Celestial navigation tables

[Markku_from_Finland]

I have developed a computer program to calculate the line of position (LOP) as a function of the latitude of the observer, and the altitude and parameters of the star. The output is the Greenwhich hour angle of the observer.

Is anybody interested in this kind of stuff or is this useful? I can very easily produce the tables for the main sailing stars and post them to this forum, if you find them useful.

 

[PaulK]

How does the time work into this?

 

[Markku_from_Finland]

Well, yes. It's actually the hour angle of the observer. You have to subtract the effect of the time to get the geographical longitude. I will check out the correct formula tomorrow.

 

[Markku_from_Finland]

The answer is really very simple. You get the geographical longitude ("easting") as right ascension of the zenith minus time passed since noon, spring equinox. The time is here measured in a circular manner so that each hour contributes 360/24 degrees and each day contributes 360/356 degrees. The Greenwich hour angle ("westing") of the vessel you get of course vice versa, as time minus right ascension of the zenith.

All this boils down to the fact that Eastern stars come above the head as time passes, and if you know the point above your head and the standard time, you know the longitude.

Personally, I find the different measures of longitude a bit confusing: https://en.wikipedia.org/wiki/Hour_angle#/media/File:Hour_angle_still1.png - the Greenwich hour angle and the right ascension depend negatively on each other, but they don't have the same origin! If I was navigating, I would use a rough star map to check which point is roughly above the head and what it implies to longitude, before taking any sights.

If there is interest in this forum, I could develop my tables and calculations into an emergency navigation system with the accuracy of perhaps half a degree. (Of course, you have to check that everything goes well and the system is safe, which I believe I'd be capable of doing, having done scientific work before.) If there isn't sufficient interest, I'm happy to just gaze the stars. 

 

[tane]

in no way wanting to diminish your achievement I still have to say:

in the last millenium(time...) I rtw-ed twice using only celestial navigation for position finding, NA, HO 249 & "Selected Stars" (leaning more & more towards using exclusively star-sights). I never could comprehend, why people would want a computer program or special calculators (starting to coming in vogue at the time): the arithmetic always was the easiest part by far, taking the sights was the thing that required skill & practice, particularly starsights in rough weather. & for "emergencies" (like sitting in the liferaft or total power loss) computer programs would be pretty useless too.

 

[Markku_from_Finland]

in no way wanting to diminish your achievement I still have to say:

in the last millenium(time...) I rtw-ed twice using only celestial navigation for position finding, NA, HO 249 & "Selected Stars" (leaning more & more towards using exclusively star-sights). I never could comprehend, why people would want a computer program or special calculators (starting to coming in vogue at the time): the arithmetic always was the easiest part by far, taking the sights was the thing that required skill & practice, particularly starsights in rough weather. & for "emergencies" (like sitting in the liferaft or total power loss) computer programs would be pretty useless too.

I appreciate your comment. I don't have experience of taking sights myself. The idea was that I could use my computer program to generate the tables and then people could print those. I have the image that conventional celestial navigation requires either electronic devices or complicated calculations involving e.g. trigonometry and long division. Doing those might be error prone in a hurry or rough water? The idea was that by using tables, you could pretty much eyeball your position up to one degree.

 

[tane]

the calculations are extremely easy, the most "difficult" part is "making up" from say 32' to a full degree, i.e. 28', & simple additions in the hexagesimal system. It really is child's work, only a bit confusing in the beginning for someone, who's school-days are decades behind, but after doing the "calculations" five or ten times you'll be smiling. Even easier when using selected stars.

Absolutely no knowledge of trigonometry (least of all sperical tr.!) is needed, no understanding of the process is required, just mechanically following a scheme of additons & substractions of values that you pick out of books.

NOT SO EASY the taking of sights, particularly starsights when the sea is up a bit. The precision required for e.g. finding (or avoiding) offshore reefs is somewhere <3nm, finding high islands of course requires less precision. This can, imho only be reached by practice, practice & more practice. Twilight isn't overly long in the tropics, 1h is the max you have, if I remember correctly (unless you take sights in moonlight).

If I would have to rate the degrees of difficulty of the "calculations" against the taking of sights I would say 1:100, in force 7 maybe 1: 200 or worse.

