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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. enter image description here

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.

george
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  • If your axis of rotation is a hinge, it does make sense. – Koyovis Jul 14 '17 at 07:43
  • 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? – george Jul 14 '17 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. – Koyovis Jul 14 '17 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 = Cd1/2 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 = -dDsin(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 – george Jul 14 '17 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. – Koyovis Jul 14 '17 at 20:43
  • So the equations i ve shown above are incorrect? Because Drag is given from the thrust there which is zero. However, the problem is how to find L which implies Cl which implies α for cruising condition. If i can find this parameter then i can find everything i assume. – george Jul 15 '17 at 14:45
  • You're using definitions for wings. The term lift is for wings, not propellers, they deliver thrust. Drag is for wings, torque for propellers. Most of the aerodynamic data for the profiles can be used, but 1. the propeller rotates which makes the aerodynamics a bit more complicated than those of a wing 2. $C_L$ should be called $C_T$ for thrust 3. It works the other way around: find $\alpha$ from airspeed and local rotational speed, find $C_T$ ($C_L$) for this $\alpha$ from section data, find thrust from integrating over the propeller length. – Koyovis Jul 15 '17 at 15:02
  • Ok let's start from 3. I know airspeed and i know rotational speed. From them i am calculating the resultant velocity Vr. Now i can find the flow angle φ (sinφ = Vinf/Vr). Now, how α can be computed only from airspeed and rotational speed? Also Ct is interdependent with Thrust, how can be calculated if both are unknown.? – george Jul 15 '17 at 15:36

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