Open letter to concerned readers of the June Cruising World article on sextants.
June 2, 2000 — more recent additions are listed at the end.

My name is David Burch, I am the director of Starpath School of Navigation in Seattle. Information about our school can be seen at and my background is outlined at I have written navigation articles for CW in the past. We are also periodically an advertiser in CW.

As CW is one of the leading boating magazines worldwide I am sure you strive for the highest quality content at all times. I am sorry to say, however, that the June article on sextants falls below your usually high standards. I fear it dilutes the entire knowledge level of celestial navigation, particularly with regard to the accuracy and use of sextants — the very goal of the article.

In the popular description of technical matters, we should naturally be as simple as possible, but not simpler. In an attempt to present these matters in an interesting way to the general reader, the subject was over simplified in the article. As a result, the conclusions drawn from the study are not valid, and since the quality of the data presented were so poor, it also implied limits on celestial navigation itself that are very far from the truth. The article also presented an "accuracy ranking" for various sextant brands that is not correct, and in particular made a far too disparaging report on the plastic sextants from Davis Instruments.

More specifically:
The question presented was, is it the sextant itself or the user that determines cel nav accuracy. The real answer to that is "neither," it is mostly a matter of proper procedures that determines the overall accuracy of celestial navigation. As for the sextant sights themselves, most readers would likely guess the right answer without the article: with equal instruments, the better trained person gets the better results, and with equally trained persons, if one sextant is indeed superior to another, it will yield superior results. Corollaries are: a poorly trained person cannot do well with good or bad instrument, but a well trained person can indeed eke good data out of an even inferior instrument with careful analysis. That is the answer to the questions raised in the lead to the article, but that is not what the article concluded.

With regard to sextant rankings: almost always (not 100% of the time, but way more often than not) a typical metal sextant meets its factory specs — and continues to meet them as it grows older. And despite the near random origin of the instruments used, there was no evidence presented that any of them was indeed inherently defective — presumably the clamp defect mentioned on one unit was not crucial to the measurement or it would be even stranger to include it in the comparison. Now, since the factory specs of each is way higher than the measurement ability of most navigators, and since a well trained navigator can indeed take sights to within a 1 or 2' spread — especially standing still on land — then we must conclude from Table 1 that either all the sextants were bad or all sights themselves were bad.

A more realistic outcome of such a comparison would be that essentially all metal sextants give about the same result. If you maybe found one out of ten that was bad in a random selection, that might not be a surprise, but the data presented are far outside of statistics.

If one were to rank sextants, it would have to be based on other factors rather than actual practical sight accuracy. This is why the $485 Chinese sextant is so much more popular these days than $2000 German or Japanese instruments. Whether you have done a hundred sights or a thousand sights, and whether you are in a 30 footer or an aircraft carrier, you will not find any significant difference in the actual results you get as you switch back and forth between these two instruments. If that were not the case, the Japanese and German sextants would still be selling well — despite the profane price rise they have undergone during the past ten years.

The article describes (or implies) the sight takers as one good, one less experienced, and maybe one in the middle…. Yet all the sights averaged out to about the same, regardless of skill level. This is not a valid result — it was referred to as "surprising." This wrong conclusion (as well as the totally improbable result that all three ended up with the same ranking of instruments) most likely comes about because the article states that the table includes only the "best sight" of each taker. It is not valid to compare sight taking ability by only listing the best sight of each… we should see how many actual sights were taken and we should see the actual spread in values…. Indeed the entire premise of accurate celestial navigation is to take many sights and average them — which is something that should be stressed in any discussion of celestial navigation. It is particularly misleading to those who might be learning the subject to just list one sight each and, worse still, that the chosen one was somehow ranked the best of their individual sets (which you could only know since you knew your position) and call this representative. If there were some other error floating around, you may not have chosen the best of each after all. There are standard procedures for evaluating a series of sights from any one individual (see, for example, How to Average Sextant Sights) and these should have been followed. You cannot just numerically average them since the height is changing with time, but there are other procedures — although the proper analysis is most difficult at precisely the time they chose to do the comparison!

contour intervals in feet

chartlet is about 0.6 nmi across

More on the accuracy listed in Table 1.
To evaluate the sights the inquisitive reader needs to know: where exactly they were standing, i.e. the exact Lat and Lon on Brenton Pt. that they knew to "40 yards." Also we need to know the actual times of each of the sights. "We figured our height of eye as 10 feet." But again, where were they standing at what time. The beach is at 10 feet, the road at about 15 feet according to the chart. But these are heights relative to MHW which is about 4.1 feet in the region. Midday sights there could have been a tide of anywhere from -0.1 to about 4.2 over the past few months. Standing up as shown in the picture on dry land, it seems the HE had to be at least 15 feet or so, and if the tide were 0, the HE would be another 4 feet or 20 feet. The difference between 10 and 20 in HE is a sight error of 1.3 miles, but we do not know enough to evaluate this. Or, of course, the HE could have been exactly 10 feet as stated.

