Is the angle of attack of a rectangular wing influenced by the dihedral ($\Gamma$) of the wing? If e.g. a wing exists with $\Gamma$ = 0$^{o}$ it has angle of attack $\alpha$. If the dihedral is set at $\Gamma$ = 89$^o$ (fictional example, no practical value) I suspect that the effective angle of attack should be:
$$
\alpha_{eff} = F(\Gamma) \cdot \alpha
$$
Such that $\alpha_{eff}$ is close to zero and with $F(\Gamma)$ being a factor dependent on the dihedral angle.
Is there such a relation between angle of attack and dihedral?
Edit:
The answers given did sound logical, but after fiddling around with simple 3D drawings I still can't understand that dihedral has no effect on the angle of attack.
Here's a zero degree dihedral flat plate wing at 0$^{o}$, 20$^{o}$ and 40$^{o}$ angle of attack.
Here's a wing with an 80$^{o}$ dihedral and again 0$^{o}$, 20$^{o}$ and 40$^{o}$ angle of attack.
I understand that the lift vector tilts with the dihedral, but in the last picture I also clearly see that the wing does not have an angle of attack of 40$^{o}$ w.r.t. the free stream. Sure the middle part does (as it is unnaffected by the dihedral) but the left and right part certainly don't. Imagine if the diherdal would be 90$^{o}$ then it would be just a vertical plate tilted back with no angle of attack.
So my question is still: how does the dihedral influence the angle of attack.
Best Answer
The angle of attack will not change. However, the lift vector will change direction. Thus, at $\Gamma=89^\circ$, the wings' lift vectors will be almost at odds with one another, but they will still have the same angle of attack as they did when $\Gamma=0^\circ$. The purpose of the dihedral (as you probably know) is to change the angle of attack when horizontal forces are present when lift is not opposite the effective weight vector. Dihedral prevents spiraling by improving the lift of the lower, up-wind wing relative to the higher, down-wind wing, thereby opposing the roll of the aircraft.