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Figure 45: Minimum curvature method.
Imagine a unit vector tangential to a survey point. Its shift in x, y and z would be as shown above. The angle between any two unit vectors can be derived from inverse cosine of the vector dot product of the two vectors. This angle is the angle subtended at the centre of the arc and is assumed to have occurred over the observed change in measured depth. From this the radius can be derived and a simple kite formed in 3D space whose smaller arm length follows vector A then vector B to arrive at position B.
Notice however that the method assumes a constant arc from one station to the next and particularly when using mud motors, this is unlikely to be the case.
CONTENTS
Points to Ponder
Minimum Curvature has become the universally used survey calculation method and, even when not the best, any calculations you do in a spreadsheet will be compared against software that uses the minimum curvature method and your results will not match otherwise. When programming this calculation, be certain to identify a separate calculation for intervals in which the inclination and azimuth are unchanged (straight). Also be careful with the angle units as most spreadsheets assume angle arguments are in radians.
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