How to define pitch angle for a passive variable pitch propeller?

This question is a continuation of the question How to calculate variable pitch propeller parameters? mentioned before.

Actually, the theory described as an answer on the question above is the exact one i am using at the moment. However at the current stage, i want to make the calculations only for a 2D sectional symmetric airfoil, supposing a rectangular-shaped blade and not considering any twist. Also i forgot to mention before that my idea is to attach a rod on the root of the blade, set in an offset of the aerodynamic centre Xa.c (variable) and place a gear on it to connect with the opposite blade and synchronizing it. Also counterweights will be attached on the rod for balancing purposes but this is for later studies.

In this case i have ended up with the following formula for the pitching moments:

dM = dMa.c - dL*Xa.c

As can be seen here dM and dL are correlated there are two unknown there which are the lift coefficient Cl and angle of attack α.

from literature i found that Cl can be expressed as Cl0 + Cla* α and then to 2π*α (from thin airfoil theory), as well as Cm = 0 for symmetric airfoils.

Using these assumptions and moment equilibrium i end up on α=0 which doesn't make sense.

• If your axis of rotation is a hinge, it does make sense. Commented Jul 14, 2017 at 7:43
• But let's say this is for the take off condition where V=0 m/s and RPM = 2000. What about cruising and landing conditions?? Will α still equal to zero? Commented Jul 14, 2017 at 11:20
• At $\alpha$ = zero there is no thrust. You'll need to compute required thrust to overcome aeroplane drag, then compute $\alpha$ required from speed at radius r and $C_L$. If there is no twist, $\alpha$ will be a different value at every r. Commented Jul 14, 2017 at 16:05
• I suppose that when there is no twist, α will be the same along the blade (that's the reason i am using simple rectangular shape for the blade). Also, Thrust is calculated from dT=dLcos(φ)-dDsin⁡(φ) where dD = Cd*1/2 ρV^2 cdr, where dD the drag of the propeller blade and Cd the drag coefficient (unknown). if i use the α=0 (no thrust, dL =0) the dT = -dD*sin(φ) =0 which implies drag =0. I understand that at static thrust condition these parameters will be zero. The question is how to calculate them for the next flight operation Commented Jul 14, 2017 at 17:13
• Thrust is computed from L. Torque to drive the blade is computed from D. Unfortunately, D can never be zero, there is a $C_{D0}$. Only a blade with twist has an $\alpha$ that is continuous along the blade, for airspeeds other than zero. If $\alpha$ = 0 there is no propeller thrust. Commented Jul 14, 2017 at 20:43