angles, directions and azimuths

7/25/2019 Angles, Directions and Azimuths

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Angles, Directions and Azimuths

CVNG 305

Saint Louis UniversityTom Bryant PLS


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Angles

360 in a circle

60 in a degree

60 in a minute

3600 in a degree

One circle = 360

360 = 21,600 =

1,296,000


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Angles

Sexagesimal System

Base 60

Ancient Sumerians 3rdmillennium BC

Today used in

Time

Angles

Geographic Coordinates Latitude 38 30 30N

Longitude 90 45 25W


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Angles

Usually angles are expressed in Degrees,Minutes and Seconds (DMS)

Can be expressed in any combination of units

35.37 (Decimal Degrees (DD))

2122.2

127332

348172 352212

All express the same magnitude of angle


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Angles

The last form, Degrees Minutes Seconds, isthe preferred form

352212

Notice that minutes and seconds over 60 arecarried over to the next larger unit anddegrees and minutes do not have decimals inthem.

Decimal seconds are acceptable

451235.5


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Angles

For performing some mathematical

operations with angles (trigonometric

functions, adding and subtracting) it is easier

to convert to DMS to DD, perform the

necessary math and convert back to DMS.


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Angles

DMS>DD

231218

23 + (12/60) + (18/3600) = 23.205

DD>DMS

42.885 = 42+ (.885x 60)=4253.1= 4253 + (.1 x 60)= 425306


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Angles

Convert

352345 to Decimal Degrees

Convert

67.456 to Degrees Minutes Seconds


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Azimuths

00000 is Due North

Azimuths are measured clockwise from North

No azimuths over 3600000 Abbreviated AZ


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Azimuth


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Azimuths

North 0

East 90

South 180

West 270

Azimuth AB= 60

Azimuth AC= 172

Azimuth AC= 284


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Azimuths

What is the angle

between AB and AC?

172-60= 112


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Azimuths


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Azimuths

When we measured horizontal angles with outtotal stations, we were measuring angles, notazimuths.

We set 00000 on out back sight

The direction of our back sight could be anydirection

This Azimuth to the back sight will be provided toyou or you will calculate it from coordinates

We must use the azimuth to our back sightcombined with our measured horizontal angles tocalculate the azimuths to our side shots


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Azimuths

Azimuth to Back Sight + Measured Horizontal

Angle = Azimuth to Side Shot

Azimuth to Back Sight = 340000

Measured Horizontal Angle = 1103025

340000+ 1103025= 1443025 Azimuth to

Side Shot

EACH azimuth to side shot is computed from theazimuth to the back sight


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Azimuths

RememberNO Azimuths over 360

Azimuth to back sight = 900000

Measured horizontal angle = 3100000 90 + 310 = 400

What??? Cant be

So 400 - 360 = 40Azimuth to Side Shot


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Reverse Azimuths


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Sketch for Azimuth Computation


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Bearings

Besides Azimuths, Bearings are also used tomeasure directions

Bearings are measured from North and South

and do not go over 90 Mostly used in North America

Computers and modern methods prefer

Azimuths You need to be aware of Bearings, but we will

use Azimuths in this class


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Bearings


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Reverse Bearings


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CONVERTING

Converting Azimuth to Bearing:

North East: the prefix N and the suffix E must be added

Ex: 76o30 = N 76o30 E

South East: the azimuth angle is subtracted from 180oand S and

E are added

Ex: 168o40 = 180o168o40 = S 11o20 E

South West: 180ois subtracted from the azimuth angle and S and

W are added

Ex: 195o22 = 195o22 180o= S 15o22 W

North West: the azimuth angle is subtracted from 360oand N

and W are added

Ex: 314o35 = 360o314o35 = N 45o25 W


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Zenith Angles

angles, directions and azimuths

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