Chapter 21 The propeller as an application of the aerofoil
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It seems to me that the propeller depends on the successful use of aerofoils. I want to look at it carefully to see how it really works as distinct from how it is thought to work.
The propeller, or airscrew, could not have fewer components yet, when it is made to sensible engineering standards, it turns out to be extraordinarily versatile and quite efficient.
It would be very pleasing if one could just give an analysis of the airscrew or propeller and, at the end of it, say what its shape should be. I think that this is not possible because we have too few boundaries to permit us to influence the flow. We are forced into making a propeller to a shape that is determined by some concept of how the propeller works and making it turn using an engine or motor and letting the flow pattern through and around the airscrew take care of itself. There are many different shapes.
It makes sense to start by looking at propellers that are known to work acceptably and then to use our knowledge of mechanics to gain an insight to their mode of operation and perhaps justify their shapes and behaviour. Figures 21-1a and 1b are two photographs of a model propeller to show its shape. Clearly the blades are twisted and the twist changes much more with radius at the root than it does at the tip. In figure 21-1b the manufacturers name is on the leading faces of the blades and these faces are curved. The other faces have a profile that appears to be like that of a "flat-bottomed" aerofoil. Each blade is a small wing with a pronounced twist that must, in some way, be determined by geometry.
There is no question that such a propeller when it is stationary on, say, a model aeroplane that is anchored to a stake, produces a very considerable thrust and a fast moving stream of air behind it that appears to move without rotation. That same propeller running at the same speed will take the aeroplane through all sorts of aerobatic manœuvres at speeds of about 80 km/h. So the same propeller appears to be able to produce a thrust when there is no relative velocity between the natural air and the propeller and also when the air seemingly approaches at 80 km/h. I think that we can take it that a propeller can be matched to an aeroplane and accept that big aeroplanes require big propellers or even more than one propeller in order to give satisfactory performance. Nevertheless all propellers seem to share the same basic shape although one must expect refinements. The very fact that about half of the propellers in use have blades that can be adjusted by rotating them about a radial axis tells us that a propeller of fixed shape is not wholly satisfactory.
So this simple device is not so simple when it comes to analysis and just deciding how to analyse it is not at all obvious. The only analysis that I have seen treats the propeller as a device that behaves like a short convergence with one-dimensional flow. A moment's thought will show that, whilst this might be true for a stationary propeller, the flow through a propeller in flight is anything but one-dimensional so I regard the analysis as being of very limited application. I shall have to propose an explanation of how a propeller works and try to find out whether it all fits together by putting numbers to realistic devices so that I can check the magnitudes as I go along. I shall do that for a propeller that might be used on a light aeroplane.
I have already observed that a rotating propeller can produce a thrust when it is stationary relative to the natural air and also when moving through the natural air. I think that this involves two quite different modes of operation. The key observation for the stationary propeller is that it appears to produce a fast, steady flow of air as a result of a pair of twisted blades that are really wings rotating at high speed when the blades occupy a very small fraction of the area swept by the blades. For the model propeller the fraction is about 0.1 including the relatively large hub. For a propeller fitted to a light aeroplane the figure would be lower. It is a matter of some importance to decide how this stream of air is created by two blades of such small area. However I must leave that and deal with the much more simple problem of the propeller in flight.
If the blades occupy so little of the area swept by the blades what happens when the propeller is in flight? I think that we need to look at some realistic figures in order to get a better idea of the mechanical device that we are trying to understand.
An aeroplane in flight has some speed relative to the air that I shall call the airspeed. If the engine of the aeroplane, and therefore the propeller, is turning at a steady speed it is a simple matter of division to find out how far the aeroplane moves in one revolution of the propeller. There are no simplifications involved just a statement of fact. We can explore this simple relationship for realistic ranges of airspeed and engine speed. Light aeroplanes have cruising speeds in the range of say 75 to 150 knots. Engines for light aeroplanes rotate at speeds from about 700 rpm when idling to about 4,000 rpm. It is instructive the see how the advance per evolution varies for different combinations of airspeed and engine speed.
