Help w/ Sextant + Artificial Horizon calculations

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YakFruit

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I am an aspiring sailor currently building a traditional navigational foundation by learning how to utilize a sextant for celestial navigation. I possess a Davis Instruments plastic sextant for training and a Davis Artificial Horizon. For someone with no background in these activities, the instruction booklets for these items seem lacking in explanations of proper calculations, especially when utilizing the artificial horizon. I am in need of expert advice in my calculations from my sextant reading, so I hope someone in this esteemed online community could lend me some advice.

It is likely that I am making significant errors in my actual reading taking, but it is difficult for me to know because I am also likely making grievous errors in my mathematics in translating my sextant reading into coordinates. If a wise person could review my below calculations and point out which step in the process I am messing up, it would be a great service.

I live in eastern Washintgon State, and my most recent reading and calculation places my backyard in the Arctic Ocean about 1,000 miles off the coast of northern Russia. So… my accuracy has some room for improvement.

Utilizing my sextant and my artificial horizon on my back porch:

Reading of 47*30’ at 17:28PM local time (PST), which is 00:28 GMT I believe.

47*30’ divided by 2 = 23*45’ (halving the angle due to using an artificial horizon)

Then, using formula: Latitude = 90* - Reading +- Seasonal Deviation

90* - 23*45’ = 66*15’

66*15’ + 14*12’ = 80*27’ (using chart for August 15th)

My Latitude = 80*27’


For Longitude:

Local noon = 19:54 GMT

19:54 GMT – 12:00 GMT = 7:54

7:54 x 60 = 474 Min (covert to minutes)

474 min x 15 = 7110’ of arc (for arc of sun)

7110’ divided by 60 degrees = 118*30’ (convert back to degrees)

118*30’ – 1*09’= 117*21’ (subtract seasonal deviation for August 15th)

My Longitude: 117*21’

My Position: 80*27’ 117*21’ = Arctic Ocean north of central Russia.


What am I doing wrong here? I feel like I should need to compensate for taking a reading at a different time than noon, but the artificial horizon booklet doesn't indicate that I need to.
 
With the priviso that I've only just messed about myself with a sextant and have absolutely no expertise in this, the best place to start is with noon sights.

Next start taking sights then use something on the web to work them up. I used a US site initially, but the best I can find with a quick search tonight is this https://www.nauticalalmanac.it/en/navigation-astronomy/celestial-navigation.html

Taking it one step at a time just helps break it up so that you can learn how to do the sights and index corrections in one step then how to do the calcs in another.

I was really impressed that I could get noon sights on land down to within 1 or 2 miles like this, but my subsequent first real sight with the sun whizzing up and using a pro forma for calculations was 50m out. I blame the timekeeper. :)
 
Ususlly these problems come from adding when you ought to have subtracted...
Lets take
Then, using formula: Latitude = 90* - Reading +- Seasonal Deviation
Click to expand...

If you read that (as mathematicians should) to be
90 - reading + deviation (as you did then) yeah its not so good.
But if you read it as
90 -(reading + deviation) then that gets you 52oN abit better than just north of Russia!

Now...
Longitude needs E or W, you appear to have gone the wrong way from Grenwich.
Try Google 52 N 117 W
You might be a bit closer to home.

edit add:
Mebby scrap the bit about latitude... you either take the reading at noon or compensate.
 
Last edited:
If its basic instructions the OP wants then no-ones mentioned that there's no height of eye correction for an artificial horizon and your divide the sextant angle by two to get Ho. Then apply the normal corrections...

PS Welcome to the new member/user. Nice to see you in the YBW community for the first time. A wealth of experience and knowledge is now at your beck and call. You just have to sift the dross from the pearls of wisdom.
 
Hi and welcome.

I don't think that I can be a great deal of help as I don't recognise the method that you're using. Most sailors, I believe, use the Intercept Method, aka Marcq St Hilaire. A Google search will doubtless give you more info. There are numerous text books written on the subject, some easier than others to follow.

Using this method, a single sextant observation gives a Position Line. You can't get a lat and a long from a single sight so you need a second PL to derive a fix. Observing the sun passing overhead at local mid day, so-called Meridian Passage, will give latitude directly. Hence many sailors on passage will take sun sights 3 times per day; one in the morning, one at midday and one in the afternoon. The navigator will use these 3 position lines to maintain a running fix to establish and update position.

Before using the value in calculations, the angle measured by sextant needs to have a number of corrections applied. There are normally 3 of these but only 2 apply if using an artificial horizon.

First, apply Index Error. This is found by calibrating the sextant against the horizon each time you use it. The sextant should read zero when sighting the horizon. If it doesn't, the index error will either be "on" or "off" the arc and the amount should be subtracted or added respectively.

The second correction is dip for height of eye but this is not applicable when using an artificial horizon. In this case, divide the sextant altitude +- index error by 2 and apply the third correction.

The 3rd correction gives Observed Altitude, Ho. A Correction Table for this is found in the Nautical Almanac. The arguments are apparent altitude, sun upper or lower limb and season.

Many people argue that celestial navigation is totally unnecessary. Let's not go there! It is, however, immensely satisfying and rewarding.
 
