Luiz,

A craft never overtakes or cuts/pierces through its own bow wave. The bow wave travels along side the craft at exactly the same speed. Same for planing craft, they too never overtake their bow waves.

What happens it something different.

With displacement hulls the stern wave detaches from the hull and moves back this increasing the wave length of the system and allow it to travel faster, remember Froude's law. This means their is a higher water level at the stem then there is at the stern. This creates a pressure difference along the hull which leads to a force pointing to the rear of the craft = drag. This drag needs to be overcome by increasing engine power or sail power. The faster the craft moves the further the stern wave falls behind the hulls, the larger the pressure difference, the larger this wave-making drag. On beach cats this drag component is relatively small compared to other drag components like wetted surface drag and induced drag from the daggerboards and the sails themselves. As such, encountering this situation on a beach cat is hardly noticeable. The large rigs, needed to overcome much larger drag components, have ample power to simply overpower this "theoretical hull speed" limit.

On planing hulls the situation is a little different. The size of the wave system (bow wave, stern wave) is determined by the displacement of the hull. In effect if the displacement of the hull is reduced then so too will be the wave system. This is was planing does, it lifts the hull higher in the water thus reducing the amount of displaced water. In turn the wave system is made significantly smaller and LESS excess power is needed to overpower the "theoretical max hull speed". Of course planing itself requires additional power as well, but it was found that this requires less additional power then overpowering the wave system when in full displacement.

Of course foiling in an extreme case of the planing situation. Partial foiling or bruce foiling is somewhere in between.

Wouter