 

[Markku_from_Finland]

Absolutely no knowledge of trigonometry (least of all sperical tr.!) is needed, no understanding of the process is required, just mechanically following a scheme of additons & substractions of values that you pick out of books.

I wonder how the navigation forms can eliminate the need to do long divisions. All formulae for the star altitude involve a rational function of some trigonometric function of the longitude / right ascension / hour angle. This may be irrelevant for you, if you're not into maths, but consider for example the haversine formula: https://en.wikipedia.org/wiki/Haversine_formula At the very least, you should be able to apply a number of trigonometric tables and to do some arithmetics involving division. (I specifically pick on division because it's nasty to do by hand.) However, I agree that you don't need to understand trigonometrics to apply the formula. You just have to be very careful.

In the system I imagine, the only tables you would have would be LOP tables for chosen stars and the only math you would need to do would be taking means and working out the effect of time (which you can't avoid in the traditional system, either).

But you may be right; guys and girls who can sail the oceans and take the sights may be apt to use a more complicated system.

 

NOT SO EASY the taking of sights, particularly starsights when the sea is up a bit. The precision required for e.g. finding (or avoiding) offshore reefs is somewhere <3nm, finding high islands of course requires less precision. This can, imho only be reached by practice, practice & more practice. Twilight isn't overly long in the tropics, 1h is the max you have, if I remember correctly (unless you take sights in moonlight).

Does the moonshine mess up the sights? I didn't know that.
 

 

[tane]

Regarding the volume "Selected stars", as you seem not to be familiar with them:

for every full degree of Latitude & Local hour angle of Aries the tables list 6 stars with their Azimuth & corrected Altitude

https://www.thenauticalalmanac.com/Pub. 249 Vol. 1-2020-Dec.pdf

There is a little "skill" involved in choosing your Latitude, you precompute LHA  Aries for a time after the beginning of civil twilight (if dusk sights) or naut. twilight (if dawn sights), with handbearing compass & sextant you wedge yourself in the companionway (after having folded away Bimini & dodger), choose the star with Azimuth approx. on your beam (so that the distance the boat moves between your first & last sight does not interfere too much with the outcome, you take the sights of stars astern or in front of you last), set your sextant to the Hc shown in the tables, look over your handbearing compass in the direction of the stars Azimuth, raise your sextant, take two timed sights of the star & write Alt. & time + stopwatch-seconds down immediately. After you have done this of as many of the six stars as possible (the sails will be blanketing a star or two), you correct the Altitudes you have taken, & the difference between your corrected Altitude & the Hc in the table (this is the most "complicated" math) you have your intercept.

For 2 x 5 stars this used to take me abt 1h, because I ended up with 10 LOP it only took moderate experience to discard the odd outlying LOP & sometimes made me arrive at 1nm of precision (during our 3rd rtw in the late 90s we had a little pocket GPS (that I didn't trust at all) & to keep inpractice I took starsights just as on our two previous, celestial-only, rtws. - & comparing it to the GPS position I was usually within 3nm or better). After longer sailing pauses the first rounds of starsights had the LOPs more scattered than at the end of an ocean crossing.

NO, I assure you NO, trigonometry needed, none! These are navigation procedures developped for bomber navigation during WW2, AFAIK. Worked splendidly for us! Hardly a greater satisfaction in life than seeing the horizon "growing hairs" ahead, hairs that develop into palmtrees as you near your landfall on an atoll in the Pacific, after you have navigated with just sextant, stopwatch, NA & tables. Alas, gone now, GPS in cellphones, cameras, computers, iPads, ...

 

[Markku_from_Finland]

So, basically, you first guess the latitude and longitude, and that gives you altitudes of the stars. Then, you take observations and compare these to predicted altitudes and the difference helps you to correct the longitude?

Please, bear with me and try to explain this in as simple English as you can.

 

[Markku_from_Finland]

And what the heck is the hour angle of Aries?

edit: Ok, I have a guess on this one. It might be the local hour angle of the First Point of Aries; but to know the LHA, you need an initial guess of your longitude.

By the way, how easy/difficult it is to guess the latitude on the Southern Hemisphere? 

 

[tane]

of course you need an initial "guess" of your position. This is why you keep a dead reckoning. As your last position is - usually - no older than 24h you are not too far out. But even if you are out 2° you will see, that you have a huge intercept & choose another one. Your assumed pos. must always be full degrees of latitude & lon. must complement GHA Aries to full degrees of LHA Aries.

