Intercept method: Difference between revisions

Revision as of 05:48, 19 March 2014

Revision as of 09:52, 5 May 2014

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The intercept method is based on the following principle.

The actual distance from the observer to the geographical position ('''GP''') of a celestial body (that is, the point where it is directly overhead) is "measured" using a sextant. The observer has already estimated his position by [[dead reckoning]] and calculated the distance from the estimated position to the body's GP; the difference between the "measured" and calculated distances is called the intercept.

[[Image:Diagram showing GP distance = ZD.jpg|thumb|right|500px|]]

The diagram on the right shows why the zenith distance of a celestial body is equal to the angular distance of its GP from the observer's position.

The rays of light from a celestial body are assumed to be parallel (unless the observer is looking at the moon, which is too close for such a simplification). The angle at the centre of the earth that the ray of light passing through the body's GP makes with the line running from the observer's zenith is the same as the zenith distance. This is because they are [[corresponding angles]]. In practice it is not necessary to use zenith distances, which are 90° minus altitude, as the calculations can be done using observed altitude and calculated altitude.

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Next, the altitude and azimuth of the celestial body are computed for a selected position (assumed position or AP). This involves resolving a spherical triangle. Given the three magnitudes: local hour angle (LHA), observed body's declination (dec.), and assumed latitude (lat), the altitude Hc and azimuth Zn must be computed. The local hour angle, LHA, is the difference between the AP [[longitude]] and the hour angle of the observed object. It is always measured in a westerly direction from the assumed position.

The relevant formulas (derived using the [[Spherical_trigonometrySpherical trigonometry#Identities|Spherical trigonometric identities]]) are:

: {{math|size=large|sin(Hc) {{=}} sin(lat) · sin(dec) + cos(lat) · cos(dec) · cos(LHA)}}

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{{overline|Hc}} = 90° - Hc.

The relevant formula for Zn is

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Professional navigators are somewhat split in usage between sight reduction tables on the one hand, and handheld computers or scientific calculators on the other. Either method is equally accurate. It is simply a matter of personal preference which method is used. An experienced navigator can reduce a sight from start to finish in about 5 minutes using nautical tables or a scientific calculator.

The precise ___location of the assumed position has no great impact on the result, as long as it is reasonably close to the observer's actual position. An assumed position within 1 degree of arc of the observer's actual position is usually considered acceptable.

The calculated altitude (Hc) is compared to the observed altitude (Ho, sextant altitude [Hs] corrected for various errors). The difference between Hc and Ho is called "intercept" and is the observer's distance from the assumed position. The resulting line of position (LOP) is a small segment of the circle of equal altitude, and is represented by a straight line perpendicular to the azimuth of the celestial body. 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.

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==Running fix==

A fix is called a ''running fix'' when one or more of the LOPs used to obtain it is an LOP advanced or retrieved over time. In order to get a fix the LOP must cross at an angle, the closer to 90° the better. This means the observations must have different azimuths. During the day, if only the Sun is visible, it is possible to get an LOP from the observation but not a fix as another LOP is needed. What may be done is take a first sight which yields one LOP and, some hours later, when the Sun's azimuth has changed substantially, take a second sight which yields a second LOP. Knowing the distance and course sailed in the interval, the first LOP can be advanced to its new position and the intersection with the second LOP yields a ''running fix''.

Any sight can be advanced and used to obtain a ''running fix''. It may be that the navigator due to weather conditions could only obtain a single sight at dawn. The resulting LOP can then be advanced when, later in the morning, a Sun observation becomes possible. The precision of a running fix depends on the error in distance and course so, naturally, a running fix tends to be less precise than an unqualified fix and the navigator must take into account his confidence in the exactitude of distance and course to estimate the resulting error in the running fix.