Engineering assignment

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surveying_notes_99.docx

P. L. Phillips 10/31/2016 1

Surveying Angle Measurement Types

The azimuth is measured from the North line in a clockwise direction, with a range from 0 to 360 degrees.Figure 1 depictsazimuth angles in each of the four quadrants. A bearing angle is measured from either the North or South line and can go clockwise or counter-clockwise. As such, a bearing angle uses N/S and E/W indicators and angles are reported in degrees, minutes, seconds form like N45d30’15”E. The range for a bearing is between 0 and 90 degrees. Figure 2 shows examples of bearing angles in each of the four quadrants.

Figure 1. Azimuths for angles in each of the four quadrants.

Figure 2. Bearing measurements for angles in each of the four quadrants.

Converting between DMS and Degrees

To convert an angle given in degrees, minutes, and seconds (DMS) we need to understand the following: there are 60 minutes to a degrees; there are 60 seconds to a minute. Therefore, there are 3600 seconds in a degree. The conversion from DMS to degrees is

where is the angle in degrees, and the angle in terms of DMS is given as whereis the degrees, minutes, and seconds. The conversion from degrees to DMS is a multistep process where

yields the degree portions of the angle in DMS. The expression int( ) yields the integer portion of the number inside the parentheses. For example int(3.1415) = 3.Then the minutes portion is found using

and the seconds portion is found using

Converting from Bearing to Azimuth

The conversion from a bearing measurement to an azimuth measurements is straightforward once the conversion from DMS to degrees is performed using Eq. . For example, the bearing measurement S30d20’30”E has a DMS portion equal to 30d20’30” which can be converted to degrees using Eq. to yield 30.34166 degrees. We then need to follow the rules for the different quadrants shown in Figure 3and given below:

The following convention holds for all quadrants; is the angle in degrees; is the azimuth of the angle

NE

SE

SW

NW

Figure 3. Conversion from Bearing () to Azimuth (). Black arrows are bearing measurements. Red arrows are azimuths.

Converting from Azimuth to Bearing

The conversion from an azimuth to bearing measurements follows the rules below:

The following convention holds for all quadrants; is the angle in degrees; is the azimuth of the angle

Once the angle in degrees, , is computed, use Eqs. , , and to convert the angle from degrees to DMS. Lastly, append the correct N/S and E/W headings.

VBA Application

Write two VBA functions:

1. Function called ‘bearing2azimuth(bearing)’ to take a bearing string in the form N45d15'12"W and output the corresponding azimuth in decimal degrees (ex. =bearing2azimuth(N45d15'12"W) returns 314.7467)

2. Function called ‘azimuth2bearing(azimuth)’ to take an azimuth angle in decimal degrees and output the test string for the corresponding bearing (ex. =aximuth2bearing(314.7467) returns N45d15'12"W).

Test your functions using the four cases in the table below.

Bearing

Azimuth

N13d45'34"E

13.7594442

S56d6'14"E

123.896111

S9d59'59"W

189.999725

N45d15'12"W

314.746674

603600

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