length and chord length, or shorter chords are used tomake the error resulting from the differencenegligible. In the latter case, the following chordlengths are commonly used for the degrees of curveshown:100 feet—0 to 3 degrees of curve50 feet—3 to 8 degrees of curve25 feet—8 to 16 degrees of curve10 feet-over 16 degrees of curveThe above chord lengths are the maximum dis-tances in which the discrepancy between the arclength and chord length will fall within the allowableerror for taping. The allowable error is 0.02 foot per100 feet on most construction surveys; however,based on terrain conditions or other factors, the designor project engineer may determine that chord lengthsother than those recommended above should be usedfor curve stakeout.The following formulas relate to deflectionangles: (To simplify the formulas and furtherdiscussions of deflection angles, the deflection angleis designated simply as d rather than d/2.)Where:d = Deflection angle (expressed in degrees)C = Chord lengthD = Degree of curved = 0.3 CDWhere:d = Deflection angle (expressed in minutes)C = Chord lengthD = Degree of curveW h e r e:d = Deflection angle (expressed in degrees)C = Chord lengthR = Radius.Figure 11-1O.—Laying out a simple curve.SOLVING AND LAYING OUTA SIMPLE CURVENow let’s solve and lay out a simple curve usingthe arc definition, which is the definition you willmore often use as an EA. In figure 11-10, let’s assumethat the directions of the back and forward tangentsand the location of the PI have previously beenstaked, but the tangent distances have not been meas-ured. Let’s also assume that stations have been set asfar as Station 18 + 00. The specified degree of curve(D) is 15°, arc definition. Our job is to stake half-sta-tions on the curve.Solving a Simple CurveWe will begin by first determining the distancefrom Station 18 + 00 to the location of the PI. Sincethese points have been staked, we can determine thedistance by field measurement. Let’s assume we havemeasured this distance and found it to be 300.89 feet.Next, we set up a transit at the PI and determine thatdeflection angle I is 75°. Since I always equals A, thenA is also 75°, Now we can compute the radius of thecurve, the tangent distance, and the length of curve asfollows:11-8

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