How to find trim condition of a sectional airfoil without knowing the angle of attack? I am using a reflexed airfoil designed for positive pitching moments to achieve a pitching angle matched to the changing of free-stream velocity (Aerodynamically tailored).
I ended up with a pitching moment equation
$$
dM = c*Cm_{a.c} - (C_{l_0}+C_{l_α}*α)*Χ_{a.c}
$$
where $c$ the chord length, $Cm_{a.c}$ the pitching moment coefficient about the aerodynamic center of the airfoil $Cl_0$ the zero lift pitching coefficient, $Cl_a$ the lift coefficient at a certain angle of attack and and $Xa.c$ an offset distance about aerodynamic center.

I want to design a propeller and the data i have is free stream velocity, RPM, and geometry of the blade.
I assume a thin airfoil so the lift coefficient ($(C_{l_0}+C_{l_α}*α)$) is roughly $2π*α$ and $α$ varies with free stream velocity and rotational speed: $α = Δβ - tan^{-1}(V_{inf}/V_r)$ and $Δβ$ the pitch angle.

The idea is to find the ideal angle of attack $α$ that satisfies the pitching moment equilibrium condition $dM = 0$. However, pitching moment coefficient $Cm_{a.c}$ is also unknown.

*Let's say $X_{ac}$ value is given.

So, my question is how this equation can be solved? Can i get any other data from the airfoil's profile that help to find the solution?
Are reflexed airfoils have any characteristics that i should consider in such situation?
If you have access to a model of your airfoil, a moment balance, and a wind tunnel, you may determine $C_{M_{ac}}$ experimentally: the moment the wing experience may be normalized to calculate $C_{M_{ac}}$  

Then solving for alpha is trivial. Otherwise a tool like XFLR5 may be useful to find  $C_{M_{ac}}$ for your airfoil.