h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Entry: Celestial Navigation - A696882
Author: Ausnahmsweise, wie üblich (Consistently inconsistent) - U165408

I was inspired by another recent entry (Using the Sun to Orient Yourself) to write this.
Just like writing about a gearbox, it's hard without diagrams. Please let me now how it can be improved. Also if more detail is needed (but I did call it "Principles.." and not "A complete guide to.." )

How relevant is this when the other entry "How to find your way by the sun" (or whatever it was) has already been recommended? (Although by mistake, it is still listed as being in Peer Review).

The first entry describes how to estimate, very approximately, where south is. This entry attempts to describe how you find your position, using the sun and other heavenly bodies, to within a mile or two.

I don't know exactly what happened to the first one. I did notice that its title got changed from "Navigating by the sun" to something more like "Orienting yourself using the sun".

I did get in touch with the author (of the first) and let him know mine was submitted too.

Did you read mine? Any comments?


Awu

I've added a bit about the Nautical Mile because it may not have been obvious how the altitude (tablulated or observed) resulted directly in a distance from the G.P. of the sun. But I don't want to get into triangles on a spherical surface.

I dind't want to get into Greenwhich Hour Angle and Declination, but I added a footnote so that the experts will know that I know that the Almanac doesn't list Lat/Long directly.

I added more about the other heavenly bodies, twilight sights. etc.

Any sailors out there ready to tear this entry to pieces? Not even the red-socked Kiwis (I know you're out there.)
Awu.

Hi Awu,

Excellent article. It's covering a totally different area to my one, so I don't see any problem with both being edited. It's also nice to know that someone liked my article enough to write their own!

So that's what a sextant does!

Gif

Hello AWU,

being a sailor myself (in the baltics, thus navigating always terrestrical), I took great interest in your article. The connection between the sun's altitude and nautical miles as well as the idea of a circle on the earth's surface where the sun's altitude is the same are very well presented.

The part about dead reckoning is a bid hard to understand, as it seems at first paradox that you have to know where you are in order to find out where you are. I suggest that you go a bit into trigonometry (how to calculate distance and direction between two points on a sphere; as far as I remember its not a terribly difficult formula) and flesh up your step-by-step section in the text with a calculation example, like "yesterday we were at 50n 20 w and since then we made about 100 miles westwards. Our dead reckoning is therefore ..., and we measure a true altitude of .... etc.etc."

Right now I try to understand the method fully from your text and I can't, although I am a sailor - really, I think an example will help.

Cheers and "immer eine Handbreit Wasser unter dem Kiel"

Hello potocki,

Thanks! That's the sort of feedback I was hoping for. I didn't want to go into too much terrestrial nav., but just enough to be able present the transition to celestial. I'll definitely expand on it though.

I think your idea of having concrete examples is good too. I'll make some up.

I actually only have the German BR Schein (that would be coastal cruising in Canada/US) and I sail now mostly in the Great Lakes, and the odd trip at Christmas to B.V.I. So I don't have a need for celestial nav. It is just a hobby - reading books on it, etc.

Cheers - Schot und Mastbruch.
P.S. My theory exam. was from a chart of the Kieler Bucht. I've never sailed there though.

Hi AWU,

on second thought you may not have to introduce the full trigonometry, but you could say a bit more about the azimuth, e.g. in what "format" it comes (degrees from true north, if I remember rightly?). Especially the line ".... You will also have the azimuth" reads a bit unconnected for me (although I as an "informed reader" know that I have it, where it came from and what it means).

Hoping that this is helpful,

pot

Oh, cross-over of replies!

A great article! I think I'll try Celestial Navigation one-day instead of using the GPS! You never know what might happen out in the open!

I think that this will be a good entry as I quite sure not many sailors know all this, but would like to! Modern technology is great as long as it works!

A windy cheers
Mcnala

Yeah, the famous "Kieler Bucht" chart, I had it too when I got my german "Sportbootführerschein See", which is the bureaucratic governmental equivalent to the BR (minus the practical sailing).

Meanwhile, my friends and I have sailed there and in southern denmark quite a lot. Usually in autumn we charter a boat for a week and have great fun in the various danish and german harbour pubs

I kept thinking about the azimuth and dead reckoning points and tried to find possible sources of errors, i.e. why the method is not exact. Assuming I did my dr really wrong (100 miles or so). In the best case I am still on the azimuth line, the difference in measured and tabled altitudes is a 100 miles and I get a nearly precise position by adding / deducting these 100 miles). In the worst case I am driectly on the "first circle" (measured altitude), I see that there is no difference between "1st" and "2nd" circle (or is there?) and don't even notice a 100-mile error. Is that a true scenario? And is it common to iterate the process (taking the last calculated position as new dr and calculate again? this would sound logic to me.

Looks like we leave the level of thearticle here, but hey, its all for fun!

Cheers, pot

If the DR position is way off, then you will not be on, or close to, the line you draw from the DR position towards the GP. But you really only draw that line, and measure off the difference between tabluated and observed altitude, so you can draw a small part of your actual position circle. Even with good dead reckoning, you are not on the intercept - just somewhere close. But you can be sure that you are exactly on the position circle (if your sighting was accurate). Hmm - I think I see what you mean. Even the short straight line portion of the circle from the observed position would be wrong because you draw it at right angles to the azimuth. Yes - I suppose it could be an iterative process, and the next one will be more accurate.

Awu

Hi Again,
(I'm supposed to be at work!)

