Question for the Astro-Navvies

[Blue Seas]

Very much appreciated folks, I'm still listening

 

[AntarcticPilot]

If you can get a copy, "Navigation with Alice" by Frank Debenham (Yes, he of Antarctic fame on Scott's expedition) is an amusing guide to the principles of celestial navigation. Also "Sextant", but I forget the author! Neither are "how to do it" but both introduce the principles in an easily digestible form.

This is "Sextant" Sextant: Book review

I think there are two issues here. First, there's the practical matter of taking sights and reducing them. That needs practice with a sextant and following a procedure using whatever method and/or tables that appeal to you. But that doesn't require my second point, which is understanding what you're doing. The books I mentioned above describe what you're doing in terms that are accessible to anyone.

Unfortunately, the various "quick" ways of reducing a sight actually obscure the very simple principles involved. Equally unfortunately, those simple principles can result in difficult mathematics, unless you're happy with spherical trigonometry.

 

[GHA]

Very much appreciated folks, I'm still listening

AI's have very much come of age now and can be very educational on their own or in conjunction with other sources, just ask like you're talking to someone. www.perplexity.ai is a good one as it collates results from various AIs & focus is one providing useful answers. Another useful tool in the learning box.

For instance, copied from an example question in the previous link >

20th June 2020
Time zone 0
Mer pass

Sextant reading of LL of sun above the horizon is 67º 30.0’
Index error zero
Lower limb
Height of eye 3.0m
Slowly and step by step calculate the latitude using data from an almanac for height of eye, calculate it as if you were a sailor onboard using data from a nautical almanac

Answer
Let's calculate the latitude step-by-step using the data provided and information from a nautical almanac. We'll follow the process a sailor would use onboard.
Step 1: Correct for Index Error
Index error = 0'
Sextant altitude (Hs) = 67° 30.0'
Hs (corrected) = 67° 30.0'
Step 2: Apply Dip Correction
Height of eye = 3.0m
From the Nautical Almanac dip table:
Dip correction for 3.0m = -3.0'2
Apparent altitude (Ha) = Hs - Dip
Ha = 67° 30.0' - 3.0' = 67° 27.0'
Step 3: Apply Main Correction
From the Nautical Almanac for summer, lower limb of sun, and Ha ≈ 67°:
Main correction = +15.9'2
Observed altitude (Ho) = Ha + Main correction
Ho = 67° 27.0' + 15.9' = 67° 42.9'
Step 4: Determine Sun's Declination
Date: June 20, 2020
From the Nautical Almanac:
Sun's declination = 23° 26.1' North
Step 5: Calculate Latitude
At meridian passage (local noon), the formula for latitude is:
Latitude = (90° - Ho) + Declination (if the body and observer are on the same side of the equator)
Latitude = (90° - 67° 42.9') + 23° 26.1'
= 22° 17.1' + 23° 26.1'
= 45° 43.2' North
Therefore, the calculated latitude is approximately 45° 43.2' North.
This method demonstrates how a sailor would perform these calculations step-by-step using data from a nautical almanac while onboard a vessel.

Books are a very personal preference so you just get what others prefer, not what's best but lots on the web now as well. Get stuck in the slightest in a book or onine tutorial just tell an AI you're a beginner and ask for an in-depth explanation like "in astronav what exactly does HS mean & find some youtubes discussing it "


