenith Distance. The true zenith distance of the object is also the distance (in arc) on the earth's surface from the observer to where that object is overhead, the geographical position of the object.
Using a Nautical Almanac, the declination (celestial latitude), and the hour angle (celestial longitude) are obtained of the observed object for the time of observation. These are used to calculate the zenith distance of the object from the observers DR position. This is referred to as the Calculated Zenith Distance.
If the observer is on the position circle which passes through his DR position, or actually at his DR position, the calculated and true zenith distances will be the same. If the calculated zenith distance is larger than the true zenith distance, then the DR position is further away from the geographical position of the object than the true position and vice versa.
To draw the position line on a chart the azimuth or bearing of the heavenly object must be known. It is usually calculated but could have been observed. A line is drawn from the DR position either towards (CSD > TSD), or away (CSD < TSD) from the observed object along the bearing. The position line lies perpendicular to the azimuth at a distance equal to the intercept.
To obtain a fix (a position) this line must be crossed with another position line either from another sight or from elsewhere e.g. a bearing of a point of land or crossing a depth contour such as the 200 metre depth line on a chart.
Sights
Until the age of satellite navigation ships usually took sights at dawn, noon and dusk. The morning and evening sights were taken during twilight whilst the horizon was visible and the stars, planets and/or moon were visible, at least through the telescope of a sextant's. Three or more observations were required to give a position accurate to within a mile under favourable conditions.
Running fix
The noon sight is a running fix. A sight of the sun is taken around 9 am ship's time and the position line is run up to noon. At noon a meridian_altitude is taken which obtains the latitude which is crossed with the run up earlier sight and a noon position obtained. As the noon sight is a running fix it is not as accurate as the star sights taken at dawn and dusk.
Calculating a sight with the intercept method can be done with nautical tables using the haversine formula.
Where
- Z = Zenith Distance
- L = Latitude
- D = Declination
- H = Local Hour Angle
The local hour angle is the difference between the observer's DR longitude and the hour angle of the observed object. This is always measured in a westerly direction from the observers DR position.
An experienced navigator can do a sight from start to finish in about 5 minutes using nautical tables or a scientific calculator.
Sight reduction tables are often used for star sights, as they can greatly speed up the process. Professional navigators, in general, do not use them for the sun, moon and planets as it is quicker to calculate these using tables or a scientific calculator.
The sight reduction tables in the British Nautical Almanac are designed to be used only if there are no tables, proper sight reduction tables or calculators available.
See also
References
- Nicholls's Concise Guide, Volume 1, by Charles H. Brown F.R.S.G.S. Extra Master
- Norie's Nautical Tables, edited by Capt. A.G. Blance
- The Nautical Almanac 2005, published by Her Majesty's Nautical Almanac Office
- Navigation for School and College, by A.C Gardner and W.G. Creelman