Survival – Latitude From The Midday Sun

Finding Your Latititude From The Midday Sun In A Survival Situation.

A full method of calculating your latitude from the altitude of the Sun can be found here.  However, in a survival situation, the following simplified method can be used.

Equipment Needed. 

1. A clinometer or other device for measuring angles.
2. A copy of the Sun’s Declination table.
3. A magnetic compass.

(A  full list of equipment required for survival astro navigation can be found here)

How to tell when it is midday in your exact geographical position.

Firstly, it is important to remember that midday in your exact position will very rarely co-incide with noon in standard time or zone time because these time systems cover very large geographical areas.  True midday is when the Sun lies directly over your meridian of longitude and so, depending on your geographical position, the Sun will bear either due north or due south at midday.  Survivors on land can make a sundial to determine the local (True Time),

Use the following method to determine when it is midday at your position.

1. Use a survival sundial.
2. If you have a compass, use it to determine when the sun’s bearing is approaching due north or south.
3. Using a clinometer and a smoked glass filter, begin to measure the sun’s altitude at frequent intervals just as it approaches north or south.  Midday will occur when the sun reaches its highest altitude.  Make a note of the highest altitude reached.

Calculating your latitude from the Sun’s altitude at midday.

The following method depends on you having a rough idea of your latitude to begin with.  For example, in the Sahara, you will be between 15^o and 35^o North; in Nepal, you willl be between 26^o and 28^o North; and in the Amazon, you will be between 0^o and 15^o South.

Method of calculating latitude.

1. Consult the declination table to find the declination for the day.
2. Determine whether the declination is north or south.
3. Determine whether your latitude and the declination have the same or contrary  names (north or south).
4. Apply the rules below to calculate your latitude.

Rules.  The method depends on the following three simple rules:

(i)   Latitude and declination have same names and latitude greater than declination:

LAT  =  DEC + (90^o – ALT)

(ii)   Latitude and declination have same names and declination greater than latitude:

LAT  =  DEC – (90^o – ALT)

(iii)   Latitude and declination contrary names:

LAT  =  (90^o – ALT) – DEC

Examples:

1.   Using rule (ii)

Scenario:  True altitude at midday: 69.7^o

Sun’s declination: 20.8^o North

Approx latitude:  0^o – 5^o North (in a coastal region of Borneo).

Sun’s expected bearing at midday: North.

LAT  =  DEC – (90^o – ALT) (rule ii)

= 20.8^o – (90^o – 69.7^o)

= 20.8^o – 20.3^o

= 0.5^o North.

2.   Using rule (iii)

Scenario:  True altitude at midday: 80.9^o

Sun’s declination: 2.7^o  South

Approx latitude:  5^o – 10^o North (in Somalia)

Sun’s expected bearing at midday:  South (but more overhead).

LAT = (90^o – ALT) – DEC (rule iii)

= (90^o – 80.9^o) – 2.7^o

      = 9.1^o – 2.7^o  = 6.4^o North.

3.   Using rule (i)

Scenario:  True altitude at midday: 72.5^o

Approx latitude: 35^o – 45^o South  (at sea in mid Pacific)

Sun’s declination: 23.2^o South

Sun’s expected bearing at midday: North

LAT  =  DEC + (90^o – ALT) (rule i)

= 23.2^o  + (90^o – 72.5^o)

= 23.2^o  + 17.5^o

= 40.7^o South.

=  40^o  42’ South

 Double Check:  You can double check your midday latitude calculation by also finding your latitude from the Pole Star (Polaris).  Click here to find out how.

Calculating Declination Without Declination Table.  In certain survival situations, we would probably not have access to declination tables but there is a reasonably accurate ‘rule of thumb’ method which enables us to calculate the declination for any day without having to rely on tables.  We know what the Sun’s declination will be on four days of the year as follows:

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 0^o.

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

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

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

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

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: 0^o plus (25 x 0.35^o) north = 8.75^o north (approx.).

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

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

 

More info? www.astronavigationdemystified.com