Answer
In celestial navigation, Hs stands for Sextant Altitude. It is the raw angle measured by a sextant between a celestial body and the visible horizon.
Meaning of Hs
Hs is the initial measurement taken with a sextant before any corrections are applied. It represents:
The angle between the celestial body (e.g., Sun, star, planet) and the horizon as seen through the sextant
The first step in the process of determining a celestial fix
An uncorrected reading that requires further adjustments to be useful for navigation
Key Points About Hs
Hs is always less than 90° (the celestial body cannot be directly overhead)
It's typically measured to the nearest minute of arc (1/60th of a degree)
Hs needs to be corrected for various factors to obtain the observed altitude (Ho)
YouTube Videos Discussing Hs
"Hs Sextant Altitude - Celestial Navigation Basics" by Jeremy Clark
This video explains how to take a sextant altitude (Hs) and demonstrates the process using a sextant4
.
"Celestial Navigation Basics - Ho Observed Altitude" by Jeremy Clark
While focusing on Ho, this video also discusses Hs as part of the celestial navigation process2
.
"Sextant to Line of Position - A Complete Sight Reduction" by Navigation with David Burch
This comprehensive video covers the entire sight reduction process, including taking the initial sextant reading (Hs)6
.
These videos provide practical demonstrations and explanations of how to measure Hs using a sextant and its role in celestial navigation calculations.

 

[Marsali_1]

AI's have very much come of age ... www.perplexity.ai is a good one

That seems to be a subject of debate: Perplexity AI - Wikipedia

 

[Frank Holden]

I think there are two issues here. First, there's the practical matter of taking sights and reducing them. That needs practice with a sextant and following a procedure using whatever method and/or tables that appeal to you. But that doesn't require my second point, which is understanding what you're doing. The books I mentioned above describe what you're doing in terms that are accessible to anyone.

Unfortunately, the various "quick" ways of reducing a sight actually obscure the very simple principles involved. Equally unfortunately, those simple principles can result in difficult mathematics, unless you're happy with spherical trigonometry.

I don't think so. Anything can be made difficult if you want it to be difficult.
Spherical trig? Just accept that Napier did all the hard work some hundreds of years ago.
Also accept that while in plane trigonometry we use two parts to find a third, in spherical trig we use three parts to find a fourth.
In a simple sun sight we use sun's local hour angle, sun's declination, and our DR latitude to find the calculated zenith distance.
We also use haversines which are positive all the way from 0º to 360º which means that when combined with logarithms all our working is simple addition ( with one exception - see L~D below).

Armed with the three parts mentioned above ( and a copy of Nories tables which contains the log and nat cosines and haversines required ) it becomes -
Log Haversine Local Hour Angle (LHA)
+ Log Cosine Latitude (Lat)
+ Log Cosine Declination (DEC)
= Log Haversine 'Theta'.
Convert Log Haversine 'Theta' to Natural Haversine 'Theta'

Get the difference between the Latitude and the Declination ( L~D ) . This is sometimes additive sometimes subtractive, Simple rule 'Same Name Subtract, Opposite Name Add'

Look up Natural Haversine L~D, add to Natural Haversine 'Theta'

Nat Hav L~D + Nat Hav 'Theta' = Nat Hav Zenith Distance (ZD)

Convert Nat Hav ZD to Degrees. Job done. 9 lines of addition.

Hardly either advanced or difficult mathematics

Easier than faffing about with the air tables.

 

[Frank Holden]

I did my astro courses back in the 1980's (RYA/DOT at that time) but GPS was just about to come in and basically I never really used the sextant side of things after that even on ocean crossings so it never became 'natural' or routine to me. I want to take it up again for what may well be a final swansong circuit both to keep the brain cells going and as a back-up but also to get swmbo involved (she stopped at the coastal skipper stage again in the 1980's).
My question therefore is what resources (books, videos etc.) would be recommended these days? I still have my originals but the movies that were my teaching aids were the WW2 black & whites used for USAF pilots! Also, could anyone suggest a shortlist of what exercises I should be able to do to get by on rather needing to re-learn a lot of peripheral gumph that will never be used?
And yes, if anyone has a good sextant to sell......

I would recommend this bloke Freiberger nautical drum sextant #000086 (blue) | eBay
Vendor is an instrument maker. He seems to have struck the mother lode of ex Royal Australian Navy sextants. I bought one from him a few months back just because I could. Mine is 000063, first two digits are year of manufacture so 63rd Freiberger from year 2000. This one is similar.
Don't know what the postage to the UK would be.

 

[john_morris_uk]

Lots of ideas on here. But we’re all different.

