A Simplified Guide to Small Marine Craft Navigation.

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Chapter 4 (v.1) - Working in Angular Measurements.

Submitted: December 02, 2016

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Submitted: December 02, 2016



Working in Angular Measurements.


Keeping the previously mentioned basic facts in mind it is quite easy to add up or subtract “angles”. If for instance you wished to add  50°24'48" to 37°41'15” this would be done by:


+ 37°41'15”

=  88°06'03"


Note that when the seconds were added together, these came to 63" but there are 60” I in a minute so 63" = 1'03" and the l' is carried forward leaving 03”. Similarly, when the minutes were added together the total was 66' = l°06' so 1° was carried forward making the total number of degrees 88°. If we subtract the same two “angles” this is done by:


- 37°41'15”



Here in the minute’s column the 1' taken from the 4' leaves 3', but 40' is taken from 60' leaving 20', which, added to the 20' in the top line leaves 40' remaining, and l to carry forward to the bottom line of the degree column. Note that an “angle” cannot be greater than 360° since this represents a full circle, so that if an addition of “angles” comes to more than 360°, 360° must be subtracted from the result to give the correct answer as thus:


+ 112°57'52”

= 428°43'01"

- 360°00'00"

 = 68°43'01"


When dealing with angular measurement in navigation, it is often necessary to reduce minutes to decimal fractions of degrees, or to reduce seconds to decimal fractions of minutes. Since there are 60" in 1', it follows that 6” are equal to one tenth of 1', that is 0‘.1; similarly, 12” are equal to two tenths of 1', or 0'.2, and so on. Thus, we find the rule: To reduce seconds to a decimal fraction of a minute, divide the seconds by 6. Since there are also 60' in 1°, the same rule applies when reducing minutes to a decimal fraction of a degree. For example:-


Expressed in minutes 17'18" = 17'.3 by dividing the 41'36" = 41'.6 seconds by 6

Expressed in degrees 35°42' = 35°.7 by dividing the52°54' = 52°.9 minutes by 6

It is usually sufficient, when thus reducing, to work only to one place of decimals, in which case :-

12'17” becomes 12'.3 (nearest)

12'19” becomes 12'.3 (nearest)

12'20” becomes 12'.3 (nearest)

However, if it were so desired to work very accurately, then a cipher (0) should be added to the last figure and the dividing carried one place further. In that case, the above examples would read:

12'17” = 12'.28

12'19" = 12'.31

12'20" = 12'.33

Note very carefully that when writing decimal fractions of a degree or of a minute, the degree (°) or minute (') symbol comes before the decimal point and not after the last figure of the decimal fraction.

Thus, you write 35°.7 and not 35.7°. And you write 12'.28 and not 12.28'. This convention is important to avoid confusion, especially when mixed terms are being used.

For instance, 47°12.28' is much more likely to be misread as47°12'28" than 47°12'.28.

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