NavList:

In June I travelled from Florida to Bimini in the Bahamas and back on a 44ft catamaran. The passage of the Gulfstream was by motor in both directions. The Gulfstream itself varies in set and drift across the Straits of Florida and generally exceeds 2kts. I was taking sights with my Astra III Pro with a 7x30mm scope spaced at roughly one hour intervals to see how well I could do on a moving vessel. Although I had not planned it in advance I later realized that the sights could be used to compare the effectiveness of using a running fix to updating the DR position to the nearest point on the LoP to obtain an Estimated Position (EP) as described by John Karl in his book “Celestial Navigation in the GPS Age”, Ocean Navigator Magazine and on NavList . The problem for the running fix is that the azimuth difference between the sights is quite small and so the LoP’s intersect at very acute angles. Hence the fix is subject to large errors in a direction parallel to the LoP’s.

The attached file shows the results. These have been calculated assuming that they were plotted on a chart centred at 26°N. Since this analysis was not planned in advance I did not keep very careful track of the speed as recorded on the log but assume it was 7kts. The Gulfstream was taken to be a constant 2.5kts at 10° True. It is also possible to update the estimate of the set and drift for one sight to the next but I found in practice that that didn’t make much difference to the accuracy of the position obtained. In the interests of full disclosure generally I took multiple sights near a given time and I have selected the one with the smallest intercept.

The passage out was hand steered with wind on the nose most of the way. Towards the end we hoisted sail but made little progress as the wind had become very light. This explains why the DR position errors become quite large after 10am.

The passage back was under autopilot with no significant wind. Again a constant speed of 7kts is assumed with the Gulfstream running 2.75kts at 10° True.

From the starting GPS position the DR was computed. This was adjusted to obtain the Estimated Position (EP) as the nearest point to it on the LoP by dropping a perpendicular. The next DR position was computed starting from the EP. The distance of the DR and EP from the true GPS position is given in the columns labelled “Position Updating”.

In the case of the running fix, a fix was obtained by crossing the current LoP with the prior LoP advanced to the current DR position. The next DR position was computed starting from the fix.

The exercise was repeated with the intermediate sights discarded and using only the earliest and latest possible which yields the smaller tables.

On the passage out “Position Updating” performs well with the EP always being closer to the GPS position even when the DR estimates start to go awry. The EP error remains around the 2-3nm mark throughout. For the “Running Fix” the EP in some cases has a greater error than the DR and these errors become compounded when the DR estimates deteriorate with a final error of 31nm in the fix.

Neither method does well if only the sights at the beginning and end are used.

On the passage back the DR positions are remarkably accurate and the EP using “Position Updating” increases the error in some cases but it still remains at 2nm or below. The “Running Fix” starts out well but begins to compound errors later in the passage leading to a final error of 13nm. Even when only the earlier and latest sights are used the error is 10nm compared to 2nm for EP updating.

Is there any way to wring greater accuracy from the running fix applied to these observations?

Robin Stuart

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