We have not yet explained why all propeller blades are twisted from hub to tip in such a way that the blade angle is smaller at the tip than at the hub. Let us see why this is. We will begin by looking at the main points we have learned about propeller efficiency.
1. A fixed-pitch propeller operates at optimal efficiency at one angle of attack only.
2. Considering any given propeller blade element of a fixed-pitch propeller, at constant RPM, the angle of attack of that blade element decreases as aircraft forward speed increases and vice versa.
3. Considering any given blade element of a fixed-pitch propeller, at constant forward speed, the angle of attack of that blade element increases as its rotational speed increases and vice versa. Remember that “rotational speed” refers to the linear speed of a blade element around the circumference described by the rotating element.
At constant aircraft forward speed, the angle of attack
of a fixed-pitch propeller will increase with increasing RPM.
A fixed pitch propeller operates at optimal
efficiency at one combination of aircraft forward speed and propeller rotational speed, only.
The angle of attack of a fixed pitch propeller
changes with changing aircraft speed, and changing engine RPM.
It is Point 3 which helps us to understand why the propeller blade is twisted: the angle of attack of any blade element changes depending on its rotational speed. If a propeller maintains a constant RPM at a constant aircraft forward speed, we might think - though we would be wrong - that the angle of attack of the propeller would be constant. The angle of attack of any single blade element will, indeed, remain constant, but considering all sections of the propeller across the whole length of the propeller blade, the rotational velocity of the individual blade elements increases as their distance from the propeller hub increases. We looked at a simple mathematical proof of this fact, earlier in this chapter.
We have already learned that blade angle of attack increases with propeller rotational speed. Therefore, even at constant propeller RPM, the angle of attack of a blade element of a given blade angle increases with increasing distance from the propeller hub. So, if the pitch angle of a propeller blade were constant along its length, the angle of attack of the different elements of such a blade, at a given propeller RPM, would increase the further the blade elements were located from the hub. Now, propellers work efficiently at one angle of attack only, so if every part of a rotating propeller blade presented a different angle of attack to the relative airflow, the propeller could never be an efficient provider of thrust.
Furthermore, if there were differing angles of attack across the length of the propeller blade, the magnitude of the thrust force would also vary along the blade, imposing considerable bending moments on the propeller.
It is, therefore, in order to maintain optimal propeller efficiency (that is, to maintain the most efficient angle of attack) along the whole length of the propeller blade that the propeller is twisted such that the blade angle is progressively reduced from root to tip (see Figure 8.21).
Propeller Thrust Explained by the Lift Equation.
Looking at the issue of propeller twist from the point of view of the wing-theory (Bernoulli) explanation of thrust gives another, related perspective on why a propeller blade is twisted. The wing-theory treats thrust as horizontal lift. Now, there is a well known equation which relates lift force to angle of attack which you learnt about in Chapter 2:
Figure 8.21 Blade angle reduces from root to tip. In order to
maintain the optimal angle of attack between the blade and the relative airflow, a propeller blade is twisted along its length, decreasing in blade angle from root to tip.
Lift = CL½ρ v² S ...(11)
Similarly, for a propeller producing thrust, in accordance with the wing-theory:
Thrust = CL½ρ v² S ...(12)
Whereρ = air density; v = rotational velocity; S = surface area of propeller blades, and CL = Coefficient of Lift ( Here, Coefficient of Thrust ).
Now, CL is dependent on aerofoil design and angle of attack. Therefore, since the
aerofoil design cannot change, CL is a variable only because the angle of attack can
and does change during the propeller’s operation.
Asρ and S are constants, the only variables in Equation (12) are Thrust, rotational velocity (v) and the angle of attack, as represented by CL.
We have learnt that in order to maintain efficient propeller operation and to prevent undesirable bending forces acting on the propeller blades, thrust should be of a constant value along the whole length of the blade. We also know that, even at constant RPM, the rotational speed, v, increases as the distance from the propeller root increases. So, referring to Equation (12), if we want to keep thrust constant as v is increasing, we must reduce another variable in the equation. But, we have just stated that the only other variable is CL, representing the angle of attack.
Therefore, in order to keep thrust constant along the whole length of the propeller blade, angle of attack must decrease from root to tip, because rotational velocity, v, increases from root to tip.
For all the reasons stated, then, the propeller is twisted such that the blade angle is progressively reduced from root to tip. Obviously, when calculating the mean blade angle, the propeller designer is mindful of the principal operating mode of the aircraft for which the propeller is intended. The value of the mean blade angle is the angle at the ¾ position (measured from root to tip). Fine pitch propellers have small mean blade angles. Coarse pitch propellers have larger mean blade angles.
Fine and Coarse Pitch Propellers.
A glider-tug aircraft needs optimal propeller efficiency at aerotow speeds of, say, between 65 and 80 kts, and for maximum acceleration from standstill to flying speed for the tug-glider combination. So a glider-tug (see Figure 8.22) will have a propeller that achieves its most efficient angle of attack at low forward speeds.
Figure 8.22 A Jodel D140 Glider Tug.
In order that the thrust force remains constant
along the whole length of the propeller blade, the angle of attack of the blade must decrease from root to tip. This is another reason why a propeller blade is twisted.
During take-off, there is considerable propeller slip and loss of efficiency, and, in the early stages, the propeller blades are liable to stall. That is why a glider-tug aircraft, which needs to accelerate the tug aircraft-glider combination to take-off speed as quickly as possible, while countering the extra drag of the glider it is towing, will be fitted with a fine-pitch propeller. However, with its fine-pitch propeller, the glider-tug will operate at less than optimal efficiency in the cruise, on the way, say, to retrieve a sailplane which has landed out, because, at the higher airspeed, its propeller’s angle of attack will be below the optimal value.
A touring aircraft (see Figure 8.23) fitted with a fixed-pitch propeller will, on the other hand, have a coarser pitch propeller than that of the glider-tug so that the angle of attack of the touring aircraft’s propeller is most efficient at the aeroplane’s designed cruising speed.
But at low speeds, especially on take off, the coarse pitch propeller will be less efficient than a fine-pitch propeller. The blades of the coarse pitch propeller will be more likely to stall on the initial take-off roll than those of a fine-pitch propeller, and propeller slip will be more marked.
Put another way, the high drag from the large angle of attack at take off, caused by the combination of coarse pitch and very low, or zero, forward speed, will prevent the engine developing full power during initial take-off. This situation will not be a problem for the touring aircraft operating from most licensed airfields, but may mean that its short-field take-off performance is poor.