If the airspeed is knots and the engine speed rev/min, the advance per revolution is given by:-
advance per revolution metres.
This can be plotted for several airspeeds. It is figure 21-2.
I have chosen a range of airspeed that covers most light aeroplanes with the lowest speed being too low. Now, when a light aeroplane is flying at its cruising speed, the engine speed will be about 3,000 rpm and, for a cruising speed of 125 knots the advance per revolution would be about 1.3 metres. This is much greater than one might first expect.
We need to think about the implications of this. The first thing that we need to recognise is that the blade of a propeller is a twisted wing with an aerofoil section that actually works in an ordinary aerodynamic way just like any other wing to produce lift. Typically the chord of the blade, at most, is about 150 mm so it is not very big.
If it is to work in an ordinary aerodynamic way it must operate in a flow of air that is not affected by any other solid boundary that is always in the vicinity. In the case of a propeller the only other solid boundary is that of the other blade or blades. NACA when they set up their programme of testing of aerofoils accepted that models of 20 inch chord in a tunnel of 7.5 feet in height would give data that was unaffected by the presence of the walls of the tunnel. This gives a ratio between the chord length and the distance to the nearest wall of 0.44. In our propeller we have an aerofoil of about 0.15 metres and to match the NACA conditions it would need to be at least 0.35 metres from either the nearest solid boundary or any other disturbance. A blade advances into undisturbed air but behind it there is the wake from the other blade. This is the only factor that might affect the aerofoil action.
We need to know what space a propeller blade has to work in. It is not just the distance to the nearest blade
It is inevitable that the path through space of any point on a propeller blade as it rotates at constant speed and moves forward at constant speed will be a helix. Figure 21-3 from Wikipedia shows trails of water vapour coming off the tips of the blades of a six-bladed propeller in flight. These trails show that the pressure at the tips of the blades has dropped below the dew point probably in locally rotating flow. The trails, even for this six-bladed propeller, are a long way apart axially. I think that we can say that they are far enough apart for the blades over their whole lengths to be producing wakes that are effectively isolated one from another. It follows that there is a wake coming off each blade from root to tip.
We have been considering a propeller with two blades and we can draw the side view of the helical paths of, say, the two tips and the helical paths of the mid-radii of the blades. These helical paths will also be the shapes of the wakes left by the propeller. They will all be sine waves. I have done this in figure 21-3 where both axes are in metres and have the same scale. The advance per revolution is 1 metre which is a typical figure as we have seen. The red and blue lines are for the two blades. Any small element of a blade at some radius will be a distance of from its counterpart so these do not interact.
The wakes that the propeller will leave behind are the red and blue lines and in figure 21-4. I have added an element of one blade at its tip and shown the distance between the element and the wake from the other tip. This shows that the distance between the aerofoil and the wake is about 0.5 metres so the aerofoil section is working in conditions that are at least as good as the NACA conditions.
We can proceed on the basis that the blades are working in undisturbed air except of course for natural disturbance.
Real propellers vary in size from the small ones used on military drones and models to the large ones used on heavy transports. The numbers of blades may be from 2 to 6 and airspeeds could go as high as 400 knots. In this text I cannot cope with this range and I will limit my range to that for light aeroplanes.
I want to deal with the propeller by imagining it to be made up of many sections each of some small radial width . Such a section will look like an aerofoil section cut out in card. We could imagine the blade as made up of many of these sections and that, despite the twist, we can use the ordinary expressions for lift and drag and suitable values for coefficients to find the lift and drag on these small elements. We can then integrate to find the characteristics of the propeller.
Suppose that a propeller on a light aeroplane is turning at 2,500 rpm and that the aeroplane has an airspeed of 150 knots. The propeller will have a diameter of about 2 metres or less but, as any analysis will take radius as the independent variable, this is not a constraint. I want to start by studying the flow over a typical section of the blade at a radius of 0.75 metres.
