Tiger^2 's diagram is for finding the Static CLR (hull not moving forward). That's a good start to finding the location of your false keel, but your job is not finished yet
The hull's CLR will move forward as the boat starts to develop lift off the hull. The leeward drift of a sailing ship hull (leeway) sets up a positive angle of attack, turning the hull itself into a wing - this is the true reason we can sail upwind, the dynamic lift off the hull that resists the wind's push to leeward, as opposed to the "pinched watermelon seed" explanation you might have seen. The Dynamic CLR will be located forward of the Static CLR. So, centering the keel on the Static CLR may not give you the maneuverability you desire. That is, you may end up with lee helm or excessive weather helm, depending on how far the Dynamic CLR deviates from the Static CLR. As a rule of thumb, the Dyamic CLR of a wing is at about the 1/4 chord position from the leading edge. This rule will apply pretty well to a false keel of plate or of symetrical airfoil section. The movement of the CLR for the hull itself is harder to calculate.
Because of the movement of the CLR, I don't try to precisely calculate the false keel's position. I believe sail testing is the best way, let the boat tell you, rather than you trying to tell the boat
. For my models, I design to make the keel location adjustable, fore and aft. I will test sail with the keel in different positions until I find the sweet spot that gives me the maneuverability I desire.
On my boats, I have an aluminum L screwed to the keel of the boat. I hang the false keel off the L. By drilling several holes in the L fore and aft of the calculated CLR (static) I now have the ability to move the false keel and try different positions. For some of my models, I have to move the false keel forward of the static CLR, for some I have to move it aft
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The reason I have had to move the keel on different models different directions (relative to the Static CLR) is that it is the Interelationship Between CLR and Center of Effort (summation center of lift off the sails) that is critical, not the CLR just by Itself. Depending on your sails (cut, shape, which ones are flying), the CE will shift and may not be in the same place as the real ship. So, just adding a full length false keel may not do the job.
Any method that will let you move the keel to temporary locations while you test sail will work.