Arrogant mathematicians

[jeremyparker]

Celestial navigation is difficult for a multitude of reasons but I wish to focus upon one particular- the math portion.

Learning celnav was very difficult for me because my skill at math was and isn't very good and I'm not trying to improve it.  I don't drool over formulas or abstract ideas and principles.

The endless quantity of books and web sites that supposedly explain how to perform celnav were written by people* who don't appear to be able to explain it except to other mathematicians.  That's a pity as celnav really is a dying art for ocean navigation and it certainly should be encouraged as backup.

It seems to me that since those that are promoting astronav in print are either retired physicists, engineers or math teachers there is a loftiness and arrogance conveyed that is similar to the saying over Plato's Academy door- “Let no one ignorant of geometry enter here".   There is some doubt as to whether this was really there- my guess is it was- heck- the guy wrote "Republic"!

So it comes across as, "well, little man, unless you know the law of cosines we can't help you.  Black art, I think Francis Chichester called.

But, then there's job security- keep things vague and not really understandable and you'll have job security.

By the way- the Naval academy IS NOT going to teach celnav processes- just that the method exists and no more- no sight reduction or using a sextant.

No wonder everyone has a hard time with math! It's the teachers!

Keep in mind that the navigators in the past 150 years were mostly grade school to high school educated at best.  If they could do it- so can we!


* Do you really think I'm going to buy a book on celestial navigation written by someone named "Mary Blewitt"?! Blew it?  are you kidding me?!

C Davidson

You're right - CelNav is not easy; not everything in life is easy and some things just cannot be handed to us on a plate. However, the difficulties in CelNav are not  due to complicated mathematics so much as the complex process of collecting and processing a load of data.
An ability to apply the basic principles of CelNav calls for little more than a knowledge of simple arithmetic - no geometry, no trigonometry, just adding and subtracting. Anything beyond that is, indeed, handed to us on a plate by the clever and hard working mathemeticians who have done the pre-calculation required to compile the various Sight Reduction tables currently available. These do all the work of solving the dreaded PZX triangle; all we have to do is provide the raw data to 'feed into' these precomputed tables.

But I do feel your pain because what no treatise on CelNav ever seems to make sufficiently clear is the basic, underlying principle: that when we observe any celestial body we immediately know where we are; that is to say we immediately know exactly how far we lie from that body's Geographical Position. Any corrected sextant altitude gives us the Zenith Distance, an expression of our distance from the GP. No fancy maths, no geometry, no trigonometry, just a simple sum in which we subtract the Observed Altitude from 90º to obtain the ZD. If we can manage to multiply the whole number of degrees by sixty and then add on the trailing minutes and decimals we get our distance from the GP in nautical miles. That's it. That's all there is to it.

The difficulty in CelNav lies with the plotting of this position circle on a chart. If we had a chart of an appropriate scale and projection we could simply draw a circle with ZD as its radius (indeed we could reduce this to a section - an arc - of that circle because we also have an idea of the direction of the body's GP). Then all we need is a second arc of position to cross the first and establish our position. No complex formulae, no cosines, no abstract ideas.
But such a chart does not, cannot, exist! We have to find another way of drawing a position line, and that's where the tricky maths intrude.
All of that annoying and difficult maths provides a clever and elegant way of drawing that arc of a circle of position on a large scale chart of our immediate area. Now there are methods for doing this that do require a knowledge of the trigonometry, but if all you want is to use CelNav as a simple tool to back up GPS, and provide a means of locating yourself should that tool fail, then there is no more need to understand CelNav's inner workings than there is to understand the workings of your GPS. You simply need to gather the data: the body's altitude, its GP and your approximate position and, using prepared short forms to guide you through the steps, enter this information into whatever navigational computer you have - be that sight reduction tables or some electronic device - to obtain a simple instruction as to where to draw a position line on your chart.
So remember when you are wrestling with GHA, LHA, Declination Same and Contrary Name and Assumed Position, that none of this is directly relevant to the sight you have taken. Your observation of the body has already revealed your distance from the GP. All of the additional mathematics is to find out the body's altitude and azimuth from where you are not! We already know our distance from the GP but cannot plot this on our chart. We now need to determine the altitude and azimuth from our Assumed Position; we can compare this with the altitude (and azimuth) at our actual position to find how far we are from the AP, and plot this on the chart. And we can do all of this, if we wish, with no more understanding of the inner processes than we need to be a watchmaker to read the time.

You are correct - historically, celestial navigation was developed and practiced by simple sailors with little formal education, and it was for them that the precision tools and tables were devised. If you are not interested in the beautiful and intricate inner workings of the process you can still make use of it and give thanks to those arrogant mathematicians, physicists and engineers who have made this possible - including poor old Mary Blewitt, who was most certainly not any of these things, but a simple sailor who strove, as do I, to demystify what many insist is a Black Art.

Jeremy