Regardless of the shape of the blade at this radius it has a tangential velocity relative to the hub of :-
= . The air will approach the propeller at 150 knots and be effectively uniform. Then its speed, , is :-
Given these two velocities we can draw a velocity triangle to find the speed and direction of the air relative to the blade at this radius. This gives a speed for of 210 m/s at an angle of 21.5º to the plane of rotation as shown in figure 21-5.
Suppose now that there is a short section of the blade at this radius of 0.75 metres and that it has a section such as the Clark Y and that it is working in conjunction with all the rest of the blade and the second blade to generate a thrust. If this small section is to generate its share of the thrust it must make an angle of attack with the air flowing over it. There is absolutely nothing in this system that ensures that this is the case but I have stated that the aeroplane is flying at 150 knots and so the propeller/engine combination must, in some way, be adequately matched to the aeroplane so that the propeller/air combination have come to some steady state where there is an angle of attack.
The Clark Y aerofoil is shown in figure 21-6a although the underside of the section is flat only from 30% of the chord. Figure 21-6b gives the data and its graph shows that it has the same slope as other sections and the graph goes through zero at minus 4º. It stalls at about 12º. The blade has a high aspect ratio and it would not be unreasonable to expect the angle of attack when used in this propeller to be in the region of 4º with a lift coefficient of about 0.8. I can draw the section on the velocity diagram of figure 21-5 to give figure 21-7.
It would be fair to suppose that the flow across the section of blade at 0.75 metres is two-dimensional. If we could see the flow pattern it would be just like any other flow pattern in a wind tunnel with a region of high pressure forming on the underside of the section and acting upstream to divert the flow upwards as it approaches and for some of this flow to go over the section and speed up and the rest to go under the section and slow down with the dividing line being the stagnation line. As this flow under the blade moves towards the trailing edge it speeds up again to leave along the under side having been diverted downwards by the aerofoil. This diversion is inevitable because the force exerted on the flowing air must increase its momentum somehow and that increase must be across the flow. It appears as a change in speed and direction. It follows that the flow relative to the blade in the vicinity of the aerofoil has been diverted by a few degrees as it leaves the blade
Figure 21-8 shows a part of the flow pattern for the aerofoil section of the blade at 0.75 metres radius. It shows the absolute direction of the blade as right to left relative to the aeroplane and the velocity of the air relative to the blade as . The flow pattern shows that there is the usual region of high pressure under the section and low pressure over the section. These two combine to produce a force that acts on the blade. This force cannot exist without a reaction on the air and that reaction resists the torque and produces a thrust to contribute to that required to drive the aeroplane. The air must gain momentum in both the axial and tangential directions. My diagram shows how the stagnation line has been diverted by just a few degrees. (In this diagram the diversion is about 8.5º). The air leaves along the stagnation line at a speed that is higher than but we do not know its speed.
Now there is no reason why we should not consider similar elements of the blade at other radii. I argued for the flow pattern over the element at 0.75 metres radius to alter until its steady pattern gave an angle of attack. Presumably we would want all the elements making up the blade of a propeller rotating at 2,500 rpm and moving forwards at 150 knots to settle down to divert the flow by, or to, something like, 8º. For this to be the case the blade must be twisted so that it is aligned with the appropriate at every radius. If we suppose this to be the case then velocity diagrams can be drawn for radii of say, 0.25 m, 0.5 m, 0.75 m, 1.0 m and 1.25m. We can then see how the diagrams change with radius. In figure 21-9 I have drawn these diagrams in perspective in order to separate them. I have labelled the vectors in the diagram for the 0.75 m radius. We see that the blade must twist more rapidly with increasing radius at the root than towards the tip just as it does on the model propeller in figure 21-1.
