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Why longitude method is used for the morning Sun sight?

It is used to be a common practice to take the morning sun sight by longitude method. The intention of taking this sight is to use the transferred position line, to get a running fix at noon. It is a followed practice to send the noon position report to owners, charterers, etc. The local time for this sight is close to 0900 ST. There are a few reasons for this:

  1. Sun must reach an altitude of at least 15o, so that the refraction correction is low. Though, for the altitudes smaller than 15o, refraction corrections are not available but if the actual refraction correction is even out by 2-3 minutes, the accuracy will be affected, reasonably. Whereas, if the refraction correction itself is low then chances of errors will be low too.
  2. The sight time should be closer to sunrise rather than be closer to merpass. The idea is the azimuth should be as high as possible. This is because the position line is as close to N-S as possible. The idea also being sufficient gap between the AM and noon sight. This is to provide a good angle of cut for the running fix.

The general idea of noon sight:
On any passage the morning sun sight is to test the east-west positioning of ship and merpass sight is to test north south positioning of the ship. At merpass the fix is ascertained using both the data.

The preference to morning sun sight by longitude method, over the intercept sight is for the following reasons:

  1. In a passage, the calculated longitude being east or west of DR longitude gives an idea on an E-W trans-Pacific or trans-Atlantic passage, that the ship is doing a better speed or poorer speed than expected. Or for that matter, on any passage, the eastward or westward influence of current is detected with the P-L. Thus, even though a position fix is not available at 0900 ST, there is a fair idea about the speed made good. Not that an intercept sight won’t give this idea but with longitude sight there is a direct indication about the drift.
  2. In order to transfer a position line trigonometrically, a point on the position line must be selected. In case of a longitude sight DR latitude and calculated longitude give the point or make a point on position line, which can be run using plane or rhumb line sailing principle.
    One of the difference between the two sights i.e. long by chron and intercept sight being, in the PL of former one, point on PL is known whereas in the case of later, the point on PL is not known. The other difference being in longitude sight, only the DR latitude is used for calculation, whereas in case of the intercept sight, DR lat s well as DR longitude are used in calculation.
  3. The basic formula used at the time of merpass sight is d’long = d’lat x ‘c’. This is based on the formula:-

In traditional system of noon fix calculation, a watchkeeper, while taking the altitude at merpass used to do the calculations mentally. He probably would think, “position appears to south of DR lat, looks like she is doing a better speed”. Thus with the difference of computed sextant altitude and a sextant altitude that he finds, multiplied with ‘c’ correction, using his pocket calculator, the second officer would know the correction to be applied in DR longitude.

Thus, the ease of transferring morning P/L and applying ‘c’ correction was one of the reasons for using longitude sight.

4. As we know calculated longitude does not give longitude of ship but gives, just a common point with DR latitude that was used in calculation of sight; to draw the PL. In a situation where L & D are of same name and D < L, the body crosses observer’s Prime Vertical. If the sight is taken at this instant, i.e. when the body is over observer’s prime vertical, the azimuth would be 90o and the PL would be NS.

This is the situation with following advantages:

  1. At AM sun sight, the actual longitude of ship is obtained.
  2. At merpass, there is no longitude correction even if the latitude error is high.
  3. The so called longitude of ship at noon can be stated at the calculation of AM sight itself and the noon position determination is quicker.

By the way as a matter of interest the other situation when you get the ship’s actual longitude is when the latitude used for calculation is actual latitude of ship.

Thus, with the traditional practice since one of the responsibility of a longitude sight was to give the idea of longitude of ship, this sight is not taken when the body is close to merpass or the azimuth is low.

A small error on the latitude used will give a large difference in ship’s longitude and calculated longitude. Thus, in latitude 30oN, if the azimuth of Sun was N8oE, thus for an error of 5’ in latitude the difference in ship’s long and calculated long would be

Of course PL obtained would be same as that from an intercept sight. A comparative plotting would reveal that an intercept sight would provide a small intercept. P-L is drawn from a point close to DR.

However, a mariner must also understand the following points:

  1. A zero intercept does not mean that DR position is actual position. It simply means that P/L passes from DR that was used.=
  2. On the other hand, if latitude used is actual latitude, the longitude calculated will be actual longitude of ship.

The two sights may be compared in a spherical triangle where the spherical triangle is constructed from 3 parts available.

A spherical triangle has 6 parts viz. 3 sides and 3 angles. Longitude and intercept sights can be worked by basic Cosine formula. In long methods, hour angle is found from the data viz. one assumed side and two confirmed sides. Whereas, in intercept sight, a side is calculated from the data viz. one assumed side, one assumed (included) angle and one determined side. Though, intercept method uses two of the parts of the assumed values, this does not dilute the accuracy of the intercept as the zenith distance obtained is the distance of GP from the assumed position.

Rate of change of altitude Sun = 15o Cos lat Sin azimuth.

Considering above formula, the rate of change of altitude will be high when azimuth is close to 90o and will be very small when azimuth is close to 00 (small). But this is true for both the sights. For both the sights:

  1. Rate of change of GHA is constant, throughout.
  2. Rate of change of altitude depends on the size of azimuth.
  3. Chronometer or GMT for the observation is noted.

Error in intercept = longitude error x Cos lat x Sin azimuth
Error in intercept = Error in latitude x Cos azimuth

In case of a body close to merpass Sin Azimuth is very small, close to zero & Cos azimuth is close to unity. This means a longitude error will not affect the value of intercept and a latitude error can cause a maximum error in intercept equal to error in latitude itself.

It is for this reason that an intercept sight can be taken when the body is close to meridian or when azimuth is low.

In today’s time when all the sights are taken by scientific calculator, no short cut by ex meridian tables is found effective. An intercept sight can be preferred to an ex meridian sight. The single formula usable for all the three observations is as follows:

  1. Bracket on RHS is always –ve.
  2. P = LHA or 360 – LHA.
  3. To calculate L ~ D, same names subtract different names add.
  4. To use this formula for intercept, keep ZD on one side, shift everything on other side, write LHA for P.
  5. To use it as ex meridian formula, use MZD for L ~ D and TZD for ZD, LHA for P.

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