Boring tool tracking fundamentally based on drill string length, pitch and roll
A boring tool moves having a pitch orientation, a yaw orientation and a roll orientation and is steerable underground using the roll orientation. A maximum drill string curvature is established for steering. The boring tool is advanced over a path segment. An averaged roll characteristic is determined for movement of the boring tool along the path segment. A path segment pitch orientation is established based on at least one measured pitch orientation along the path segment. Using the maximum drill string curvature in combination with the averaged roll characteristic and the path segment pitch orientation, the yaw orientation is determined. The averaged roll characteristic is determined based on a series of incremental roll measurements that are spaced across the path segment. A set of coupled ordinary differential equations is used to characterize movement of the boring tool.
1. In a system for tracking a boring tool which is moved in an underground region using a drill string having a length that extends to the boring tool and said boring tool having an overall orientation that is characterized by a pitch orientation, a yaw orientation and a roll orientation and which is steerable underground in the region using said roll orientation, an apparatus comprising:
a processing arrangement that is configured for determining an averaged roll orientation of the drill string based on a given extension of the drill string starting at a given pitch orientation and for further determining a portion of the given extension that contributes to a change in a horizontal position of the boring tool and thereby influences the yaw orientation of the boring tool based on the given extension, averaged roll orientation and given pitch orientation.
2. The apparatus of claim 1 wherein said processing arrangement is additionally configured for determining another portion of the given extension that contributes to a change in a vertical position of the boring tool and thereby influences the pitch orientation of the boring tool.