I know lots of people (and several in this thread) rave about Mary Blewitt but I don’t follow her half as easily as Tom Cunliffe.

Some people find the Haversine method simple. I was brought up on AP3270 and much prefer it.

So what? My advice to the OP is to revise what her originally started with and try a few different authors/youtubers until he finds one that clicks with him. There’s no absolute best. Just ones that work for you.

 

[Skylark]

I don't think so. Anything can be made difficult if you want it to be difficult.
Spherical trig? Just accept that Napier did all the hard work some hundreds of years ago.
Also accept that while in plane trigonometry we use two parts to find a third, in spherical trig we use three parts to find a fourth.
In a simple sun sight we use sun's local hour angle, sun's declination, and our DR latitude to find the calculated zenith distance.
We also use haversines which are positive all the way from 0º to 360º which means that when combined with logarithms all our working is simple addition ( with one exception - see L~D below).

Armed with the three parts mentioned above ( and a copy of Nories tables which contains the log and nat cosines and haversines required ) it becomes -
Log Haversine Local Hour Angle (LHA)
+ Log Cosine Latitude (Lat)
+ Log Cosine Declination (DEC)
= Log Haversine 'Theta'.
Convert Log Haversine 'Theta' to Natural Haversine 'Theta'

Get the difference between the Latitude and the Declination ( L~D ) . This is sometimes additive sometimes subtractive, Simple rule 'Same Name Subtract, Opposite Name Add'

Look up Natural Haversine L~D, add to Natural Haversine 'Theta'

Nat Hav L~D + Nat Hav 'Theta' = Nat Hav Zenith Distance (ZD)

Convert Nat Hav ZD to Degrees. Job done. 9 lines of addition.

Hardly either advanced or difficult mathematics

Easier than faffing about with the air tables.

It's a dull Sunday morning so I've blown the dust off my 1963 "New Revised Edition" of Nories.

Using real data I used:-

GHA 84deg 35.5min
Dec 21deg 28.7S
DR Lat 14 deg 28.5min N

One line needed to get whole angle GHA of 27deg. AP Lat 14 deg

Enter AP3270 Air Table, Lat 14, LHA 27, Dec 21, Contrary.

Adjust Hc for 28.5min Dec

Covert Z to ZD.

Seems much less of a faff, and fewer opportunities to read Tables incorrectly, than your above 9 lines of addition?

I enjoy trying new (to me) methods, but what am I missing?

 

[Blue Seas]

All very useful indeed chaps, I browsed Frank's excellent pdf (post 19) this morning and soon picked it up again (Thanks Frank).
It won't take as long as I feared so clearly the 'penny dropped' as Skylark says in post 4. This is a surprise to me as my astro theory was done on the 5-day crash course at St George's army barracks in Gosport - I got off to a pretty poor start as I hit a patch of black ice on a roundabout at Alverstoke on my motorbike suffering a slow-speed 'off' - by the time I'd been to hospital for a check-up the others were 5 hours ahead of me on the first day - they had already watched 2 or 3 of the USAF introduction videos so when I finally joined in the conversation they might as well have been a dozen Swedish chefs speaking Mandarin Chinese. I had to burn some midnight oil that week to catch up - so I'm surprised it stuck in as well as it has done.
Better get the water maker on order.....

 

[capnsensible]

Lots of ideas on here. But we’re all different.

I know lots of people (and several in this thread) rave about Mary Blewitt but I don’t follow her half as easily as Tom Cunliffe.

Some people find the Haversine method simple. I was brought up on AP3270 and much prefer it.

So what? My advice to the OP is to revise what her originally started with and try a few different authors/youtubers until he finds one that clicks with him. There’s no absolute best. Just ones that work for you.

Yeah, Blewit does seem to have a fan group. But for me, along with any others, it may as well have been written in Swahili. As you say though, it doesn't matter how one learns the theory.

The bit I find really satisfying is showing people how to take and reduce sights ona wobbly yacht.

