In the present article, it has been tried to compute hydrodynamic forces and moments in coupled sway, roll, and yaw motions of planing hulls. For this purpose, wedge water entry has been considered in its generalized form with vertical, horizontal, and roll velocities. Using potential theory, new added mass formulas for coupled sway, roll, and yaw motion of planing hulls have been derived. Moreover, by introducing oblique-asymmetric 2D+T model and implementing momentum theory, sway force, roll moment, and yaw moment have been computed. The obtained hydrodynamic forces and moments have been compared against experimental results and previous empirical method. It has been observed that the method is accompanied with large errors and under-prediction, in the cases with zero and negative roll angle, especially at a yaw angle of 15 degrees, which is a related limitation of the method. Better accuracy in prediction of sway force and yawing moment is observed at a trim angle of 6 degrees and roll angles of 10 degrees and 20 degrees, especially for small yaw angles. The main sources of errors are found to be as follows. 1) Flow separation from the wedge apex in negative roll angle at large yaw angles, which results in under-prediction of sway force, rolling moment, and yawing moment 2) Tendency of the flow to move from starboard to port at a trim angle of 6 degrees for the vessel with a deadrise angle of 30 degrees at a negative roll angle and yaw angle of 15 degrees, which cannot be simulated by the current method. 3) Reduction of contribution of hydrostatic pressure at a speed coefficient of 4.0, which is not well modeled by the proposed method and results in under-prediction of rolling moment. 4) Over-prediction of center of pressure at a yaw angle of 10 degrees and 15 degrees, which results in under-prediction of yawing moment. 5) Prediction of nonzero values for chine wetted length at roll angles of 10 degrees and 20 degrees for the yawed vessel at a trim angle of 6 degrees, which results in under-prediction of rolling moment. 6) Over-prediction of starboard wetted length at negative roll angle at a trim angle of 6 degrees.