The velocity of the air relative to the blade, , increases very nearly linearly with radius towards the tip. This seems to be quite innocuous but keeping in mind that the forces on the blade are dependent on the square of the relative velocity we must expect to find that it is the outer part of the blade that produces most of the thrust and absorbs most of the power.
It must be possible to explore these characteristics for this propeller that I have been using as an example.
Suppose that we have a propeller of radius 1.25 m (I have added the 0.25 m to include the propeller that was used before.) having a suitable twist in each blade. Now suppose that the propeller rotates at 2,500 rpm as before and that when the propeller is advancing at 150 knots the coefficient of lift is 0.8 (All these parameters can be changed at will in the mathematical modelling.) Now let me divide the propeller into elements each of length. We can consider one element at radius . From the triangle of velocities in figure 21-4 we can find the velocity of the air relative to the blade from:-
If we put and where is the speed of rotation in rpm we can substitute to give:- and this can be plotted and is given in figure 21-10 together with the Mathcad program. It is showing that the speed relative to the blade is tending towards the tangential speed which is apparent from figure 21-9.
Now what we really need to find out is the thrust produced by the propeller and the efficiency of the propeller. All we have is aerofoil data in the form of expressions for lift and drag in terms of coefficients of lift and drag. We can apply these expressions to the elements of the blade of radial thickness .
We know that in the usual notation. In this case where is the width of the blade and I have ascribed a value to . We already have an expression for .
We have a similar expression for drag but we have no idea of the magnitude of . In chapter 19 I plotted several graphs giving ratios of and the lowest value was about 25. But these figures were for roughened, well-made test models of 2 feet chord. This propeller has a chord of only about 5 inches. I will use a ratio of 12 that can be changed at will because this figure is probably the worst case. So where is the ratio .
Now I have to make use of this information.
To this end I have drawn figure 21-11. The lift generated by the blade element will be at right angles to and the drag will be in line with . These two can be added vectorially to give the total force on the blade element. The forward component of this force is the thrust produced by the element and the component in line with is the force acting through the blade to resist the torque produced by the engine. These two components can be calculated and used in suitable expressions to give thrust and efficiency. This is facilitated by the presence in the diagram of several similar triangles in the proportions of the vector triangle in figure 21-5.
The thrust is clearly equal to the forward component of the lift less the forward component of the drag. The forward component of the lift is given by and the forward component of the drag is given by so thrust can be calculated. Similarly the tangential component of lift is given and the tangential component of the drag by .
If, say, we let the blade have uniform width of 0.12 metre we can find out how the thrust generated by an element of one millimetre in radial width varies with radius.
I have plotted the variation in thrust on such an element with the radius at which the element operates in figure 21-12.
If we know the thrust produced by any element we can integrate from the centre to any radius to get the thrust produced out to that radius. Then we only have to multiply the thrust produced out to the tips by the forward speed to get a figure for the power produced by the propeller to drive the aeroplane.
Similarly, if we know the drag acting tangentially on any element we can multiply by the tangential speed to get the power required to drive a propeller of any radius.
I have plotted the two powers in figure 21-13. The order of the power produced by a propeller of one metre diameter is about 150 kilowatts and 250 kilowatts at 1.25 m diameter. Typically a 4.5 litre petrol engine will produce about 160 kilowatts so these figures are realistic although not to be used without consideration of all the decisions taken in producing this graph.
Then the ratio of these two powers is the efficiency of the propeller. This is given in figure 21-14.
The orders of magnitude of this efficiency seems to me to be realistic but it will be dependent on the value chosen for .
We can see immediately that the increasing slope of the thrust versus diameter curve means that the power absorbed by the propeller increases non-linearly with diameter. Presumably one would look to match a propeller to an aeroplane and an engine. The aeroplane will have a best cruising speed, that is a speed at which it is most economical, and the engine will also have a combination of speed and power at which it is most economical. Now we need a propeller that matches these two and absorbs the right power at the right speed of rotation and at the right forward speed. This is a tall order and not to be met by calculation I think. It will involve trial if the propeller is rigid. If the propeller can be adjusted the problem becomes much easier to deal with.