When sighting from land, we need to be sure that they were not looking toward some distant shoreline in which case a "dip short" correction might be needed, but this is unlikely if right at the tip of Brenton Pt. We also need to know the temperature and pressure just to be sure there are no extreme values at hand (which could be another few tenths), and, of course, we need to see the actual sight data. We need to see all the sights, not just the "best" one. And since we are dealing with just one set of sights — as opposed to a triad of sights — we need to have very specific description of the index error measurements and data. It could well be that Table 1 is just a comparison of their errors in index errors!

In short, it would be nice to figure out why the sights were so poor. Except for 5 sights out of 27, the data in Table 1 would not pass most certification tests for sextant use for rank beginners. Peary did much better than that lying on his stomach on the ice at 40 below in a blizzard using an artificial horizon. Any article like this would be best served with some brief discussion of cel nav and sighting accuracy in general. Then it would be obvious that we have a problem.

Data presented in reputable magazines (like Cruising World) are taken for granted as true. A beginner will assume that this data represents typical or maybe even expert sight taking. They will walk away from this thinking cel nav can only be done to an accuracy of 3 to 6 miles on land, even, which sows a false seed in their minds about the standards that can be achieved and thus lowers their expectations when they learn it.

Setting aside the plastic-sextant sights for the moment, half the sights are more than 3' in error, and six were 4' to 6' in error. Refer to the figure below to see the scale of things. The diameter of the sun is about 32', so it is easy to picture what a 4' error looks like in the sextant itself:

This sun's lower edge is supposed to be precisely on the horizon at the time of the sight. It does not take special skill to see that the sun in the figure (4' above the horizon) is not aligned. My feeling is that there is some other error floating around that we are missing since we do not have all the info. You can see from this that even a 2' error is very unlikely — that is, after all, the beauty of celestial navigation. It may not get us the 40 yards accuracy of the GPS (referred to in the article), but when we do get a fix we are confident it is right at the time. In contrast, if you rely on GPS to cross an ocean, you will not know if you are right until the last day.

The sights using plastic sextants take special mention. Your magazine I am afraid is propagating the old adage that plastic sextants are not any good because they warp if left out in the sun. This is much like the sharks eating the taffrail logs — which in reality were most likely not maintained and just frayed off. I would ask that before repeating this info any further — too late again — that you procure some real data that the accuracy of a plastic sextant changes during the time it is "heated up by the sun taking the sights." This is for the most part one magazine article quoting another… and it all starts out with data like this for these plastic sextants. These data are the most in error of any of them.

These instruments are not at all that bad, but they do require special care in their use. The index error is most crucial on these, as partly pointed out, but there was no indication that the real issue was addressed… namely that the IC can be different when turning the dial CW vs. CCW. Many tests must be made. In one sense, it is not fair to compare metal and plastic since the plastic ones take much more care in the sight taking…. With that care taken, however, I would propose that a dependable accuracy of some 5 miles would be much closer to the truth than the 14 to 24 quoted in the article. We have done this many times ourselves with the model that is a giant step below either of those you mentioned.

The argument that if you leave them in the bright sun for a long time they will melt, is not a valid one, since we would not leave our $1,000 metal sextant out in the sun for a long time, so why should we leave the plastic one out…. A set of sun sights takes a few minutes, it is unlikely that these sextants change much during that period. (Again, we do not know the temperature when the sights were taken.) To repeat such speculation untested (I presume) is poor policy. (We tell our students who just bought a plastic sextant to immediately get a magic marker and write $600 on the box in bold letters and treat it as if it cost that much and they will be OK.)

Furthermore, is it even true that plastic expands more when heated than metal does? I don't know. Do the authors? Also, if the entire instrument, that is all of the worm gear along the arc, expands some amount, why would the accuracy change? To first order it seems you just get a bigger sextant. There are definite features of plastic construction that limit their ultimate accuracy, but I am not convinced that temperature is a key factor in this at all.

Smoking gun?
The intercepts listed in Table 1 do not include the signs, + or -, Toward or Away. They were either all the same or they were different and just not listed. In either case there is a problem. If they were all the same, then there is without doubt some hidden error. It is statistically impossible to take 27 "best sights" from 3 different people using 9 different instruments and have them all be off in the same direction. If this were true celestial navigation would not work! Only some index error, HE error, time error or other persistent error could account for this. Or maybe the GPS was wrong... did anyone plot the GPS position on a chart to check that?

