DEFLECTION ANGLES AND CHORDS
Figure 11-8.-Length of curve. Then, solving for
L, This expression is also applicable to the chord definition. However,
L., in this case, is not the true arc length, because under the chord definition, the length of curve is the sum of the chord lengths (each of which is usually 100 feet or 100 meters), As an example, if, as shown in view B,
figure 11-8, the central angle
(A) is equal to three times the degree of curve
(D), then there are three 100-foot chords; and the length of “curve” is 300 feet.
Middle Ordinate and External Distance Two commonly used formulas for the middle ordinate
(M) and the external distance
(E) are as follows:
DEFLECTION ANGLES AND CHORDS From the preceding discussions, one may think that laying out a curve is simply a matter of locating the center of a circle, where two known or computed radii intersect, and then swinging the arc of the circular curve with a tape. For some applications, that can be done; for example, when you are laying out the intersection and curbs of a private road or driveway with a residential street. In this case, the length of the radii you are working with is short. However, what if you are laying out a road with a 1,000- or 12,000- or even a 40,000-foot radius? Obviously, it would be impracticable to swing such radii with a tape. In usual practice, the stakeout of a long-radius curve involves a combination of turning
deflection angles and measuring the length of chords (C, Cl, or CZ as appropriate). A transit is set up at the PC, a sight is taken along the tangent, and each point is located by turning deflection angles and measuring the chord distance between stations. This procedure is illustrated in
figure 11-9. In this figure, you see a portion of a curve that starts at the PC and runs through points (stations) A, B, and C. To establish the location of point A on this curve, you should set up your instrument at the PC, turn the required deflection angle
(all/2), and then measure the required chord distance from PC to point A. Then, to establish point B, you turn deflection angle D/2 and measure the required chord distance from A to B. Point C is located similarly. As you are aware, the actual distance along an arc is greater than the length of a corresponding chord; therefore, when using the arc definition, either a correction is applied for the difference between arc
Figure 11-9.-Deflection angles and chords. 11-7