In this animation I experimented with moving the pivot point of a turn and watched how it changed the way surfboard fins moved through water (animation at the bottom of the page).
I chose two pivot points. The pivot points (fulcrum points) are a mental concept to help me think about what is happening.
The animation doesn't model the effect of rocker, nor does it take into account rail design and bottom profiles.
In the first half of the video the pivot point is in the centre of the inside fin. If you watch carefully you will notice that neither the outside, nor the inside fin have any appreciable sideways movement throughout the turn.
Using body torque and compression/extension forces we can tranfer our energy to the board. One of the ways to do this is via the fins. But for the fins to add forward energy to the board (drive) they must have a sideways vector.
We can see how this works in the example of a side slip. Generally a side slip occurs where there is almost equal energy/water/whatever being forced off the front and back of the fin.
In a slide slip, as the fin begins to hold we find that the force vector is pointed toward the tail.
When this happens we begin to generate forward motion.
A corollary: if there is no sideways force vector on the fins they are generating little or no drive.
Look at the second half of the video. Here the pivot point is at the centre of the inner rail (an impossible situation in real life because our knee would have to pushing on the nose!)
Watch how the fins move sideways relative to the water surface (the water surface is the plane of the camera).
You can see that both outer and inner fins generate drive in this example.
The drive can come form our body torque or our compression/expansion movements,
Conclusion 1) Usng this short animation we can see how drive from fins varies through the turn, assuming that: a) In the first part of the turn we have our pivot point forward; and b) in the second half of the turn our weight is further back.
Conclusion 2) We can also see how locking in the front rail on quads, tris and twinnies helps harness drive from our body via the fins - even the outer fins.
Conclusion 3) Toe in reduces drive generated from the outside fin regardless of pivot point - but more so when the pivot point is near the tail.
Conclusion 4) This is very relevant to quads that stay reasonably flat during a turn (quads with fins further back tend to go on the rail more). See video at the bottom of the page of a slow motion quad turn.
Conclusion 6) We can begin to see one of the ways that concaves generate drive in different situations
Conclusion 7) It doesn't really matter.... as long as we are in the water.
The videos; Please click the play button twice.
Erratum: The statement: "With the fulcrum point at the back there is no sideways force on the fins" is incorrect because of rake etc. The axis of a fulcrum point at the centre of the base of the fin will not necessarily continue through at the centre of the tip of the rake - it depends on the lengthways angle of the board in the water)
You can see how much of the board is buried and consequently how much of the time the outside fins are in the water. (This board has a 14 mill concave so perhaps it buries more easily)