Converting Deflection Angles to Bearings

CHAPTER 13 HORIZONTAL CONTROL

Converting Azimuths to Bearings or Vice Versa

Engineering Aid 3 - Beginning Structural engineering guide book
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This figure shows two meridians or parallel lines that are intersected by another line called a traverse. It can be proved geometrically that the angles A and Al, B and B1, Az and A3, and Bz and B3 are equal (vertically opposite angles). It can also be shown that angles A = A₂, and B = B2 (corresponding angles). Therefore, It can also be shown that the sum of the angles that form a straight line is 180°; the sum of all the angles around the point is 360°. Figure 13-2 shows a traverse containing traverse lines AB, BC, and CD. The meridians through the traverse stations are indicated by the lines NS, N´S´, and N´´S´´. Although meridians are not, in fact, exactly parallel, they are assumed to be, for conversion purposes. Consequently, we have here three parallel lines intersected by traverses, and the angles created will therefore be equal, as shown in figure 13-1. The bearing of AB is given as N20°E, which means that angle NAB measures 20°. To deter- mine the deflection angle between AB and BC, you proceed as follows: If angle NAB measures 20°, then angle N’BB’ must also measure 20° because the two corresponding angles are equal. The bearing of BC is given as S50°E, which means angle S´BC measures 50°E. The sum of angle Figure 13-2.-Converting bearings to deflection angles from given traverse data. N´BB´ plus S´BC plus the deflection angle between AB and BC (angle B´BC) is 180°. Therefore, the size of the deflection angle is The figure indicates that the angle should be turned to the right; therefore, the complete deflection angle description is 11°R. The bearing of CD is given as N70°E; therefore, angle N´´CD measures70°. Angle S´´CC´ is equal to angle S´BC and therefore measures 50°. The deflection angle between BC and CD equals The figure indicates that the angle should be turned to the left. Converting Deflection Angles to Bearings Converting deflection angles to bearings is simply the same process used for a different end result. Suppose that in figure 13-2, you know the deflection angles and want to determine the corresponding bearings. To do this, you must know the bearing of at least one of the traverse lines. Let’s assume that you know the bearing of AB and want to determine the bearing of BC. You know the size of the deflection angle B´BC is 110°. The size of angle N´BB´ is the same as the size of NAB, which is 20°. The size of the angle of bearing of BC is The figure shows you that BC lies in the second or SE quadrant; therefore, the full description of the bearing is S50°E. Converting Bearings to Interior and Exterior Angles Converting a bearing to an interior or exterior angle is, once again, the same procedure applied for a different end result. Suppose that in figure 13-2, angle ABC is an interior angle and you want to determine the size. You know that angle ABS´ equals angle NAB, and therefore measures 20°. 13-2

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