If they were in fact different signs, then the conclusions of the article are wrong regardless of issues raised here. The logic is not right. You cannot say that 3 miles away is the same or even comparable to 3 miles toward, they are 6 miles apart. This is why they should use the proper average of each of the sight takers and not their best values. In short, the entire process has been oversimplified to the point that the results are not useful.

Some peripheral details that contribute to the dilution:
"We took the sights at mid day to have the sun as high as possible and also to benefit from a sharp horizon." There is no virtue nor reason whatsoever to make sextant sight comparisons with the sun "as high as possible," indeed, in the extreme the sights get more difficult as the height becomes very high — so this is a misleading sentence to beginners. Also it would be very rare atmospheric conditions that would have the horizon "sharper" at noon than at say 10:07 or 15:23, or any time at all when the sun is more than some 15° above the horizon and this latter limit is chosen for an entirely different reason of more accurate refraction corrections.

(As an aside there is also an implication in the article that since the GPS "polled 7 satellites" that the position it obtained was more accurate than if it had, say 3 or 4, satellites locked in. This is a bit misleading, but off the subject at hand. We do not want to imply to readers, however, that the quality of their GPS fix is related to the number of satellites it can see at any one time.)

There is also a difference in the stability and accuracy of the gray plastic sextants over the black ones, and the authors ended up making just the opposite conclusion. I would have hoped that the authors would have contacted either Davis Instruments or some one else familiar with the devices before presenting them in such a poor light. — Needless to say, we recommend a metal sextant, but that does not give us rights to claim the plastic is worse than it is… nor to repeat untested rumors on the subject.

The issue of full-view vs. traditional-view index mirrors that was presented overlooked much of the main issues in that specific comparison…we discuss that on our web page (mirror discussion).

Reference is made to doing the sight reductions with a DOS program called "PC Navigator from Davis." The Davis program is called "PC Astro Navigator." There is another popular — or at least one time popular — program from another company called "PC Navigator," a competitor of sorts. We cannot test this since the data were not presented, but if this was the Davis program, then it was my understanding from years ago, that there were possibly some errors in early editions of that product — I recall that is what PC Navigator said about Astro Navigator! It is certainly a very long shot that that might account for the poor results reported here, but in any event, like any use of computers at sea, we should always compare our results with a second method. It takes just minutes in this case. These sights can even be reduced online direct from the USNO web site to the highest precision possible, without having to refer to a program that is some 20 or so years old — or was it? There was no need to be vague about this very important aspect of the analysis.

I will not pursue much the issue of whether or not some people might prefer a heavy sextant over a light one. One of the author's said he did, so that is that. The only other place I have heard that, however, is in the ads for $2,000 sextants that weight 4+ pounds. Hold a half-gallon of milk in your left hand up in front of your face for a few minutes to get a feeling for the issue. When our arm starts throbbing with pain, we tend to agree with ourselves more readily that the sun is indeed perfectly aligned with the horizon. In short, unless the goal was to subtly support the heavy models, it would only be fair to state that most of the world would prefer lighter sextants because they are easier to use and they get the same results. (Again, there is a long story required here to address this issue properly having to do with how well brass can be machined vs. alloys at various times in history and how the quality control of the final product is handled, etc...but it stretches physics to imply that the inertia of the instrument improves or aids in the sight taking — else it seems we would have very heavy cameras at the top of the line.)

Yes, this is the age of GPS, but I believe that as mariners we should learn and preserve the traditions of navigation whenever we can. Cherish them and enhance them, not dilute them. In the long run this can serve us well. We cannot rely on electronics. They will fail us at some point. These days we have tools that let us do celestial navigation superior to that done in the past — and tremendously faster — so we have no excuse whatsoever for doing worse. See Why celestial in the Age of GPS? for more on this subject.

I am standing by to answer any questions or responses that might arise from this note. It is presented here as a web page so it can be easily referenced, passed on, and accessed by other navigators or interested persons who might make their own comments on mine. Naturally there are varying opinions on some of these matters, but we always try to promulgate the right ones!

For what it might be worth, we have offered to reevaluate the data providing the full set of all measurements and particulars of the sights are still available. Oftentimes a careful analysis will reveal the source of apparent discrepancies. That is, again, one of the beauties of celestial navigation.

Added July 25: new article on Celestial Sights with Plastic Sextants... this work was motivated by the above issues.

Added August 8: plastic and metal sextant sights taken on land and underway to illustrate the points above can be seen at Vic-Maui Sights.

— david burch