EL INTERNATIONAL COUNTRY RISK GUIDE (ICRG 1982)

Though it is beyond the scope of this book, a further relationship between the power and efficiency of propellers, which is interesting to consider, is that, for a given power, both propeller efficiency and thrust increase as the diameter of the propeller increases. This is the reason why man-powered and solar-powered aircraft, which at the end of the 20th Century achieved impressive performances for distance flown, used large diameter propellers which turned slowly, imparting a small acceleration to a relatively large mass of air.

Increasing the propeller’s diameter will also lead to an increase in propeller torque, and so large-diameter propellers would theoretically be effective in absorbing the power produced by high-performance piston engines. Unfortunately, though, there are practical and physical limitations to a propeller’s diameter.

Firstly, a large diameter propeller would make it impossible to achieve ground clearance, unless the aircraft had an impractically long undercarriage.

Secondly, because the rotational velocity of any element of a propeller blade increases with increasing distance from the axis of rotation (the propeller hub), the tips of a propeller blade are moving through the air at a much greater velocity than those parts of the blade nearer to the hub. The tips of a large-diameter propeller could, therefore, approach the speed of sound.

Near, or at, the speed of sound, airflow characteristics associated with compression and shock waves would cause propulsive efficiency losses as well as greatly

increasing propeller noise.

Let’s look a little further into this latter statement.

The rotational speed of a point moving in a circular path is defined as the linear velocity of that point around the path’s circumference.

We can see from Figure 8.18 that the length of the circumference traced out by a point on a propeller blade increases as the distance of that point from the centre of rotation of the propeller increases. When a propeller is rotating at constant RPM, all points along the length of the blade take the same amount of time to make one revolution. Obviously, though, the elements of the propeller blade furthest from the hub have to travel a greater distance in that time. Therefore, the greater the distance of a blade element from the hub, the greater its rotational speed, for any given value of propeller RPM. It can be proven that, at constant angular velocity, (N), measured in revolutions per minute, RPM, the rotational speed of a propeller element, at distance r from the axis of rotation of the propeller, is equal to 2 × π × r × N .

Fig 8.18 The greater the distance of a blade element from the propeller hub, the greater is its rotational speed at any given value of

Rotational Speed = 2 π r N ...(10)

If r is measured in feet, Equation (10) gives the rotational speed in feet per minute. If r is measured in metres, rotational speed will be in metres per minute.

Equation(10) also shows us that, for any element of a propeller blade at distance r from the hub, rotational velocity increases as r increases.

Considering the example of a typical light-aircraft, fixed-pitch propeller of around 6 feet diameter (180 cm), at a typical cruise setting of 2 400 RPM, we can illustrate the type of speed at which propeller tips move. For our example, then, remembering that radius, r, is half the diameter:

Rotational Speed of propeller tips = 2 π r N

= 2 × 3.142 × 3 × 2 400 feet per minute = 45 245 feet per minute

= 514 miles per hour (823 kilometres

per hour)

514 miles per hour is quite a high speed.

Using the same formula, it is easy to see that the tips of an 8 foot diameter propeller rotating at 3 000 RPM would be moving at 857 miles per hour (1 371 kilometres per hour). This latter speed is, of course, supersonic. It is very difficult to extract satisfactory performance from propellers whose tips are rotating supersonically, and difficult, too, to cater for the stresses, vibrations and noise of transonic operations. These, then, are the main factors which limit the speed of propeller-driven aircraft.

THE PROPELLER AS A ROTATING WING.

Up to now, we have considered, principally, the Newtonian, or simplified momentum theory of thrust. But, propeller blades are aerofoils. A propeller blade, then, acts like a rotating wing, and, like a wing, the propeller blade, in its normal operating range, meets the relative airflow at a certain angle of attack.

These wing-like properties of the propeller, especially the fact that it cuts through the air at a certain angle of attack, can of course help to explain how air is accelerated rearwards when the propeller rotates, just as a wing induces a downwash to the air flowing over it (see Figure 8.19). But the propeller blade’s aerofoil cross section also gives us another view on how thrust is produced.

Figure 8.19 The rotating-wing analogy of propeller thrust.

The tips of a propeller blade are the fastest moving parts of

the propeller. If the blade tips approach the speed of sound, propeller efficiency decreases sharply. Tip speed is a major factor in limiting airspeeds of propeller driven aircraft.

Many versions of propeller theory offer the explanation that, because a propeller blade is an aerofoil, when the propeller rotates and cuts through the air, an aerodynamic force is generated by the blade (similar to the lift generated by a wing) as a result of increased pressure behind the blade and reduced pressure ahead of the blade. In the case of the propeller, this aerodynamic force acts forwards in the direction of flight and is called thrust (see Figure 8.19). So, according to this “wing-theory”, the propeller might even be considered as pulling the aircraft through the air. This view is sometimes referred to as the Bernoulli explanation of thrust, after the Swiss scientist Daniel Bernoulli who propounded the constant pressure energy theory.