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212    Cha pte r  F i v e


          Depth/Setback Implications
          If the determined setback distances or drill rig carriage angle consis-
          tent with the project maximum depth specifications are not practical,
          consideration should be given to receiving approval from the owner
          allowing increased depths in the transition area following the entry
          pit. If necessary, smaller diameter, more flexible, drill rods may be
          considered if consistent with anticipated thrust and torque loads.
          Smaller radii of curvature than the manufacturer’s limits may be
          used by the contractor if it is recognized that reduced service life may
          result for the drill rods. If the steering conditions in the soil preclude
          a sufficiently sharp upward turn, mechanical assistance may be pro-
          vided at the entry pit to apply an upward bending moment on the
          rod. It is noted that the corresponding radius of curvature is not nec-
          essarily applied to the product pipe, which may only be pulled as far
          as the entry pit. Otherwise, the product pipe bend limitations dis-
          cussed above should be observed.

          Horizontal Distance to Rise to Surface
          Figure 5.16 also illustrates the horizontal distance required for the
          head of the drill string to reach the surface from its present bore path.
          The minimum distance to reach the surface from a point on a level
          trajectory (e.g., point 3) corresponds to that of steering upward at the
          minimum radius of curvature, and is given by:

                                    ½
                  (S )   = {2 d  (R )  }  {1 – d /[2(R )  ]}½
                    3 min   3  rod min    3    rod min
                         ≈ {2 d  (R )  } ½                      (5.8)
                             3  rod min
          where (S )   = distance to rise on arc from level trajectory, ft
                 3 min
                   d  = depth at point of level trajectory, ft
                    3
             This distance, S , is shorter than the distance, S , corresponding to
                          3                         5
          rising partially on an arc and then (e.g., point 4) continuing boring at
          a straight path at an upward angle to the surface:
              (S )   = (R )  Sin α+ {d  – (R )   (1 – Cos α)}/Tan α
                5 min  rod min     3    rod min
                     ≈ (R )  α+ {d  – (R )  α /2}/α             (5.9)
                                            2
                        rod min   3   rod min
          where (S )   =  distance to rise on arc from point on level trajectory
                 5 min
                       to specified exit angle, ft
                   α =  bore exit angle, radians or (approximately) percent
                       grade.
             The horizontal rise distances S  and S  from a level trajectory are
                                       3     5
          shown in Fig. 5.18 for a 100 ft radius of curvature and various exit
          angles. The maximum possible exit angle is limited by the depth.
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