A simple technique has been devised for gaining insight into the directional performance of a wide range of drilling systems. The software for simulating the directional behavior of drilling tools has reached a high level of technical sophistication. However, this has not rendered the analytical path redundant. The role of the computer is vital to both approaches. In the former, it is the immense number-crunching power, and in the latter, it is an ability to search for an explanation of what the complex mathematical forms actually mean.

The technique employed will be accessible to engineers with a basic understanding of circuit analysis. The lateral borehole propagation response of a wide class of directional drilling is derived as a simple, first-order delay differential equation. The “delayed” part of the expression is determined by the contact points of the bottomhole assembly (BHA) with the borehole. With this insight, a succinct and intuitive method for constructing the transfer-function response of a drilling system’s directional tendency consequent upon the influence of gravity, weight on bit (WOB), and active steering actuator influences will be explored. The analytical approach gives simple algebraic forms for a tool’s dogleg capability and leads to simple graphical techniques for determining if the trajectory will be smooth or spiraled.

The directional capability of passive BHAs to build, drop, or hold is considered first as a springboard to analyze today’s rotary steerable systems (RSS) wherein the strength of the steering actuation overshadows the BHA’s inherent gravity-induced directional tendency. This leads to an understanding of how closing the loop around a directional drilling system will impact the performance of a wider automated steering system.