What’s The Point Of Calculating Our Latitude From The Altitude Of The Sun At Midday?


cover with Jester in useReferring to my earlier post ‘Calculating Latitude from the Midday Altitude of the Sun’, the question has been raised “what is the point of this if you already know your latitude”?  The answer to this question is quite simple, if we are using astro navigation at sea without reliance on GPS, we never know what our exact position is and the midday altitude gives us a handy check on our DR position.

As explained in the link above, to calculate latitude from the midday Sun, we need to know three things: the Sun’s declination, an accurate altitude reading and our approximate latitude.  Armed with this data, we can calculate a reasonably accurate latitude. (Note.  The only reasons that we need to know the approximate latitude is to enable us to know whether it is greater or less than the declination as explained in this link).

 Even in the best circumstances, the accuracy of astro navigation is only ±1 minute of arc or 1 nautical mile.  This level of accuracy may seem to be unacceptable in the light of modern electronic navigation systems such as GPS but before the advent of such systems, astro is all we had to rely upon.  Click here to learn more about the accuracy of astro navigation.

 It might be said “now that we have GPS, what’s the point of an inaccurate method such as astro navigation”?  The answer to that question is that we could lose GPS at any time through a variety of causes such as solar storms, cyber attacks, power failures, system failures, and so on (see my post ‘Could the Global Positioning System Fail’).  On the other hand, the Sun, Moon, stars and planets will always be there and so we will always be able to use astro navigation.

 Furthermore, in certain situations, it might not be advisable to use GPS anyway; just as a mobile phone can give our position away so can a GPS device.  Like all electronic devices, a GPS device emits ‘side-channel electromagnetic signals’and these emissions can be easily detected with modern sophisticated electronic warfare systems.  So for special forces and those in ‘escape and evasion’ scenarios, it might be advisable to find another way of navigating (see my post ‘Astro Navigation in a Survival Situation’

It was not until John Harrison invented the chronometer in the 18th century that navigators had a method of calculating longitude). Before this time, navigators relied on dead reckoning to give them an approximate longitude.  However, they would have been able to calculate their latitude from the midday altitude of the Sun and they would able to use this to revise their DR position. To calculate latitude from the midday Sun, they would need to know two things, their approximate latitude and the declination of the Sun.  They would take their approximate latitude from the DR position and they would have had tables listing the Sun’s declination for each day.  So, the whole point of  knowing the approximate latitude was to enable them to calculate a more accurate one. 

 If we use astro navigation today, we ideally need to be able to take star and planet sightings during  nautical twilight.  If however, the sky is covered during these times, then we have to rely on the Sun and the Moon when they are visible.  In these circumstances, a midday sighting of the Sun is invaluable because not only does it give us our latitude, we can also use it to calculate our longitude as long as we have a chronometer.  When the Sun reaches its highest altitude from our position, we know that it is exactly over our meridian of longitude and so we know that, at that point, it is noon (local time) at our position.  A chronometer will give us GMT, so if we know when it is noon at our position, we can calculate our longitude.  In conclusion, the midday Sun enables us to check our DR position in terms of both latitude and longitude.

Midday Sun in Survival Situations.  In certain circumstances such as survival situations, we would probably not have access to declination tables but there is a ‘rule of thumb’ method which enables us to calculate the approximate declination for any day without having to rely on tables. 

Please note that this method is not very accurate and you are only be likely to use it in a survival situation.  We know what the Sun’s declination will be on four days of the year and with this simple knowledge, we can calculate an approximate value for declination which will help us to calculate our approximate latitude: 

At the Vernal Equinox (March 20/21) and at the Autumnal Equinox (September 22/23)  when the Sun is above the Equator, its declination will be 0o

At the Summer Solstice (June 20/21) when the Sun has reached the northerly limit of its path, its declination will be 23.5o north.

At the Winter Solstice (December 21/22) when the Sun has reached the southerly limit of its path, its declination will be 23.5o south.

Between these dates it moves north or south accordingly at an average rate of approximately 0.35o per day.

Armed with this information, we can calculate the Sun’s approximate declination for any day of the year.

For example, April 15 is 25 days after the Vernal Equinox so the declination on that day will be: 0o plus (25 x 0.35o) north = 8.75o north (approx.).

October 15 is 23 days after the Autumnal Equinox so the declination on that day will be:  0o plus (23 x 0.35o) south  =  8.05o south (approx).

If you check these answers with the Survival Declination Table, you will see that they are accurate to within one degree.

To learn how to calculate your lat and long in a survival situation, go to these links:  Lat from Sun    Lat from Polaris     Long.

To return to the original question, as long as we have an approximate latitude and an approximate declination to work on, we can  calculate our latitude from the midday Sun.  The whole point of doing this is to enable us to check our DR position and revise it if necessary.

Links:

Astro Navigation Demystified

What is Astro Navigation?

Accuracy of Astro Navigation – U.S. Navy

Astro Navigation in a Survival Situation

The Astronomical Position Line

Altitude and Azimuth

Altitude and Zenith Distance

Calculating Latitude from the Midday Sun

Calculating Longitude

Relationship Between Latitude, Longitude  & the Nautical Mile

Dead Reckoning

Lunar Distance

Planning Star and Planet Observations

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8 Responses to What’s The Point Of Calculating Our Latitude From The Altitude Of The Sun At Midday?

