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Getting the Right Answer...

In each of our courses, there is a useful philosophy to keep in mind when comparing the answers you get with the answers provided in the materials. This is important because in navigation — both underway and when learning it — we are dealing with numerical results that are not always exact. We often arrive at an answer with some combination of graphic plotting and computation. The computation may be precise, but the precision of graphic plotting depends on the size of the drawing and the care that goes into it. In short, when I get, say, 4.382 for an answer and the book says the answer is 4.5, should I consider this wrong or right? Should I just let this go, or redo everything and try to get exactly 4.5?

There are several factors that enter into this seemingly simple issue. And they are not all so simple. But first a few aspects that are more simple.

In the celestial course, which we have used for many years, we ask that you treat the answers given as exact, as specified. In the above example, any thing that did not round off to 4.5 should be considered wrong… especially those problems early in the course that are pure computation. And try to track down the difference, or contact us with a question.

We say that about the celestial, especially early in the course when we are doing only sun sights, because the consequence of errors for the sun are very different from those for the moon and planets. Some specific error in the paperwork for the sun might lead to an error of 0.1' in the final results, but this identical error for the moon might give an error of say 14'. Roughly a tenth of a mile in the for a sun sight, but some 14 miles for a moon or planet sight. If we are doing something wrong, it is best to detect it early if possible.

We would also use the same guidelines for the Inland and Coastal Nav course whenever the answer is derived from pure computation or computation plus looking up some numbers in tables. Times of tides and currents, ranges of lights, etc are examples of the latter, speed, time, and distance problems are examples of pure computation.

Whenever there is plotting involved, in either course, the situation is not so simple, and you might have to make a judgement call on it… Obviously it is good experience to apply some form of practical criteria… if the nearest hazard is 5 miles off, an error of 0.1 miles is likely not crucial. If we are navigating 1 mile from some hazard, then 0.1 mile is beginning to be significant. There are several exercises in both courses that show the effect of plotting errors…. i.e. what happens if we plot a line at 204 T and meant to plot it at 205 T. It depends on how far away the intersection is etc.

In celestial you can always get more accurate results by plotting on a smaller scale, i.e. 24 miles across the page, rather than 240. This is usually not an option for chart work in this course, but sometimes it is in practice when you have more charts at various scales to work with.

And use this criteria: say the stated answer is 10.5, and you have repeated the process several times and you get 12.3. You then check each source of error that you can think of and you learn that the largest discrepancy these errors could cause is some 1.0 miles. That is, you are confident that your answer is 12.3 plus or minus 1.0, or somewhere between 11.3 and 13.3, which does not agree with the printed answer. So either the printed answer is wrong, or you are doing something wrong, and we need to figure out which.

This type of analysis is good practice. In navigation, it is often just as important to know how well we know something as it is to know the thing itself. We can compute, for example, by fairly straight forward procedures, that a light should be visible in, say, 80 minutes — a good example of a computation that depends on many factors. But what if it is not visible in 80 minutes? or in 90 minutes? or 100 minutes? Is that within our uncertainties, or outside of them. When you don't see a light when you should (i.e. within your uncertanties), it is time to stop and figure out why.

Which brings us to the more important issue about "the answers." It is best to practice in training what we should practice continually when underway. That is, we should strive to understand all that we observe — even those things which seemingly do not affect our navigation. Safe efficient navigation always proceeds as a series of checks and double checks.

If you see a red light where a white light should be, or you see one that flashes in groups of 2 and you thought it should be 3, or a headland bears 050 and you figured it should be 070, etc… these are things that should be figured out. Not just accepted or presumed to be some insignificant error. Or more tricky, you figured the current should be helping you along and your GPS tells you that it is against you. Etc.

In one of our practice problems, 7-3b in the Columbia River set, we had a problem with an error in it for many years — the error is still there, since we use a new set of problems now. But the error did not affect the final answer, so apparently no one mentioned it until just recently, which is what motivated this note in the first place. The point here is, you should mention it. If you do not understand something about a problem, do not hesitate to ask us about it. Treat the problems as real navigation underway and strive to understand all aspects of the problem and answer.

In one of the most famous maritime accidents of our time, a female third mate informed the male third mate in charge that a particular navigation light was on the wrong side of the bow. This observation was reported in time to prevent the accident, and was even reported a second time. For one reason or another this observation was not acted upon. The lives of thousands of people were adversely impacted for many years as a result of the subsequent accident. [This is obviously a cursory analysis of a complex event with many nuances. It may or may not have been crucial to the course of that history... but the point here is it might have been; we have simply not had time to do the full research in this specific case.]

Even without this famous example, however, the guidelines above remain paramount to safe efficient navigation. There are numerous other examples. Observe and digest everything you see or are told, and don't accept or discount anything you don't understand — we have another real example in our practice exercises that begins with this seminal comment from a totally untrained crew member "Wow, I didn't realize you could see Smith Island Light from here."

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