Angles in Surveying Calculations

In the United States, the most common angular unit employed is the sexagesimal system. Here, the angular notation is given in increments of 60 degrees in a whole circle of 360 degrees.

Read On: Horizontal Angles in Surveying - Deflection Angles

Here, 

• Degrees are divided into 60 minutes
• Minutes are divided into 60 seconds

Each unit has a corresponding symbol: degrees are indicated by °; minutes by ´; and seconds by ˝.

Therefore; 

1 circle = 360° = 21,600´ = 1,296,000˝ 

1° = 60´ = 3600˝ 

1´ = 60˝

They are represented as 34° 81´ 72˝. Here, the minutes or seconds equal to greater than 60 are carried over to the next larger unit. The degrees and minutes do not have decimals, while decimal seconds are acceptable. 

Conversion of Degree- Minute-Seconds to Decimal Degrees

The angles measured in surveying can be represented as 23^o12’18^’’  or as 23.205^o. 

Example 1: Convert  23^o12’18^’’ to Decimal Degrees

Solution:

23^o12^’18^’’ = 23 + (12/60)^o + (18/60)^’ = 23 + (12/60)^o+ (18/3600)^o

As explained above, the 12’ is converted into a degree by dividing it by 60. The 18’’ (seconds) is converted initially into minutes by dividing it by 60, which is then divided by 60 to convert it into degrees. 

Example 2: Convert 42.885^o into Degree-Minute-Seconds

Solution:

42.885^O = 42 + (0.885 x 60’) = 42 + 53.1’’ = 42^o + 53’ + (0.1 x 60)’’ = 42^o53’06’’

In the above problem, 0.885 degrees is converted into minutes by multiplying it by 60. Here, the minutes obtained is 53.1', where 0.1 minutes is converted into seconds by multiplying it by 60. This is done so that, there are no decimal places in minute places of the angle.

Unit of Angles

Radian

The primary unit of angular measurement in the metric system is the radian. A radian is defined as the angle between radius lines from either end of an arc of radius length.

Circumference  C = 2π.r (Where, r= radius of the circle)

1 circle = 360 degrees = 2π.radians

1 rad = 360/2π = 57.29.degrees

Radians is used to deal with circular and spiral curves.

Grad or Gon

Grad or gon is defined as the 1/400 of a circle. It is used in the metric system, but lesser than radians.

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