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?