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Pr oject Considerations for Horizontal Dir ectional Drilling   213


            140
                           Rise distance (100 ft. radius of curvature)
            120
           Total horizontal rise distance, S 5 , ft  100  20° (36% grade)
                         5° (9% grade)
                                         10° (18% grade)

             80
                                                      13° (58% grade)
             60
             40

             20

              0                              Rise at constant curvature, S  3
                0       50     100      150     200     250      300
                                      Depth, in.
          FIGURE 5.18  Horizontal rise distances. (Source: Outside Plant Consulting
          Services.)


             For a drill head oriented at an upward grade, the horizontal dis-
          tance to rise to the surface (e.g., from point 4) is

                                S  = d /Tan α
                                 4  4
                                   ≈ d /α                      (5.10)
                                      4
          where S = distance to rise to surface at constant rise angle, ft
                 4
                d = depth, ft
                 4
             The values for the depth  d  and elevation angle  α used in the
                                     4
          above formula may be obtained by information provided by the drill
          head locating system. This formula corresponds to a rise at a constant
          grade angle, and the results are shown in Fig. 5.19.

          5.4.3  Overall Bore Path Layout and Design

          Bore Path (Horizontal) Planar Trajectory
          In plan view, typical bore paths are relatively straight trajectories
          between the entry and exit points, and pass through intermediate
          access points, as required. A degree of route curvature in the hori-
          zontal plane may be accommodated by the steering capability of the
          Mini-HDD system, consistent with the recommended bend radius
          of the drill rods (and product pipe) and steering capability within
          the soil.
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