Thursday, April 16, 2020

Accuracy of Backup Cel Nav using a Mark 3 Sextant

In early printings of our textbook GPS Backup with a Mark 3 Sextant we discussed the accuracy of the shortcut procedures using our custom sun almanac.  These notes did not account for the type of sextant being used, but now that we have a dedicated online course for Backup Cel Nav that includes a Mark 3 sextant, it is now assumed that we would be using that type of sextant, so we need to fold in its own inherent uncertainties.

We have numerous examples that show that our custom long-term sun almanac can usually provide declination to within about ±1' and GHA to within ±2', and then we have approximations to the sun's semi-diameter (we call it 16' always) and we have abbreviated Refraction and Dip tables, so on the Latitude reckoning we have about a ± 2' uncertainty, with more like ± 3' on the Longitude reckonings.

We have a sextant (the Mark 3) that can only be read to ± 2’ and we have to effectively do this twice counting the index error measurement. Independent uncertainties add as the square root (sqrt) of the sum of the squares, so this sextant uncertainty is about sqrt (4 + 4) = 2.8'.

So for a Latitude sight we have a total uncertainty of about sqrt(2.8^2 + 2^2) or about 3.4'.  We thus estimate that we can find latitude as:

Latitude ± (3 to 5) nmi

This is to be compared to best possible with a good metal sextant and full almanac and a 1000-sight experience of ± 0.5’ for either a Lat or an actual fix of both Latitude and Longitude.

For Lon we can assume the watch is right, so sextant error is not really a factor, and we are left with finding peak time of the LAN curve of sextant heights versus UTC, which we combine with our GHA uncertainty of ± 3'.  

We can typically find the center of that curve to within  about 1 minute if we have good sight data. Sometimes half that, but for safety let's call this a 1 minute uncertainty, which in turn leads to a Lon uncertainty of ± 15'.  We combine this with the GHA uncertainty of ± 3' for a final value of sqrt(15^2 + 3^2) = 15.3.  Thus for longitude sights at LAN we have:

Longitude ± (10 to 20) nmi.

We expand the 15' a bit as there can be other uncertainties if we are moving very much in the N-S direction during the time we are measuring the curve of Hs vs UTC. This distorts the Hs curve, and the center does not reflect the actual location of the sun crossing our meridian.  For typical yachts this is usually a small factor.

This backup method has a large Lon uncertainty, but we must remember that this does not mean the Lon is wrong by that much. It most likely is not, but it is just uncertain by that much and we have to keep that in mind during decision making.  Indeed if we do several LAN fixes over a few days and our DR is agreeing with these fixes, then we have learned that we are likely doing better than this large uncertainty.


Anonymous said...

Hi. Why do we adjust set screw 2 before we adjust set screw 1 when adjusting index mirror? thank you very much.

David Burch said...

In the book diagrams, 2 is side error; 1 is the index error. The order is not actually crucial, but 2 is a bit easier as we do the first main check and adjustment viewing the arc itself, which is fast and easy. Also, if 2 is off a lot, it will make the index adjustment harder. In any event, it is an iterative process as there is cross talk between the adjustments. 2 then 1, then 2 then 1 etc

Unknown said...

My Mark 3 is very stiff and impossible to make fine adjustments when taking a sight. Any suggestions on a lubricant to free up the arm? Wax, silicone, grease?? I don't want to use something that could damage the plastic.

David Burch said...

I would be reluctant to put anything on it, for fear of getting it too loose. We do need it snug for the best settings, which are done with a final sort of biased squeeze between middle finger and thumb on each side of the arm that spans the arc. We are not so much trying to move the arm per se at the final setting. If that makes sense.

Have you tried moving the arm from one end of the arc to the other, back and forth a few times to see it that loosens it up? Also, if this method of final setting has not been tried, have a go at that to see if that helps.

Jim Long said...

Thanks for the suggestion. I left the Mark 3 on the dining room table and every time I walked by I cycled it a dozen or more times. Now, it's at least 50% easier to move. As I watched the Olympics, I continued to cycle it and started taking sights of the TV, bookshelves, and clock. Upper and lower limbs of the clock. The practice taking sights inside has to carry over into actual sights. Plenty of practice reading the angles.

David Burch said...

That should be enough of that. I think next step is outside for real sights with thew squeeze method mentioned above.