Both the rotating wing theory, which views thrust as horizontal lift, and the simplified momentum theory, which explains thrust as a reaction to air accelerated rearwards, require the propeller to operate at an efficient angle of attack of around 4 degrees. So, in this section, we will look more closely at the angle of attack between a rotating propeller blade and the relative airflow. You will learn that propeller angle of attack varies with aircraft forward speed and with changing propeller rotational speed. (See
Figure 8.20).
To begin with, we will consider a single, cross-sectional element of the blade of a fixed-pitch propeller, taken at approximately mid way between hub and tip. (See
Figure 8.20) Note that the cross section of the blade that we are considering is an
aerofoil, and that the blade angle is defined as the angle between the chord line of the blade section and the plane of rotation of the propeller.
A propeller may be considered as a rotating aerofoil or wing where the reduced pressure in front of the blades and increased pressure behind the blades produce the kind of “horizontal lift force” which helps explain the nature of thrust.
We know, of course, that the propeller blade is twisted, but we’ll come back to that later. For the moment, by confining ourselves to the examination of a single element of the blade, we can ignore the twist.
First of all, let us consider a stationary aircraft, just about to start its take-off run, with its propeller rotating at a given RPM. Because the aircraft is stationary the propeller blade is not moving forward and, therefore, there is effectively no helix angle. The rotating blade will meet the air at an angle equal to the blade angle, so that, while the aircraft is stationary, the blade angle is equal to the angle of attack. This would be the situation in Figure 8.20 if the “true airspeed” vector were zero. This initial angle of attack will, invariably, be of a positive value, but less than the stalling angle, and, so, the propeller will generate thrust. After all, if it did not, the aircraft could never begin its take-off roll.
But when the aircraft begins to move forwards through the air, the airflow over the propeller blade takes on two components: one as a result of the blade’s rotation, and the other as a result of the blade’s forward movement through the air. On an aircraft in motion, therefore, a rotating blade describes a helical path through the air as shown in Figure 8.14. The angle of this helical path, called the helix angle, is represented in Figure 8.20.
Figure 8.20, depicts the blade cross section with a triangle of velocities imposed
upon it. Each side of a triangle of velocities is called a “vector”, because the length and direction of the line represents both the magnitude and direction of the velocity component it refers to. The black vector represents the rotational velocity of the propeller around its axis of rotation. The blue vector represents the air mass flowing through the propeller disc, at right angles to the disc, the magnitude of the blue vector being equal to the forward speed of the aircraft (its true airspeed), plus the extra velocity of the induced airflow into the propeller disc
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. The green vector represents the airflow relative to the propeller blade as it cuts through the air, describing a helix as depicted in Figure 8.14.The helix angle for the blade element under consideration is the angle between the rotational plane of the blade and the blade’s resultant path along the helix as the aircraft advances through the air. The blade is shown set at a small positive angle to the relative airflow. This is the angle of attack. You will remember that if the blade element is to generate an effective aerodynamic force, the size of this angle of attack must lie within a particular thrust-producing range (approximately from 1º to 15º), with the most efficient angle of attack being around 4º.
If we consider the case of constant propeller rotational velocity at a given engine RPM (so that the length of the black line is constant), it should be clear that any increase in magnitude of the aircraft’s true airspeed (i.e. an increase in speed, while maintaining direction) will be represented by an increase in length of the blue vector. This will increase the helix angle and decrease the angle of attack of the blade element. Conversely, if the aircraft’s forward speed decreases, the helix angle will decrease and the angle of attack will increase.
Of course, though we are considering constant propeller RPM and, so, an unchanging length for the black propeller rotation vector, in reality, as aircraft forward speed increases, and blade angle of attack decreases, propeller torque will decrease and the rotational velocity of the propeller will increase. All pilots of aircraft powered by fixed-pitch propellers will be familiar with the fact that engine (and, therefore, propeller) RPM increases as the aircraft’s forward speed increases, despite the fact that the throttle setting has not been touched. However, the percentage increase in propeller RPM is small compared to the percentage increase in forward speed so the principle of the variation of blade angle of attack with forward speed, given above, holds good, and, for the purposes of this explanation of thrust, we may ignore the increase in rotational speed.
If, then, the aircraft’s forward speed increased to the point that the helix angle equalled the blade angle of our cross-sectional element, the angle of attack would be zero and the propeller would be unable to develop any thrust.
At the other extreme, if the aircraft were stationary, such that the helix angle were zero, the angle of attack of the rotating propeller will be at a maximum. It is, of course, up to the propeller designer to ensure that the angle of attack does not exceed the stalling angle in this condition, so that sufficient thrust can be generated to start the aircraft moving.
Because the angle of attack of a fixed pitch propeller varies with the aircraft’s forward speed, we see again that there can only be a limited range of aircraft speed within which the propeller can do its job efficiently.
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The extra velocity of the induced airflow will be small: very approximately equal to the velocity of airflow into the propeller disc when the aircraft is stationary. Consequently, at high aircraft speeds, the extra velocity of the induced airflow will be negligible,At any given power setting, the angle of attack of a fixed pitch propeller decreases as aircraft forward speed increases, reducing torque.
At any given power setting, an increase in forward speed will cause the RPM of a fixed- pitch propeller to increase.
Unfortunately, the situation we have just been considering is far from being the whole story.
The angle of attack of a fixed pitch propeller varies not only with the forward speed of the aircraft but also with the propellers rotational speed, by rotational speed, you will recall that we mean the linear velocity of any blade element around the circumference described by its rotation.
Now, for any given element of a propeller blade, at a given distance from the propeller hub, rotational speed varies both with propeller RPM and with aircraft forward speed. Referring to diagram Figure 8.20 let us consider the case of an aircraft flying at constant airspeed but at varying values of propeller RPM. In the diagram, if the forward speed of the aircraft remains constant, the length of the blue line will remain the same. In this condition, we can easily see that any increase in propeller RPM, which will be represented by an increase in length of the black vector, will decrease the helix angle and increase the angle of attack of the blade element. Conversely, if, at constant forward speed, propeller RPM decreases, the helix angle will increase and the angle of attack of the blade element will decrease.
Knowing that the angle of attack of the propeller blade varies both with airspeed and engine RPM, and knowing that the blade operates at its most efficient at one given value of angle of attack only, it is fairly easy to deduce that a fixed-pitch propeller operates at its most efficient at only one given combination of aircraft forward speed and propeller rotational speed. In all other flight conditions, propeller efficiency will be less than optimal.
Having arrived at this conclusion, you will probably already appreciate why advanced propeller-driven aircraft have powerplants which drive a variable pitch propeller at a constant rotational speed which can be determined by the pilot. On aircraft fitted with a variable-pitch, constant speed propeller, the angle of attack of the propeller can be maintained at its optimal value over a wide range of airspeeds and flight conditions. Variable-pitch, constant speed propellers are discussed further, below, and are covered in detail in the Aeroplanes volume of this series.