Coupled heave and pitch motions of planing hulls at non-zero heel angle

• Asymmetric 2D + T theory is applied for the motion prediction of heeled planing hulls.
• Formulas are presented for the added mass of wedge sections in two directions.
• Formulations of heave and sway force, as well as roll restoring and pitch moments are derived.
• Predicted results are compared against available experimental data in six steps.
• Sway force and yaw moment acting on the heeled warped planing boats are determined.

Current paper presents a mathematical model based on 2D-asymmetric wedge water entry to model heave and pitch motions of planing hulls at non-zero heel angles. Vertical and horizontal forces as well as heeling moment due to asymmetric water entry are computed using momentum theory in conjunction with added mass of impact velocity in vertical and horizontal directions. The proposed model is able to compute sway and yaw forces, roll moment, as well as heave and pitch motions in calm water and regular waves. Validity of the proposed model is verified by comparing the results against existing experimental data in both symmetric and asymmetric conditions. Ultimately, different parametric studies are conducted to examine the effects of non-zero heel angle on dynamic vertical motions. The resulting sway and yaw forces due to asymmetric motion are also derived and effects of heel angle on these side forces are investigated.