If your assumed pos. is wildly out you will probably need several tries working yourself closer.

Best tuition bar none:

https://www.amazon.com/Celestial-Navigation-Yachtsmen-Mary-Blewitt/dp/0070059284

 

[tane]

"Does the moonshine mess up the sights? I didn't know that"

often there is strong reflection on the water, but only when the moon is low & in the direction of the moon. Then you cannot use the star(s) with azimuth close to the moon's, but there still are the others. When a difficult landfall - low lying islands (like Tuamotus) or an offshore reef you want to visit (Mellish Reef), is planned, we picked our date of departure to have our projected date of arrival coincide with nearly full moon to be able to take starsights the whole night long.

Additional huge benefit when using Selected Stars: you do not have to know the "heavens" at all, not a single star. Sometimes one takes a sight not of the intended, but a different one with Azimuth & altitude close to the one in the tables (happened to me, but only very rarely), you will see this immediately when plotting is LOP, because it will be wildly "out".

In my "prime" I guess I was pretty good for a self taught "amateur navigator", but my skills are long gone, fallen out of use. When after a 19year break we set out for the Pacific in 2018 I tried to revive them, but counted 14 GPSs on board made me lack motivation & after the first round of starsight having terrible results I only took a few sunsights & then left it. Proves too that the idea "in an emergency I'll learn it" is a fallacy...

Those 14 GPs were on board not because we were nuts, they just "happened": plotter (came with the boat), 4 iPhones, one iPad, 2 cameras, satphone, emergency handheld GPS, 2 laptops, AIS, VHF...three people on board.

For bluewater-cruising as we knew it in the 80s & 90s & celestial the same goes: it was great, absolutely great & the lady & I feel very privileged to have been able to make these experiences - but it's irrevocably gone, victim of it's own success & technical innovation.

 

[Markku_from_Finland]

Oh, what a shame! The world is digitalising so fast.

 

[trisail]

Good afternoon,

It is about 35 odd years since I've used celestial navigation as my only means of position finding.

Two days ago I wrote a short piece on the subject for a the social media page of a friend sailing in the Golden Globe Race. It all came back to me as if it was yesterday.

Look at the attached work sheet. There is no rocket science involved, no trigonometry. Just adding and subtraction. If you've made a mistake, it soon becomes obvious and is easily corrected.

As said above, the skill lies in getting a good sextant sight from a rolling deck and a horizon blocked out by a running sea.

In this day and age of cheap little GPS sets, there is no need to "develop" anything new for celestial navigation. 

Have fun.

 

[Jud - s/v Sputnik]

In this day and age of cheap little GPS sets, there is no need to "develop" anything new for celestial navigation. 

Sailing is a very “intellectual” activity/sport, so I can see the see the appeal of trying to do  something new.  If only as a mental challenge. Like working out a lunar.

 

[Hitchhiker]

Interesting thread.  The last celestial I did was 2005 Transpac which IIRC was the last time it was required as part of the race. I don’t recall it being required in 2007 or any race thereafter.

I think for me now the hardest step in celestial would be the very first step.

Finding my sextant!

 

[Svanen]

I have the image that conventional celestial navigation requires either electronic devices or complicated calculations involving e.g. trigonometry and long division.

Happily, your impression is incorrect. trisail has it right: using one of the readily available sight reduction tables, only addition and subtraction are required.

William F. Buckley, a keen amateur navigator, wrote that he specialized in making silly little errors that threw his calculations out of whack. It’s easy to make such errors, especially when you’re tired. However, I doubt that any new method of calculating longitude would eliminate such occasional annoyances.

 

[Markku_from_Finland]

Interesting comments, all.

I admit I have kind of re-invented navigation. Didn't bother to read in the first place... My guess is that those systems that you have shown appear so simple because they are based on correcting an initial guess. Take for example the form @trisail has posted. I get it that it has calculated altitude for the Sun (based on the initial guess of position), denoted as Cal Alt. And then there is an appropriately corrected sextant observation, TA. Then you subtract TA from Cal Alt at the end of the form and make the conclusion that you are 6.7 minutes away from the initial guess... But to what direction? Do you correct the latitude, the longitude or both?

Sorry to bother you!