Maximum horizontal stress determination from breakout angle

Breakouts are a consequence of stress anisotropy in the plane perpendicular to the wellbore. Hence, knowing the size and orientation of breakouts permits measuring and calculating the direction and magnitudes of stresses that caused such breakouts. This technique is very useful for measuring orientation of horizontal stresses. In addition, if we know the rock properties $UCS$ and $q$, then

$$S_{Hmax} = P_p + \frac{UCS + (1+q)(P_W - P_p) - \sigma_{hmin} \left[ 1 + 2 \cos (\pi - w_{BO}) \right]} {1 - 2 \cos (\pi - w_{BO})}$$ (6.15)