# Assumed position

May 6, 2015Every now and then I receive a call from some soul who wants to learn celestial navigation. I don't usually teach the practice, but the theory is essential to understanding how it all works. Once we begin a course of instruction, I expect they will stay the course until they “get it.” This could be an arduous process both for teacher and student for any number of reasons.

My teaching usually begins simply with graphic representations of the celestial bodies’ geographical position (GP). I use globes and laser pens, and all sorts of visual aids so that the student understands what we are solving for: the distance and bearing (azimuth), from the observer to the GP of the celestial object. Usually that goes pretty easily and it is not too long before those visual representations are connected to the numbers for GHA and declination in the Nautical Almanac. I want the scholars to see the connection between what we are discussing and the numbers.

“See?” I say. “The GHA of the sun is changing 15 degrees every hour. That makes sense, right? We have the apparent sun moving around the earth, a sphere of 360 degrees every hour.”

And so on. Most everybody understands that and a great smile lights up their face and the numbers correspond to what I have been saying. All is well and golden until we begin discussing the entering arguments and sight reduction tables.

“We need,” I say, “three things: the declination, the assumed latitude and the LHA in a whole number of degrees, no minutes or tenths.”

Heads nod.

“Okay,” I continue. “The formula states that in west longitude LHA equals the difference between the GHA and the longitude, okay?”

More nodding.

“But,” I add — and this is where tempers flare and voices rise — “we have to assume a longitude based on our dead reckoning longitude that, when subtracted from the GHA, gives us a whole number of degrees.”

Silence. What? Huh?

At this point we have entered into the realm of the Sisyphean challenge that every student has to overcome if they want to understand the process. It is usually about this time that more coffee has to be made and a break is called for — a smoke on the front porch, if necessary.

It does seem for the acolyte that the concept of the assumed position is the bar that keeps many students from entering the holy ground of understanding.

I explain, once tempers have calmed, that if they use a celestial calculator or computer, the concept of the assumed position is not necessary to understand, as they can enter the DR position and get the GHA from their electronics. But if they want to be old school, they need to understand the concept of the assumed position.

The idea of the assumed position is one of the two most important foundation blocks in the way that modern navigation is practiced. The other is the Sumner Line of Position. Briefly then: Captain Sumner in 1837 discovered that by taking a series of sights and using different latitudes that the position of the celestial object was at right angles to his bearing line — a very important discovery, and even now when we plot a line of position we utilize that premise. That discovery made the solution of finding out where mariners were much easier, though still not simple. Captain Sumner came up with the idea of circles of equal altitude and that a line of equal altitudes is actually a line of position that is at right angles of bearing to the celestial object.

It took the Frenchman Marcq Saint-Hilaire to perfect what Captain Sumner had begun. In the 1870s he developed what he called the “methode du point rapproche,” or the method of finding that position which is closest to the true position. We know this now as the standard intercept method that every navigator uses. It is the method by which we solve celestial navigation problems graphically. Simply put, Saint-Hilaire said that we should assume a position close to our DR. This position would yield a calculated altitude (Hc) that would correspond to that position. Then what we do is use the difference between this calculated altitude (Hc) and our observable altitude (Ho), subtracting one from the other to find out if we are closer or further away from the celestial object.

This method uses a difference between an estimated or an assumed position and the observed position as based on the difference between the HC and HO, where HC is the calculated altitude and HO is the observed altitude. From this development sight reduction tables evolved into a tabular form that pre-computed the ZN and the HC. These tables calculate what the bearing and altitude would be from an assumed position. The entering arguments have already been stated: a whole number of degrees of latitude and a longitude that when subtracted from the GHA gives a whole number of degrees to yield the HLA.

The methods we use now — specifically, HO249, which is my preferred method — are the descendants of Dreisonstock, HO208, HO204, HO214 (which morphed into HO229) and, of course, the air reduction tables of HO249. Anyway, as I was saying at the beginning of this, if the student cannot grasp why we use an assumed position in order to find out where we are not and if the teacher cannot explain this, then all progress ceases. Hands are shaken, goodbyes said, and that’s that. But if — and it sometimes happens — the student persists and the teacher is clever enough, then this concept is understood and in no time at all the completed process of solving a sight can be done and we all live happily ever after.

