Analytic Solution the Design Problem of a Hyperboloidal Arch Type Trajectory of Equal Curvature for Step-Horizontal Hole Sections

This study investigated the design constraints on the analytical method of solving equations for quickly and accurately solving the system of restricted equations for the design problem of hyperboloidal arch type trajectory of equal curvature for step-horizontal sections.An explicit formulation of the characteristic polynomial was given by taking advantage of the known result of the theory of quasi-analytic solution for three dimensional trajectory design.An implementation strategy for polynomial numerical calculation was given by taking advantage of object-oriented C++ programming techniques.To test the correctness of the analytic solution formulation,a theoretical model was constructed,and the key data of trajectory was calculated using this model,then they solved the system of restricted equations in which the equal curvature was one of the unknowns and above key data were known.The analytic solution method was not only able to discriminate exactly the true solution from pseudo solution,but also giving the true solution the same to known data.An analytic solution formulation for the solution’s existence was given for the trajectory design problem,and could be used for quick calculation.The result showed that the analytic method was a new programmable algorithm for solving the system of restricted equations of trajectory design,which had the advantages of quickness,accuracy,reliability,and usefulness in drilling software development.