# Reader decries direct sight-reduction article

The editors of Ocean Navigator should be embarrassed for publishing the recent article on the ESAE system of direct sight reduction (“Ultimate Celestial?” Issue No. 77). True, the title does contain a question mark, but the text uncritically hawks an allegedly “new” algorithm for celestial navigation implemented in a software system called ESAE by Triangle Navigation. Apparently, the author obtained all his information from the company and an independent evaluation was never sought. Unfortunately, the result is a disservice to your readers. I am sure you will be hearing from others, but some of my specific problems with the article include:

1. The mathematical solution of a two-body fix, without use of an assumed position, is hardly “new.” The article mentions the methods of Dozier, Kotlaric, and others described in Bowditch. Apparently ESAE is just a variant of Kotlaric’s methodthe same three triangles are used. There are many other direct solutions of the two-body fix that do not require an assumed position. Among the modern ones are those of A’Hearn and Rossano (published in 1977), Bennett (1979), Matthews (1979), and Van Allen (1981). All of the latter are sufficiently simple that they can be programmed on a hand calculator. In 1978, Janiczek and Watkins published an elegant matrix method of sight reduction that can accommodate any number of observations and does not require an assumed position if three or more observations are available.

2. Just how complicated is the ESAE algorithm? The article casts a critical eye on other direct methods that contain “line after line of trigonometric formulation.” However, certainly the solution of the three spherical triangles used by EASE must contain many lines of spherical trig. Sure enough, we read that “the triple triangle created in a direct sight reduction method such as ESAE is much more intimidating [than the traditional celestial triangle]. The formulae to solve these triangles and arrive at a lat/long fix are indeed frightening. . .” And later we are told of the “large numbers of paths for the calculations to follow to take into account the large numbers of possible triangles… Triangle Navigation performed endless calculations to arrive at these paths. . .” This hardly sounds like an elegant solution.

3. Readers are lead to believe that ESAE, a particular piece of navigation software, is the end-all and be-all of celestial navigation. Yet there are many software applications already on the market, in addition to special-purpose calculators, for celestial navigation. No real comparison of ESAE with any of these other products is presented, other than the statement that during the Ocean Star tests, ESAE fixes were “right on” with other sight-reduction methods.

4. No explanation is given of what the software does with three or more sights. One is left with the impression that it can only handle pairs of sights, and that the navigator is left with the task of somehow averaging the results of various pair combinations.

5) The article contains the naive (if not dangerous) statements that the ESAE algorithm provides “the ability to use two short-interval sun sights for a precision celestial fix” and “the result of all this number crunching is a latitude and longitude fix from two sights only minutes apart.” A mathematical fix involving two perfect observations of the same object taken minutes apart may indeed be possible (as it is with other methods). But navigators never deal with perfect observations, and no mathematical reformulation of the problem is going to eliminate the geometric degeneracy of two imperfect (that is, real) closely spaced observations of the same body.

George H. Kaplan is an astronomer at the U.S. Naval Observatory in Washington, D.C.Editor’s note: It is true that the method used by ESAE for performing sight reduction is not new. As Mr. Kaplan and other readers have noted, there is a long list of similar efforts by some very impressive minds. Clearly, by not mentioning anything of the earlier work in this field, we may have given less knowledgeable readers the wrong impression that the ESAE method was a fresh approach.

However, it should be noted that, unlike the theoretical constructions mentioned above, ESAE is a turnkey product that a navigator can run on his or her computer today. Mr. Kaplan notes that some of the existing methods “are sufficiently simple that they can be programmed on a hand calculator.” True enough, but in the age of GPS, it seems few sailors are inclined to learn basic celestial navigation, let alone get started in celestial nav programming.

Which brings us to our final point, that ESAE is interesting and worthy of coverage simply because it represents a new effort in a field that is in something of a decline given the ease of electronic methods. As long-time supporters of celestial navigation, we are happy to give coverage to those who are trying to make celestial more attractive to the average mariner.