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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

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