The goal is to generate more lift with less drag (improved Lift to Drag Ratio, ie. L/D) to increase speed.  The first step is to identify the flow under the board.  Paddling out we typically see a rider on a wave trimming or turning with the spray sheet starting at the stagnation line/spray root and coming off the shoreside rail.  We need to look under the surface to see what is taking place behind the spray root.

The above photo shows a board on a right taken with the Camber Cam mounted at the top of a tall center fin.  The flow wrapping up and around becomes the spray sheet.  The streamers behind and parallel to the spray root illustrate the stagnation line showing the flow moving transversely across both rails.  The flow across the outside rail is the most obvious.  The flow across the inside rail and back up the wave face is less obvious but still very important.

The surfer at this point is basically flying the bottom of a glider wing across the water. On the shore side of the stagnation line the flow up the face the wave is reversed and flows toward the shoreside rail.   On the wave side of the stagnation line the flow moves transversely across the bottom toward the wave side rails due to the momentum of the water flowing up the face of the wave.  However, since the forward velocity of the board is high in relation to the now slowed transverse flow, the flow appears to be mostly parallel to the centerline of the board on the wave side. In addition, since the fluid is accelerated away from high pressure regions under the board, toward low pressure regions near the rails and out from under the board (to near atmospheric pressure), the flow accelerates toward both the wave side and shoreside rails.  Both rails essentially function like the trailing edge of a glider wing.  The Camber Surfboards bottom is designed to slow the motion toward the rails and create higher pressure under the bottom of the board.  

How do we improve performance now that we know the direction of flow?  A flap at the trailing edge of wing is commonly used to slow down the flow and increase pressure under the wing thereby increasing lift.

The exit angle, area and shape of the bottom area adjacent to the rail are more important than the depth of the concave. For example, a board with a one-inch deep concave that has an arc from rail-to-rail will actually have a relatively shallow angle at the rail that may not be very effective.  That is one of the reasons why a Camber Surfboard has a flat center section.

The orientation of the board is constantly changing relative to the wave and, therefore, the direction of water flow over the bottom is also constantly changing.  The inside rail becomes the outside rail, and vice versa, as the surfer changes direction and puts pressure on one rail or the other to turn.  The challenge is to design a bottom configuration that works well over a wide range of flow conditions to achieve the best lift to drag ratio (L/D).