We now have a mathematical model for a propeller based on various initial decisions. If one keeps those decisions in mind the input parameters can be changed as required in order to explore the behaviour of a propeller. The most important decisions were to presume a shape for the propeller that, with uniform approach flow, would give the same angle of attack at every section. We are now in a much better position to consider these decisions.
There must be a best shape for a propeller but finding that shape by analysis is unlikely ever to be possible because of the difficulty of investigating the flow pattern. However we can make some progress.
The shape of a propeller is produced partly by the typical twist of the blades and partly by the outline of the blades which normally taper towards the tips. I have given a drawing of a three bladed propeller that shows both the twist and the outline of the blades in figure 21-15. Figures 21-1a and 1b show a model propeller and I have to explain both the twist and the outline.
Most people visualise the propeller as screwing its way through the air. As I have explained this is an apt way to look at the propeller when it is in flight. It leads us directly to the helix as I have said above. We need to get to grips with this idea of a helix because it is very widely used.
In figure 21-16 I show a visual model of a helix. It is just a piece of paper stuck to a light wooden disc to act as a circular former. On both sides of the paper I have drawn an enlarged version of figure 21-5 and called it fig 21-17. The lines on the two sides coincide. I have added two blade profiles at an appropriate angle of attack. The paper was trimmed so that it is possible to see inside and then stuck to the disc. What was a straight oblique line is now a helix that advances in one revolution by a distance that I have shown as the pitch. The line has become the path of a point moving on a circle that is moving at right angles to its plane of rotation and it is shown on the paper model. Clearly there is a direct connection between the helix and the design of a propeller. What has been shown as an angle of 21.5º is in fact the helix angle.
In my model, the line is the path of the section of the propeller and, as the section makes an angle of attack to that line, the section will lift as I have explained earlier in this chapter. It seems that a good angle for the blade at this radius is the helix angle plus the angle of attack.
Before this idea came to be recognised propeller blades were made to have the appropriate helix angle at every radius and such propellers worked quite well but, of course, even under the best conditions, the propeller could not follow the helix on which it was designed for the want of a built-in angle of attack. The propeller was said to slip and this was blamed on the perfidy of fluids. When blades began to be made with a built-in angle of attack they were called non-helical pitch propellers and the slip was much reduced.
However there is a grey area in this business of deciding on how to define an angle of attack. It is simple enough to define if you are charged with gathering experimental data on aerofoils but an engineer can often have a propeller and want to measure the blade angles to try to decide whether it would suit some application. Most propellers have sections that for most of the underside are flat and so the obvious thing to do is to set the propeller up and simply measure the angle between this flat part of the section and the plane of rotation at various radii. This angle is made up of the helix angle and whatever angle of attack has been built into the design. Unfortunately the reference line for defining the angle of attack is at the whim of the experimenter. In figure 21-6a I showed the reference line as passing through the trailing edge and the centre of the nose radius. This is the NACA way of defining a reference line. It inevitably leads to having positive coefficients of lift at negative angles of attack. Yet for the Clark Y section, that is so commonly used, it is clearly much more convenient to use the tangent to the flat portion of the bottom which would give an alternative, more practical line. The angle between these two possible reference lines is 2.25º. So, even if you have measured the angle of the blade at some radius it is very difficult to decide how this angle is shared between the helix angle and the angle of attack. I have laid out the problem in figure 21-18 and, in order to get over the difficulty, it is usual to measure the angle at 75% of the radius and regard this as a helix angle and deduce the pitch from it. It is clearly not very satisfactory but at least it is easily understood.
The analysis that was developed from figure 21-5 depended wholly on the vector triangle between , and . The angle between and came out to be 21.5º and we now see that it is also the helix angle. However the vector was the same for all radii and so the triangles will change in shape from root to tip as we have seen in figure 21-9. We can compute to see how the helix angle changes with radius for different pitches.
