NavList:

Hello,

The resent discussion here in NavList about lunar accuracy forced me to summarize my own lunar observation data from the last 7 months. This post will breafly cover two aspects: 1) lunar observation accuracy and 2) sextant main arc calibration.

All the observations were maid using SNO-T sextant (N871430) with 7x power scope. I bought it about 3 years ago. The instrument was made in 1987, but was not used. Unfortunately there were some issues at the very begining, but I succesfully solved them. Then disaster struck: the main spring of the micrometer mechanism broke and the instrument became unusable. I won’t now describe all the details how I overcame these obstacles, because I think this is of little interest for the most of NavList readers, therefore I will jump back to the main topic: arc calibration. Calibration was necessary becauce I was not sure of the instrument’s accuracy after the spring was changed and after the readjusment of the micrometer.

But as other NavList members discussed lunar accuracy problems, I will start with this.

LUNAR ACCURACY

In the last 7 months I have made 126 sets of lunar disances from known location (in fact: more than 126, but these are within range 0°-120°). Each set contains about 3…6 individual lunar observations. The data were entered in Excel table. There I entered observed angular values, calculated values (these I got from Paul Hirose’s Lunar4.4) and index correction as well as shade corrections. As a result I got the difference between observed and calculated values wich gave me an average arc error for each set. I put them in the graph (see attached Fig.1).  

Each dot (small ellipses) in the graph represents one individual lunar distance set. If the ellipse is horizontal, it means the sextant was held more or less vertically (as with ordinary altitude sights); if the ellipse is inclined, it represents the inclination to the right or left from the vertical. This is done to get some additional information about the effect of the inclination to the accuracy, but may be ignored in the context of this post.

Each cell in the graph represents 1 degree of the main arc (horizontally) and 0,1’ arc correction (vertically). Main arc degrees are shown from the right to the left as it is on the sextant.

So, we have a graph showing a cloud of dots. In the middle you can see a curve, wich grahically represents the arc error deffined by factory (in the sertificate book the errors are deffined in the form of table, wich you can see in Fig.1. I transformed these values to graphical curve).

I am using factory arc error curve, because I examined  that this curve is correct. How it was done you can read below.

Conslusions:

68% of lunar sets are within +/- 0,15’

82% of lunar sets are within +/- 0,2’

89% of lunar sets are within +/- 0,25’

95% of lunar sets are within +/-0,3’

99% of lunar sets are within +/-0,4’

Maximal error: 0,47’ (1 set out of 126).

Consequently almost 90% of observations are within +/-0,25’ .

Declared accuraccy of the particular sextant is 0,2’.

It should also be noted that these errors contains ALL POSSIBLE ERRORS: instrumental, observational, sight reduction etc.

And I want to emphasize that these are REAL DATA collected during longer time period (7 months).

ARC CALLIBRATION

For checking the arc I used all the appropriate measurements I had made in the last 7 months. The types of observations are:

a) lunar distances (described above);

b) star/star distances;

d) Sun altitude sights using the artifical horizon;

e) Sun/Venus distances during daytime.

Some words about Sun altitudes. The artificial horizon (AH) doubles the accuracy of the sight. But these observations (if we want to get out 0,1’…0,2’ excactness), are dependent on accurate time. But when the Sun is approching the noon, the time accuracy is not critical. Therefore the sights around the noon are easy and very useful for calibration. But I have tested also sights at any other time. It is possible to get about 5…6 altitude observations during the double altitude change by 1 degree; and then these results can be avaraged.

For AH alitude sights I use Frank’s Antispoof App to get calculated value.

Then again all the data are entered in Excell and the arc correction value is calculated for each set. The results are put in the graph (see Fig.2).

Then I drew the average line through the cloud of points. As a result I got my arc correction curve. There is no advanced averaging technique used here, the line is drawn by hand using approximate estimate “by eye”.

The graph in the lower part of Fig.2 shows two correction curves: one is factory defined and the other – derived from observations. As we can see the two curves does not differ more than about 0,1’. Therefore I keep using factory line as the Main arc correction curve.    

Of course, there are some other small nuanses that should be considered if one desides to calibrate his sextant very accuratelly (some micrometers may introduce quite large errors, wich are dependent on minutes scale reading; shades can cause additional errors, for example, my SNO-T’s yellow index shade produces 0,2’error; index correction should be carefully obtained; SNO-T type  micrometer mechanism backlash adjusment can produce “strange” errors, wich are dependent on the position of the sextant plane and index arm position; during observations the last micrometer turn should be done in one direction; if the measured angle is changing, one should avoid get final adjustment by rotating the drum, instead of it one shoud wait the moment of contact of the direct and reflected images; telescop paralelity, etc,etc, etc. I definitely forgot more aspects….).

But the accuracy level of 0,1’…0,2’ is not actual for the most of the sextants. It is significant only for lunar type observations. If you plan to use your sextant only for standard celestial navigation tasks, you can calibrate the sextant’s arc faster and without a great attention to details. The priniple is easy: measure the angle (correct it for IE; if you know shade or micrometer errors, apply them too) and compare with calculated value. The difference is the arc correction.   

Modris Fersters