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SOLVING AND LAYING OUT A SIMPLE CURVE - 14070_244

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length and chord length, or shorter chords are used to make  the  error  resulting  from  the  difference negligible.  In  the  latter  case,  the  following  chord lengths are commonly used for the degrees of curve shown: 100 feet—0 to 3 degrees of curve 50 feet—3 to 8 degrees of curve 25 feet—8 to 16 degrees of curve 10  feet-over  16  degrees  of  curve The above chord lengths are the maximum dis- tances  in  which  the  discrepancy  between  the  arc length  and  chord  length  will  fall  within  the  allowable error for taping. The allowable error is 0.02 foot per 100  feet  on  most  construction  surveys;  however, based on terrain conditions or other factors, the design or  project  engineer  may  determine  that  chord  lengths other  than  those  recommended  above  should  be  used for  curve  stakeout. The   following   formulas   relate   to   deflection angles:   (To   simplify   the   formulas   and   further discussions of deflection angles, the deflection angle is designated simply as  d rather than d/2.) Where: d = Deflection  angle  (expressed  in  degrees) C =  Chord  length D = Degree of curve d = 0.3 CD Where: d = Deflection  angle  (expressed  in  minutes) C =  Chord  length D = Degree of curve W h e r e: d = Deflection  angle  (expressed  in  degrees) C = Chord length R = Radius. Figure  11-1O.—Laying  out  a  simple  curve. SOLVING AND LAYING OUT A SIMPLE CURVE Now let’s solve and lay out a simple curve using the  arc  definition,  which  is  the  definition  you  will more often use as an EA. In figure 11-10, let’s assume that the directions of the back and forward tangents and  the  location  of  the  PI  have  previously  been staked, but the tangent distances have not been meas- ured. Let’s also assume that stations have been set as far 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  Curve We will begin by first determining the distance from Station 18 + 00 to the location of the PI. Since these  points  have  been  staked,  we  can  determine  the distance by field measurement. Let’s assume we have measured this distance and found it to be 300.89 feet. Next, we set up a transit at the PI and determine that deflection  angle  I is 75°. Since I always equals  A, then A is also 75°, Now we can compute the radius of the curve, the tangent distance, and the length of curve as follows: 11-8



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