[Agemegos]

I have been carefully through the derivation and got a result that is consistent with the result in Wikipedia.

The mass of a tidal bulge is proportional to the area of the bulge (D squared) times its height (h), times the density of the distorted body (P). That comes out to

mass of tidal bulge = P * h/D

The tidal acceleration is GMr/R^3, or since we are ignoring constants

tidal acceleration = MD/R^3

F = ma, so

Tidal braking force = h * M * P / R^3

Torque is force times moment arm, and for a given angular displacement of the tidal bulge the moment arm is proportional to D

torque = h * M * P * D / R^3

The moment of inertia of a sphere is 0.4 * D^2 * m, so ignoring constants

I = D^2 * P

angular acceleration = torque/I

= (h * M) / (R^3 * D)

substituting h = (M * D^4)/(P * R^3) gives

angular deceleration = (M^2 * D^3) / (P * R^6)

E = A times angular acceleration

E = (k * A * D^3 * M^2) / (R^6 * P)

Woot! I love it when a plan comes together! Now there remains to chose the most convenient form for the equation and estimate the constant of proportionality. Given that the Ms and Rs are in different units according to whether we are calculating lunar or solar tides, but the D and P are always the same, the most convenient form might turn out to be

angular deceleration = h^2 * P/D^5

Which gives

E = (k * A * m/D^5) * sum of squares of tide heights.

Now to estimate k.