Figure 11-8.-Length of curve.Then, solving for L,This expression is also applicable to the chorddefinition. However, L., in this case, is not the true arclength, because under the chord definition, the lengthof curve is the sum of the chord lengths (each of whichis 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), thenthere are three 100-foot chords; and the length of“curve” is 300 feet.Middle Ordinate andExternal DistanceTwo commonly used formulas for the middleordinate (M) and the external distance (E) are asfollows:DEFLECTION ANGLESAND CHORDSFrom the preceding discussions, one may thinkthat laying out a curve is simply a matter of locatingthe center of a circle, where two known or computedradii intersect, and then swinging the arc of thecircular curve with a tape. For some applications, thatcan be done; for example, when you are laying out theintersection and curbs of a private road or drivewaywith a residential street. In this case, the length of theradii you are working with is short. However, what ifyou are laying out a road with a 1,000- or 12,000- oreven a 40,000-foot radius? Obviously, it would beimpracticable to swing such radii with a tape.In usual practice, the stakeout of a long-radiuscurve involves a combination of turning deflectionangles and measuring the length of chords (C, Cl,orCZas appropriate). A transit is set up at the PC, a sightis taken along the tangent, and each point is located byturning deflection angles and measuring the chorddistance between stations. This procedure isillustrated in figure 11-9. In this figure, you see aportion of a curve that starts at the PC and runs throughpoints (stations) A, B, and C. To establish the locationof point A on this curve, you should set up yourinstrument at the PC, turn the required deflectionangle (all/2), and then measure the required chorddistance from PC to point A. Then, to establish pointB, you turn deflection angle D/2 and measure therequired chord distance from A to B. Point C is locatedsimilarly.As you are aware, the actual distance along an arcis greater than the length of a corresponding chord;therefore, when using the arc definition, either acorrection is applied for the difference between arcFigure 11-9.-Deflection angles and chords.11-7