I have great respect for masters of the art who used to navigate, as pros, large vessels by sights. Nip out from a nice warm bridge onto the wing, take a couple of sights, nip back infor coffee, cake and reductions. I've made that a bit jokey, but those guys really knew there stuff. Admire.

The people who I think have earned the greatest respect are those who navigate the Golden Globe solo race using our heavenly bodies. Awesome.

They know that after a couple of days, 4 or so out of 5 will have stopped vomiting enough to sit below at a wobbly chart table using Neptune's gift of Pro formas and plotting sheets to get a days run down on paper. They will know how to work up an EP for real and not cheat off the GPS. They will understand as the days go by how the ships log will get increasingly wrong as it fouls up with weed and barnacles.

They will know how to check the sextant for the 3 main errors before taking every sight.

They will know the frustration of being five minutes late for a noon sight for latitude coz their ep was basically a guess after a few days overcast.

They will know how clouds suddenly appear, day or night and always at sunset and sunrise just when you've spent an hour sorting out rough azimuth and heightish of your selected stars coz even the most agile brain gets cold and tired leading to errors inconceivable in the armchair.

They will know that when it is nice weather, running down the trades, that clouds can and will frustrate. But on a longer passage as they get better and better, how Neptune lets you leave planets and stars more or less where they were yesterday.

And for some of us, they will know the buzz when the correct island turns up on the horizon in about the right place! And then taking a few bearings with the handheld compass, going yessss and putting the astro stuff away until the next long passage.

But it is an indulgence these days and for most, quite irrelevant. For me, on deliveries, a couple of handheld GPS sets ( plus a flotilla of spare batteries)and the main ships one are perfect for reducing passage times saving the owner hard earned wonga.

Even as I reminisce about those times I got basically adequate...not to pro standard....I aware that I may never use astro again. But I'm ever so glad I did!!

 

[neil_s]

In February 1994 edition, PBO published an article describing a sight reduction program for the Texas Galaxy 67 calculator. These do come up on e-bay every now and then, so I bought one. Typing in the program was a bit of a process, but I got there in the end and - it works! It is Sun only and a bit slow, but it calculates the almanac data and does the sight reduction. Results are very close to the more trad method, too.

 

[GHA]

this thread is a nice bit of motivation to dig out the sextant again & get some practice in

Graphing by hand is boring and reduction is just maths, once you've got the hang of 2 + 2 = 4 repeat as often as you want, ain't going to get any better..

Taking sights though is muscle memory like playing a musical instrument so seems a good idea to spend 10/20 minutes every day banging sights out like running through scales on a piano. And quicker than it took to type the 30 words asking an AI it wrote a webpage to plot sights against time.
Either input one a time or save on a .xlsx spreadsheet & upload.

click here
Time vs Angle Graph

There if anyone wants it, spreadsheet needs to look like >
which was a few from today.



So now it's just put the time in, trying anything which comes to mind changing halfway through & see what happens, stand different, UL or LL, bring the target up or down, try stuff with an open mind just to see what happens can be very educational & a great way to learn more imho.
Looks like >



What's your look like?

 

[Roberto]

Mary Blewitt. Celestial Navigation for Yachtsmen.

...
still in print after 30 years.

Almost 2.5x as much, 1st ed. 1950

 

[Skysail]

Almost 2.5x as much, 1st ed. 1950

Even better!

 

[Frank Holden]

Almost 2.5x as much, 1st ed. 1950

I wonder if the 1st edition still used Right Ascension.

 

[Frank Holden]

It's a dull Sunday morning so I've blown the dust off my 1963 "New Revised Edition" of Nories.

Using real data I used:-

GHA 84deg 35.5min
Dec 21deg 28.7S
DR Lat 14 deg 28.5min N

One line needed to get whole angle GHA of 27deg. AP Lat 14 deg

Enter AP3270 Air Table, Lat 14, LHA 27, Dec 21, Contrary.

Adjust Hc for 28.5min Dec

Covert Z to ZD.