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Now its not 036 in the morning in the UK I've got a few more minutes to answer. Some of the comments you've received are already helpful regarding the corrections you make to convert Hs into Ho

Hs is the normal abbreviation for the angle you read off the sextant.
Ho is the normal abbreviation for 'Height Observed' - in other words the angle the sextant has measured corrected for dip, altitude and index error.

If you want more help with the basic corrections please ask.

The simplest sight is a meridian pass to find your latitude. A raw beginner should be able to get a latitude to within a few miles from their first attempt.

You need to find the time of local noon. (Ask how to do this if you are not sure.)

Then start taking sights of the sun a few minutes before your calculated time. You will be able to watch the sun climbing in the sky until it appears to pause and then starts to drop again. Using an artificial horizon you can make the sun's images directly overlay each other, but in real life with a real horizon you make the bottom edge of the sun just 'kiss' the horizon. If you overlay the sun when you make the measurement using your sextant, you will have to allow for the sun's semidiameter in your calculations. (Its in the tables and normally automatically allowed for when you choose 'upper or 'lower limb'. Ask if you're not sure what to do.)

Making a note of the time and trying to deduce your longitude isn't accurate enough for nav purposes so don't bother. When you've got the hang of meridian passes, you can move on to sight's at other times of the day and sight reductions to produce lines of position and achieve a fix.
 
I've done a number of land based sightings too, but instead of an artificial horizon, I used a bucket of water. Arranging myself and the bucket, in relation to the sun, I could see (through the sextant) both the sun and its reflection (in the water in the bucket). Measuring the angle between the sun and its reflection gives me double Hs. (2xHs). I then assume no height of observer, so no correction for that, but have applied the single refraction correction as in the table for the halved measured angle.
I've assumed that applying on the standard refraction correction after halving accounts for the refraction in the wider angle actually measured (between sun and reflection). That sound right?

At night I found that this system works OK for stars too, but they need to be reasonably bright ones.

Doing a sun-run-sun from home I was able to find out where I live!
 
YakFruit said:
I am an aspiring sailor currently building a traditional navigational foundation by learning how to utilize a sextant for celestial navigation. I possess a Davis Instruments plastic sextant for training and a Davis Artificial Horizon. For someone with no background in these activities, the instruction booklets for these items seem lacking in explanations of proper calculations, especially when utilizing the artificial horizon. I am in need of expert advice in my calculations from my sextant reading, so I hope someone in this esteemed online community could lend me some advice.

It is likely that I am making significant errors in my actual reading taking, but it is difficult for me to know because I am also likely making grievous errors in my mathematics in translating my sextant reading into coordinates. If a wise person could review my below calculations and point out which step in the process I am messing up, it would be a great service.

I live in eastern Washintgon State, and my most recent reading and calculation places my backyard in the Arctic Ocean about 1,000 miles off the coast of northern Russia. So… my accuracy has some room for improvement.

Utilizing my sextant and my artificial horizon on my back porch:

Reading of 47*30’ at 17:28PM local time (PST), which is 00:28 GMT I believe.

47*30’ divided by 2 = 23*45’ (halving the angle due to using an artificial horizon)

Then, using formula: Latitude = 90* - Reading +- Seasonal Deviation

90* - 23*45’ = 66*15’

66*15’ + 14*12’ = 80*27’ (using chart for August 15th)

My Latitude = 80*27’


For Longitude:

Local noon = 19:54 GMT

19:54 GMT – 12:00 GMT = 7:54

7:54 x 60 = 474 Min (covert to minutes)

474 min x 15 = 7110’ of arc (for arc of sun)

7110’ divided by 60 degrees = 118*30’ (convert back to degrees)

118*30’ – 1*09’= 117*21’ (subtract seasonal deviation for August 15th)

My Longitude: 117*21’

My Position: 80*27’ 117*21’ = Arctic Ocean north of central Russia.


What am I doing wrong here? I feel like I should need to compensate for taking a reading at a different time than noon, but the artificial horizon booklet doesn't indicate that I need to.
Click to expand...

To obtain any good quality celestial LOP you must have accurate time. Go to Time.gov and correct your watch or timepiece for local time. Be sure to identify the actual time of MER PASS. it is NOT always at noon. For example, today it will be at 1202pm GMT. You can figure out the longitude at Local Apparent Noon (LAN) by finding the difference between your apparent noon and the actual MER PASS. You can calculate it by using GMT or the closest meridian that is divisible by 15. My technique is to convert the difference into seconds and then divide that result by 240. That will give you either your actual longitude (GMT) or the number of degrees you are off the base meridian.

Make sure you are lining up the sun or other body perfectly in your artificial horizon. The ideal method is to align it so that the shadow falls directly behind the box. The sun should appear directly in the center of the horizon mirror where it splits.

I use the Navy method based on the Nautical Almanac and HO249 which is what I learned as a navigator. It is simple and requires the least amount of math. For LAN, you have to know what hemisphere the Sun is in at the time of observation. You did not include the date of the observation.

Here is a good diagram that will help you to determine which method you need to use:
a9KLEK-rO


Here is the worksheet I made based on the diagram:
a9KLEK-rP
 
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