Just having some fun here when I should be doing other things.

a = toe in distance

b = base of small triangle

c = length of base of fin

X = TE to S distance, or trailing edge of fin to stringer distance.

Y = Distance from S to projection point P

Z = Projection distance from TE to P, either forward, at, or aft of the nose.

TE = Trailing edge of base of fin.

S = Point where perpendicular line intersects stringer and TE.

P = Projection point. Where you want the fins to point to, i.e., in front of, behind, or precisely at the nose.

So you want to know how much toe-in to set your fins depending on where the fins are to project to.

For example: You have fins with a 4" base, you want the fins to project to a point 12" in front of the nose, and the trailing edge of the fin base will be 5" from the stringer. Say the board is 7’ long and the trailing edge of the fin is set 1’ from the tail.

So;

X = 5", Y = 72" + 12"= 84", and Z = (Y2 – X2)1/2 = 83.85"

Since X/Z = a/c, a = cX/Z. So a = 4"x 5"/83.85" = 0.2385 inches of toe-in.

Here’s the thing; the angles are so small that you can just approximate by using the base of the fin in place of b, which is unknown. So X/Y = a/b, or X/Y more or less = a/c, so a = cX/Y. In the same example, 5"x 4"/84"= 0.2381 inches of toe-in.

I just remember it as:

Toe-in = (TE)(Fin base) / Projection distance along stringer