In order to do so we need to establish a suitable range for the pitch. I have been using the light aeroplane as an example and I will continue with that. However the rotational speeds of piston engines for aircraft are usually like those for the larger car engines that normally run up to about 3,000 rpm. The advance per revolution for the aeroplane in flight is a guide to pitch. If we take the top speed of the engine to be 3,000 rpm we can get an idea of pitch from the advance per revolution. It is, as we have seen, only the distance travelled per minute divided by the engine speed so it can be derived from the airspeed in knots and the engine speed.
I have plotted the graph of advance per revolution of the engine against airspeed in knots for three typical engine speeds in figure 21-19. For our light aeroplane the advance per revolution ranges from about 1.5 metres to about 2.3 metres.
So, if we plot helix angles for pitches between 1 metre and 2.5 metres we shall have a good idea of the way in which the blades must twist regardless of their actual design.
For any propeller regardless of its design there will be a different helix angle for every radius and we can plot the helix angle against radius for a range of pitches for helices up to say a maximum of 1.5 metres which would be about the maximum length for the blades of a propeller for a very large engine, for example 30 litres. We need some idea of a typical pitch. I have said that we might expect a light aeroplane to make 150 knots with an engine speed of say 2,500 rpm. Then the advance per revolution is given by . The pitch of a suitable propeller will be greater than this. I need to bracket this dimension so I have used pitches of 1 m, 1.5 m, 2 m and 2.5 m in figures 21-17a and 17b. Propellers with large pitches are said to have coarse pitch and propellers with a small pitch are said to have fine pitch.
In figures 21-20a and 20b I have shown how the blade angles vary with radius for a propeller, in 20a, with helical pitch and for a propeller with non-helical pitch in 20b. The graphs are drawn for propellers of different pitches.
They do not look to be very different.
Graphs are alright but sometimes it is better to draw angles properly so that, in this case. we can see the twist. I have done this in figures 21-21a and 21b for a helical propeller and a non-helical propeller. I have allowed a nominal angle of attack of 5º and close inspection is needed to see the difference between the two diagrams.
In figure 21-13 the plot of power generated by the propeller against radius shows that the power from the middle out to, say, a radius of 0.4 metres of a propeller of 2 metres diameter is a small fraction (3%) of the power from the whole propeller. In addition careful study of figure 21-1 shows that this inner portion is used to blend the blade into the hub and this is the case for all propellers. So the working part of the blade extends from about 0.4 times the radius out to the tip. I have blocked in the blade angles for this portion in red in both cases and you can see that the twist, as distinct from the blade angle, is very small when compared with the maximum of 90 º.
Suppose that we had two propellers made to these two different twists and we chose to measure the angles at 0.1 metre intervals to decide on the pitches. If it was thought that they were both designed with helical pitches the non-helical pitch propeller would appear to have a helical pitch between about 2.4 metres and 2.6 metres. Otherwise it might be thought that it was a helical propeller of 2.5 metres pitch rather than a non-helical propeller of 1.85 metres pitch. It is all very troublesome. This all means that designing propellers is rather more a matter of cut and try than numerical design and the sheer difficulty of simulating a propeller in flight just adds to the problem. No doubt manufacturers will have gathered experience on this matter over more than a century now.
I suppose that a typical shape for a propeller blade is given in figure 21-15. The dominant feature is that the blade tapers outwards from the root and then tapers in again towards the tip.
We can account for this shape partly from the need for strength in the root to resist the forces imposed on the blade and partly from the need to recognise the effect of the shape on the flow.
The blade has to withstand a radial stress stemming from the rotation, a bending stress produced by the generally forward, aerodynamic force on the blades and no doubt a twisting force that is probably small compared to the other two. Effectively the first 40% of the radius is given over to coping with these forces and the outer 60% designed to produce the desired thrust.
