We happen to have on consignment a C Plath sextant made for the Kriegsmarine in 1939 Germany. It is a prized collector's item, but we wanted to demonstrate that it remains a top of the line instrument for practical celestial navigation, and likely will for another generation or two, and there is no better way to do this than to show it can be used for lunar distance measurements, considered the epitome of sextant sights.
These sights require measuring sextant angles and index correction to within 0.1' of arc, which is the practical limit for marine sextant sights. Not having done this for a while, I was reminded of several tips that we outline elsewhere, and will note again here.I did two sets of sights. One with the 4x40 scope that is stock for the instrument and one set where I replaced that with a 6x30 monocular scope (made by the modern C Plath company), which is preferred for this measurement because it makes the edge of the moon sharper. The spread in the data were smaller with the 6x30 scope, but the resulting UTC found from the measurements was actually better with the 4x40. That was just an accident, as there is always some luck involved with these sights. The higher power scope should in longer run get better results.
This early C Plath sextant is ideal for lunars in that it is high precision and very light weight (2 lb 10z), being made from an aluminum alloy that C Plath pioneered for sextant manufacture. Lunar sights take longer than conventional sights, which reminded me of the ludicrous presumptions we periodically see claiming heavy brass sextants weighing almost twice as much, are preferred for their inertia and stability doing sights! Those sextants weigh more than a half a gallon of milk. Hold a full milk carton up to your nose with your head leaned back a bit for a minute or so to get the picture. The lighter sextant is always preferred and always the top of line in sextants.
For these sights, we even want more support if we can rig it. With an eye cup that lets us press the head against the sextant, and ideally a support to lean your elbow on. Then tune the scope to show the moon's edge as sharp as possible. The star or planet, however, will always be a point of light... in principle. In fact, that point of light will have a fuzzy halo around it when looking as close as we can, and that puts a limit on the accuracy. This could be optics or it could be we just needed some eye drops!
Here are results of the first set of sights taken from a pocket beach on Puget Sound (47º 40.5'N, 122º 24.5'W), 0.4 nmi due west of our office These sights used the stock 4x40 scope from 1939.
These were typed into Excel then plotted, and then fit with a straight line, which we can add with a button click, called Add trend line. This produces a least squares fit of the data, with the equation showing.
On the other hand, we can just plot the data manually and then do the fit by eye, ie lay the line such that it goes though or near the most points, leaving as many below as above the line. If any are notably far from the line, just remove them, as likely in error. The goal is remove the blunders and fit the random errors.
One way or the other, however, it is crucial to make the plot to find the best representative of the full set. One or two sights alone are not enough for this process, nor in fact for any traditional cel nav sight.
Note that in the analysis, we do not have to take values that we actually measured. In principle we should take a value that is on the line. Ideally we would have at least one sight right on the line and we could use that one, but not in this case.
Many lunar clearing procedures (how we get measured time and longitude from these sights) do not work well for Venus or Mars (near Planets) nor for LD less than 10º or so, but the Frank Reed app online at fer3.com should cover these, which is what we used. (Sample output screens at the end here.)
Here an easy first choice might be to use a LD= 4º 8.0' at 10:01:56 PM PDT 6/17 = 05:01:56 UTC 6/18. That measurement (#1) leads to a discovered Lon error of 3.3' as shown in the list below, which corresponds to a time error of 13s.
Since we know the equation for the fit to the data, we can do maybe better since our choice was not exactly on the line. If we use the equation to find the precise time (#2) corresponding to 4º 8.0' it would be 10:02:11 PDT or time error of just 3s. But both analyses have to be considered on the fortuitous side. Generally it is considered good lunar work to find the correct time to within 30s, and these measurements, no matter how careful, can yield even larger errors.
For example, if we remove the 3rd and 4th sights, which are off the most from the fit, we get a new best fit line, and that yields a 4º 8.0' LD of 10:02:29, shown below as #3, which now has the best looking data fit, but the Lon and time errors are larger.
# UTC LD LD error Lon error Time error Position error
1 050156 4º 8.0' +0.1' 3.3' 13s 2.2 nmi
2 050211 4º 8.0' -0.02' 0.7' 3s 0.4 nmi
3 050229 4º 8.0' -0.2' 5.4' 22s 3.6 nmi
The main goal at hand for these sights were to show that right out of the box, the 1939 C Plath sextant we have on sale could do high precision lunars. These very good results, however, must still be considered fortuitous, especially since the index correction measurement was not as precise as we would want. It was set to zero using the image of Venus, which was not as sharp as it could be with more work. In the next set of sights, the IC was readjusted and measured more carefully with the solar index method.
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For the second set, the next night, I changed to 4x40 to 6x30 and got these results for 6/18 PDT. The IC was 1.2' on the scale (see notes at the end here)
We see slightly better on the data scatter, and again if we were to take just one it would likely be the middle one right on the linear fit to the line, that leads to sight #4, which was not as good as the earlier session, though it seems the sights were better. In sight #4, the measured LD of 17º 37.7' was corrected for the IC ("If it's on; take it off!").
# UTC LD LD error Lon error Time error Position error
4 054354 17º 36.5' -0.5' 14.1' 56s 14.1 nmi
5 054405 17º 36.8' -0.3' 8.1 32s 5.4 nmi
In sight #5, to get a better fit, I removed the 3rd sight, which was off the most from the line, and then got a new slope, and used that slope to compute what time would correspond to 17º 38.0', the sextant value without IC = -1.2' applied. Note that with the third sight removed, the middle sight was no longer on the best fit line.
Excel keeps track of times in terms of fractions of 24 hr, ie. x = (38.0+376.89)/927.58 = 0.44728). This sight is more typical of practitioners like myself who do these only infrequently. Experts can average about 15s. Note that even with fairly large Lon errors, the actual position errors are not that large at mid to higher latitudes. The position error is all Lon error since we rightfully assume that we can find accurate Lat with out accurate UTC.
Here is a sample output from the fer3.com lunar clearing solution:
The index correction was measured with the
solar method using the 6x30 scope the following day. This is the preferred method for best accuracy. It requires a couple custom filters, which the article explains how to make. We have
an app online that does the simple math to find the SD from two solar measurements.
So the IC was 1.2' On the scale. The actual SD at the time was 15.75', so this IC is likely accurate to within a few tenths of a minute, but normally one would take more sights than just two.
Later I will try to post more notes about using Excel to analyze cel nav sights.
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