There are many surfboard hull shapes; most can be classified into three categories. Each category has conditions which optimize performance.
The first is the Planing Category. Surfboards which are designed to ride on the water surface are planing boards. These are generally flat bottom with or without concaves and channels for added lift. The flat bottom generates hydrodynamic lift with speed. This board works well in smooth conditions, planning on its tail. The flat bottom also performs as a wing, supporting a rider in flight. The flat bottom is not the best for high impact flat landings. The board can abruptly stop and cause injury to the rider.
The second hull category is Displacement. The bottoms are usually round or vee, thus: the board rides lower in the water. At top speed it planes a little slower than a planning hull. It can be more controllable, in chop and free falls, absorbing impact. Where flat bottoms stall in flat landings, this bottom keeps moving. In high winds this hull spills air and generates less lift, penetrating where a flat bottom gets pushed or held back. The following pictures are of Displacement Hulls.
The final hull category is Semi Displacement. The bow is usually rounded, Vee'd or both. The aft half underside is usually flat or slightly concaved. This board displaces water on impact, pushing it aside and around the board. Absorbing impact, it can recover to get back on a plane. It planes on its aft section like a planning hull. It is as fast as a planning hull at top speed and will not stall in chop or in flat landings. The forward underside spills air and and allows wind penetration and wave entry on take off. The flat underside section of the board can still act as a wing in aerial maneuvers. Pictures of Semi-Displacement Hulls follow.
There are also three phases of movement through water, which all vessels pass through. A vessel initially moves through water in the Displacement Phase. It displaces water to move. The bow is in the water and the vessel is supported more by buoyancy than speed. In this phase, speed is restricted, as the vessel generates both a bow and trailing wave. A paddle boarder or a paddling surfer in a sea without waves is restricted in this phase. Without the push of a swell, a paddler's speed is limited. He does not have the power to get his board on a full plane.
The second phase is Transition. This is when the vessel picks up speed and starts to rise. For surfers, it is the initial push of a wave. This is just before taking the drop and gaining the forces of gravity. He moves mostly by the push of the wave. As he picks up speed the bow wave disappears and nose starts to rise.
The last phase is Planing. For a surfer, the nose is off the water and he is riding on the aft section of his board. This is much like a speed boat, only a trailing wake is produced. Speed is not restricted. In smooth and gentle seas a gradual progression through these phase produce a good ride.
When the seas are rough, a vessel can go from the Planing Phase to the Displacement phase by impacting chop or waves. The Transition Phase is skipped. A surfer does this by hitting the wave bottom at high speed. Most surfboards are flat causing an abrupt stop. The surfer is launched through the air. When wave conditions are steep or when a surfboard gets airborne, chances of suddenly entering the Displacement phase increase. In this condition, a Semi-Displacement hull functions better. Impact is cushioned and the rider can remain on his feet. In a sequence from the past, Greg Noll demonstrates how Displacement Hulls work.