Seems much less of a faff, and fewer opportunities to read Tables incorrectly, than your above 9 lines of addition?

I enjoy trying new (to me) methods, but what am I missing?

I'm actually ambidextrous. In the day job I would use Air tables for stars, Mq St Hilaire /Haversines for sun sights.
(In the PDF linked to above I first introduced the students to the air tables with the Haversine method as an alternative.)
However in the day job I had the US plotting sheets and a nice big chart table. I still have those plotting sheets on my boat but I doubt many do.
My main issue with air tables on a yacht is , I think, mainly to do with the plotting.
Lets say your DR posn is 10º30'N, 20º30'W and your chosen longitude is 20º 01' W. No matter which way you slice and dice it you are going to be dealing with a 30' intercept more or less . So your plotting sheet is most likely going to have to cover a whole degree of latitude and a whole degree of longitude.
With Mq St Hilaire and a good DR you will hopefully be dealing with an intercept of only a few minutes and you can plot it on the back of an envelope, in fact you don't even need an envelope.

 

[Skylark]

this thread is a nice bit of motivation to dig out the sextant again & get some practice in

Graphing by hand is boring and reduction is just maths, once you've got the hang of 2 + 2 = 4 repeat as often as you want, ain't going to get any better..

Taking sights though is muscle memory like playing a musical instrument so seems a good idea to spend 10/20 minutes every day banging sights out like running through scales on a piano. And quicker than it took to type the 30 words asking an AI it wrote a webpage to plot sights against time.
Either input one a time or save on a .xlsx spreadsheet & upload.

click here
Time vs Angle Graph

There if anyone wants it, spreadsheet needs to look like >
which was a few from today.

View attachment 186728

So now it's just put the time in, trying anything which comes to mind changing halfway through & see what happens, stand different, UL or LL, bring the target up or down, try stuff with an open mind just to see what happens can be very educational & a great way to learn more imho.
Looks like >

View attachment 186729

What's your look like?

That's an interesting approach and, for you and other like-minded geeks (meant to be a compliment) combines a couple of your interests.

Re the plot: 1. can you correct X-axis scale? 2. if you show correct time/scale, can you make it draw a "best straight line fit"?

The (potential) problem with computer generated best line fit is that it will take all data points into consideration. When I look at my sights, I may think "oops, that one isn't right" so ignore it.

I'm afraid that I'm polar-opposite and don't find that "graphing by hand is boring", I rather enjoy the whole process.

I use a note book as a day-to-day celestial navigation log. Per the picture example, I use a page to hand-draw half a dozen sights over 10 mins, draw best fit straight line and pick anywhere along the line for convenient time and Hs. I also enjoy using Plane Sailing (dLat, dLong, Departure and so on) to find my starting point DR. I don't understand those with an obsession for Templates and Plotting Sheets. Nothing wrong with either but they are not a panacea. I use plain A3 paper. For example, a Canaries to Caribbean crossing in 2019/20 took 9 sheets and now remains a cherished momento of a nostalgic crossing. The second picture is page 8, almost there! If you look closely you'll see how close my fixes were to a GPS reading, plotted alongside.

Great thread, especially at this time of year.

 

[GHA]

That's an interesting approach and, for you and other like-minded geeks (meant to be a compliment) combines a couple of your interests.

Re the plot: 1. can you correct X-axis scale? 2. if you show correct time/scale, can you make it draw a "best straight line fit"?

Yeah noticed the x axis, I can't fix anything but know an AI that can...
Got it to write some python as well which is well on the geeky side, that will be interesting just to see what can be done & learn more about statistical analysis techniques.
Putting in some numbers and clicking plot isn't actually all that geeky, just really quick

There if anyone wants it.

edit: x axis fixed

 

[Skylark]

Got it to write some python as well........

Life of Brian was their best writing, surely you can't match that

 

[GHA]

Life of Brian was their best writing, surely you can't match that

The programming language was actually named after them, there's a load of little hidden references in the code.