When we're sailing in our latitudes (say the 50s), even with the sun at its most northerly, over the tropic, it's at least 1620 NMs away (that's ((50-23) * 60)). If our DR is off by 100 miles in the worst possible direction (not along the azimuth, but at right angles), that puts the line between the DR position and the sun's GP off by 3.5 degrees (Tangent or Sine 100/1620). When you draw the short section of your actual circle of position, it's also off by 3.5 degrees. But in practice, you can't even steer that accurately. I don't think it's significant.

I've just found a whole chapter on some of the special problems when sailing in the tropics (I'd like to have those problems now - it was -18C this morning ) where the sun is very close to overhead. Then it would be significant.
Wow - I'm learning more from writing this than anyone reading it.

Awu.

Super, we get really into this! btw, I am also supposed to be at work, at least for another hour.

I have also cracked my brain about this error source of having the dr 'on' the measured altitude circle, and I thought at first as you: The long distance to the sun's gp makes every reckoning error insignificant. But I am still not convinced, here is why:

Lets assume its midsummer, the sun is right over the equator, we sail somewhere in the northern atlantic. We happen to see the sun at, lets say, 45 degrees in the sextant, from which, in connection with the current time, we gain the sun's gp at that moment and a circle of equal sun altitudes, which we could actually draw into our chart, if we wouldn't have a shaky hand from heavy drinking last night The sun stands in the south, so its something like noon were we are (no precise measurement available).

Now we make a dead reckoning and a significant east-west error (also due to the heavy drinking). We are 100 miles further west than we think. But, as the sun is more or less south and the circle of equal 45-degree-altitudes is pretty large (3000 miles in diameter?), the stretch of the circle on wich we are goes more or less like a straight line from east to west for the next 100 miles. So, after observing a minimal (or no) difference between tabled and measured altitude, we take the dr-azimuth, cross-line it with the virtual 45-degree-altitude line and have literally no clue of our 100-miles-east-west error - sounds dangerous to me.

The conclusion for me would be to take several measurements during one day to have varoius equal-altitude circles, whose infinitesimal stretches in my area go east-west at noon and north-south in the evening and morning.

Besides from saying that a shaky hand as problably a greater influence on sextant measuring than any claculation error, what do you think?

Ahoi, pot

I'll go over a few worst case scenarios (after work!) and get back to you. This is too much fun.
Awu

OK -- I've re-thought this from a practical point of view.

The sun sighting gives us a line of position - nothing more. It's a huge circle with its centre maybe thousands of miles away. We are in the middle of the atlantic. The GP of the sun is way down in the Carribean, say. Charts aren't even produced for the middle of the ocean. They would be all blue Instead, there are work sheets. (There's a whole series so the latitude scale - according to the Mercator projection - is right for your approx. position.)

Now, you have to draw a huge circle, with its centre not even on your chart. (Imagine the protractor you would need! Wobbly from drinking or otherwise - not an easy task.) The dead reckoning position just gives us a "toe hold" so we can know where to draw a very short piece of it, as a straight line. Even if we were never at the DR position, the tabulated altitude and its azimuth are accurate. So too, is the distance between the observed circle and the DR circle. We draw a line from the DR in the direction of the far distant GP of the sun. Then we can draw a short piece of our true position circle at 90 degrees to the azumith.

It's true, that approximation of an arc may be slanting ever so slightly in the wrong direction, because we drew the wrong section. In my earlier example, it's off by 3.5 degrees. But we are going to take a second sight soon too. Sooner or later, we'll discard the earlier DR position as out of line with our current calculations.

Please tell me if this makes sense? I wish I could draw a picture.

Awu

P.S. I never even mentioned Mercator did I? Do you think it's enough if readers know they can plot their long/lat and measure distance on a chart? Maybe I should have started with an in depth terrestrial entry.

Hi Awu,

last question first: The introduction of mercator projections and some insight of what it means that earth is a sphere and hence all 2-d-maps of it are distorted could be a chapter itself in your article (e.g. also describing what is a "great circle" on earth's surface). For what you have written so far I think it is comprehensive without mercator, but of course it would make the whole issue more complete. In Germany in the 70ies there was a great tv series on windjammer sailing, the "Onedin Line" (might have been known in England, too?). There the old captain starts explaining navigation by holding up an orange and asking what would be the shortest connection between top and bottom of the orange ... oh, tv was better in the old days

For our main subject: Arrrgh! I wish, I could draw, too! I spent the last 30 minutes to make a sketch with slashes, underscores and hyphens, and it looked really great, but then, in preview mode all blanks disappeared ... Anyway, I think the clue to reduce errors is to to several altitudes during one day, as you suggested too. If you wouldn't move between measurements you could even get your position by crossing our two "true-position-circles", as they wouldn't be concentric any more. This should also work if you would keep track of course and distance while sailing from one measurement to the next, and then compensate for this sailing in your calculations (at least I feel it should work )

I learn a lot by this!

Cheers, pot

Hi Pot,

I've printed the whole think off and marked up some changes. I'll try to get to that tonight. I'm also having one of our company's Techincal Writers take a look. She knows nothing about sailing or navigation (which is good), but she's an expert at describing difficuly technical concepts.

I'm not sure either - about introducing Mercator, Rhumb lines, great circles. It's about finding your position, and not finding the shortest distance for example. I hope the readers will know that a Lat/Long uniquely identifies a point on the sphere and that a course is a straight line on a (Mercator) chart.

I've heard of the Onedin Line but I don't remember ever seeing it. (I only bought my first TV four or five years ago! A big mistake.)

More later,

Awu

Lots of minor changes made.

(Almost started writing an Engineering Change Notice - I thought I was still at work.)

Feedback from other sailors, and esp. non-sailors would be much appreciated.
Awu.

I'm not a sailor, but your entry is comprehensive and easy for the layperson to understand. Good job.