Referring 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 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.