I read your "Assumed Position" article with great interest. Celestial navigation is a wonderfully beautiful discipline, science, and art. I first learned it in the U.S. Coast Guard OCS in 1957, and in 1970 took two excellent courses from Thomas D. Nicholson at New York's Hayden Planetarium. He was an excellent teacher and trustee of the Amercan Museum of Natural History, as well as weatherman for NBC television. Later, he gave me permission to use his notes to teach the course myself in adult education which required updated nautical almanacs, so I had to refigure the problems in reverse! I became so enamored of the subject and read so much that I discovered and pointed out an error in Dutton's Navigation and Piloting twelfth edition (Shufeldt)that was used by the Naval Academy.

Some years ago the Annapolis Naval Academy made a decision to drop its celestial navigation course. Many of us felt this was a bad mistake and wrote letters objecting to the decision. The Academy acceded to the requests and wisely reinstated the course. The beautiful discipline continues.

Celestial navigation has remained an interest over the years as I have used it in the Marion-Bermuda Race, also taught it on a sailing trip on Alaska Eagle from Tahiti to Pago Pago in the Pacific.

Robert F. Zimmerman, Jr. LCDR-USCGR, retired

I think there are two important concepts:

First, the sextant only tells you one thing. How far you are away from the GP or in student lingo, that place on the earth where your observed body was directly overhead at that instant.

Second, the tables in effect, tell you where that spot was. Although they are designed to deliver to you an answer of where you are (on a position line). But to do that they need to know where the GP was.

Now if the tables told you, to the minute, where that position was, they'd be huge. At the moment they are to the nearest degree. So to the minute would be the intervening 59 minutes latitude times the 59 minutes longitude. Or 3481 times larger.

Impossible! So to make the problem manageable, the tables are presented to the nearest degree. So you must assume a position that correlates to a whole degree horizontally and vertically. Then a pretty simple drafting exercise to correlate it to your estimated position.

So the answer is: if you don't want to use an assumed position, you are going to need 3481 more books of tables for each book you currently have. Your choice!

I'm a great fan of Reeds Astro Navigation Tables at the moment. A slim volume that is all you need. It makes some assumptions about consistent time, and a perfect sphere, but delivers accuracy that is entirely acceptable to me. If my sighting error (because I'm not that good at managing the sextant to perfection) and the tabular error results in a position error of less than 2 miles I'm ecstatic. I reckon I'll be able to see the harbour entrance from there.'

I learned celestial navigation fifty years ago at New York Maritime College. I was fortunate to quickly understand the value of the assumed position. However, I had one classmate who just couldn't comprehend it.

I went on to use celestial navigation aboard a couple of Coast Guard cutters before moving on to navigate Coast Guard aircraft.

Thanks for the excellent article,

Charles Mason, CWO4, USCG (Retired)

Excellent article Sir, experience dictates that keeping vintage albeit antiquated navigational skills is important. "Death by GPS" was the mantra during ocean nav training ( U.S. Naval Special Warfare ). Nowadays watch standers are so "gadget" crazy that plotting a course on paper charts is a chore, something that has to be done along the lines of cleaning the head. I do hope that the newer generation takes a vital interest in the beginnings of navigation and the discoveries and feats taken by John Harrison and others.

Cheers,

Erek Sanchez, USN (RET)

CIMSEC

David

Thank you for your most excellent article on AP it is as good an explanation as I have ever read. May I point out a typo "degrees to yield the HLA." which no doubt should read LHA.

I was introduced to Celestial Navigation some 12 years ago, and I readily acknowledge that I was rather bamboozled by the whole, to begin with. The introduction of "HLA" at that time would have sent me into a tailspin.

Those of us who choose to traverse the Oceans in small yachts will appreciate the "Rythm" provided by a day with the Sun, and an evening spent with the Moon, Planets and Stars. We are no doubt blessed that we can fix our position at the press of a button these days, but this is hardly satisfying. Achieving the skills and fixing one's position to within a mile or two by the means of a celestial body or three in my experience is in its all....immensely satisfying.

Those who love the Sea will do it for reasons other than practicality and will be the cognoscenti.

Top Job.