  1. Yours is a wonderful resource, but I take issue with your assertion that: “just as a mobile phone can give our position away so can a GPS device. GPS relies on two way communication with a satellite which means that your GPS device transmits radio signals and these can be easily detected with modern sophisticated electronic warfare systems.”
    This is not so. Our GPS receiver does not communicate with the satellite nor anything else and cannot reveal our position in that manner.
    Jeremy Parker

    • Jack Case says:

      Thank you for your interest and for your kind comments about the resource. I was thinking more about ‘side-channel electromagnetic signals’ than direct communications with the satellite and I guess I should have made this clear. I would be interested to know whether you think that such emissions from a GPS device could be detected by sophisticated electronic warfare systems?
      Kind regards,
      Jack Case

      • My knowledge of the technology necessary to detect side channel em signals is about zero! But for the civilian user of any GPS technology I cannot imagine a situation where a government’s sophisticated electronic warfare systems would be used to garner information about an individual’s movements. Most people appear quite content to broadcast their every move through social media, or by allowing their phones to automatically upload intimate data, and this is far more easily intercepted than whatever weak signal may be emanating from our GPS receiver!
        Neither can I envisage an elite gang of special forces going into the field armed with sextant, almanac and tables and using these to effect their getaway!
        I grew up in the UK, where it is necessary to have a licence to operate a TV set; during my childhood I recall the ‘threat’ of ‘TV detector vans operating in your area’. There were no such vans; there was no reliable technology for pinpointing the position of an unlicensed TV and I would doubt any similar technology exists to accurately detect a GPS receiver.

        Getting back on track – I stumbled over your website, and this particular page, as a teacher of celestial nav whilst looking for others’ opinions on the ‘necessity’ of taking a noon site for latitude. It seems to be deeply ingrained in many navigators that we must do a Mer Pas – but why? In the run up to LAN, any of your observations of the body could be reduced to give as good an LOP as the noon Lat. Yes, the working is easier, but what of it? If you were capable of reducing your earlier morning site and transposing its LOP to cross with your Lat, then why can’t you do the same thing 2 or 3 hours later? In my experience, hanging around on deck waiting for LAN usually results in a cold lunch and the only 8/8 cloud cover all day!
        Seriously, the need for a sight to establish latitude dates back to the days before the intercept method, where Latitude was a necessary argument in reducing a Time Sight to establish LHA, whence Longitude. In my classes I make very little of noon sights and still less of any inelegant method of determining longitude from the process.

        Thanks for a great site and for helping demystify this fascinating art. I am always looking for ways of stripping back the bullshit and exposing the very simple bare bones of astro; of reminding my students of what they are doing, and why, rather than letting them get bogged down in hour angles, assumed longitudes and the PZX triangle.
        Jeremy

        • Jack Case says:

          In my resource, I try to cover all situations where astro navigation could be used and survival is just one of those situations. Obviously, special forces don’t charge around carrying sextants and star globes but if you read this post https://astronavigationdemystified.com/2012/01/08/astro-navigation-in-a-survival-situation/, you will see that there are a number of ways that astro could be used to give an approximate position which, in a wilderness survival or ‘escape and evasion’ situation is the best you can hope for.

          • Point taken – I was being facetious.
            One of the points I try to impress on my students is how much you can glean by simple observation, without the need for instruments, tables etc., and your survival astro tips are an extension of this. An understanding of the basic principles of astro gives us a better understanding of where we are on earth and in space.
            I would counsel you against suggesting home-smoked glass as a suitable filter through which to observe the sun. Whilst this may reduce the intensity of visible light it will not necessarily filter out the harmful IR radiation. I spent some time researching this when attempting to repair some old EBBCO lifeboat sextants and the concensus was for either mylar film or fully exposed and developed black and white negative film – with the caveat that this be b+w, not colour, film, and that it be of a traditional type that contains a silver emulsion. Take a look at this page on the NASA website for more information:
            http://eclipse.gsfc.nasa.gov/SEhelp/safety2.html
            Whilst it speaks of suitable filters for observing solar eclipses, the principles are the same.
            Regards
            Jeremy

          • Jack Case says:

            Thank you Jeremy, I take the point that smoked glass will not filter IR radiation but in a desperate survival situation, it may provide a quick-fix especially as, in the days of digital photography, there is not a lot of photographic film around. It may be harmful, but in a desperate situation, it may be worth the risk.
            To return to the question “What’s the point of a meridian passage fix”, I agree that it can be tedious waiting for the Sun to cross your meridian but I see it as an extra string to your bow. Marcque St. Hilaire requires two sun-sights and there is a delay in obtaining a fix until the second sight is taken. On some days you can obtain position lines from the Sun and the Moon but that will give you only a two-point fix. I suppose there are pros and cons to all three of these methods of daytime fixing but I believe that the more tools you have at your disposal, the better.
            Regards,
            Jack

  2. Hi Jack
    Just read your post on Mer. Pas and EoT and think you’ve made an error but cannot see a link for responding to that post. Is there some way I can send you my thoughts?
    Jeremy

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