We have seen in chapter 19 on the aerofoil in figures 19-30 and 31 that a straight wing produces two counter-rotating vortices with their centres somewhere near to the tips of the wings. This flow pattern is the consequence of the pressure difference between the upper and lower surfaces of the wings. The direct consequence is that the flow over the two surfaces is skewed towards the root on the top and towards the tip on the bottom. This skewing becomes less as the aspect ratio increases. The propeller blade has an aspect ratio of perhaps 15 so the effects of vortices is small. Nevertheless there is an effect at the tips where there is nothing to impede the flow from under the blade towards the top and figure 21-3 suggests that vortices do form.
So we have a blade that is really a twisted wing with the free end going very fast indeed when compared with say the 40% radius. Some sort of rotation in the wake from the blades is inevitable and leaving the tips square will exacerbate the problem and designers reduce the blade as much as possible at the tips consistent with the need to keep the chord as large as possible to avoid a drop in the efficiency of the blade as the chord length is reduced. A compromise has to be made.
We have seen that the flow through a propeller in flight is relatively simple. It seems that the propeller in flight just "screws" its way through stationary air leaving wakes in the air from both blades and that, in fact, the fuselage and the flying surfaces disturb the air far more than the propeller. However almost all propellers must start turning when the aeroplane has no forward speed. I observed that a stationary engine produces a stream of air and there is a considerable static thrust. So, in some way, the slender blades of the stationary propeller can produce a stream of air and not just isolated wakes. This is a new flow pattern.
I need to go back to the propeller in flight. I have noted that a propeller is acted on by a torque and, in exchange produces a forward force, the thrust. It does this by imparting angular momentum to the air to resist the torque and axial momentum to the air to produce the thrust. When the propeller is in flight most of this momentum is in the two wakes coming off the blades and the main body of air is not affected by the propeller. Inevitably these wakes and their momentum will be shared out by mixing with the air left behind by the aeroplane. There is also the engine nacelle and the wing to intensify the mixing.
Now we are considering a propeller that is not moving forwards. We have seen that the blades make an angle to the plane of rotation and inevitably there will be forces the two blades. These forces will also resist the torque and create a thrust but the reactions on the air will make if flow through the propeller disc and rotate. In time the flow through the propeller will become steady with a totally different flow pattern to that of a propeller in flight.
However there is nothing in this simple system that makes certain that the propeller operating with steady flow also operates with angles of attack that are less than the angle at which the Clark Y section stalls or at any special angle at all. Indeed, because the propeller starts from being stationary, it must start by operating at angles of attack beyond the stall. It follows that we must have some idea about how the section behaves beyond the stall.
I found experimental data via aerospaceweb from Sandia National Labs report SAND 80-2114 giving lift and drag coefficients for NACA 0015 for angles of attack from 0º to 180º. (They were interested in vertical axis wind turbines.) The NACA 0015 is shown in figure 21-22. They gave their results in two graphs of in figure 21-23 and of in figure 21-24
We are not interested in the range of angles of attack from 90° to 180° so the data needed to be plotted for the range 0º to 90º and I have done for both graphs in figure 21-25.
We have the graph of and against angle of attack for Clark Y in figure 21-6b that I have bought down as figure 21-26
It is evident that the graph for Clark Y in figure 21-26 corresponds to the curve up to and slightly beyond the stall and that it closely resembles the graph for NACA 0015 for the same range. It is reasonable to expect that Clark Y will exhibit the second peak in the range for which the aerofoil is stalled and the same sort of graph relating to angle of attack. Indeed aerospaceweb tested 7 sections, all symmetrical and they all gave the same result.
We know that the angle of the blades in the most effective region between 40% of the radius and the tip will be less than 30º and, at the instant of starting, the angle of the blade is also the angle of attack. We can see from figure 21-25 that, even though the blade is stalled, the value of will be about 0.9 and that of about 0.6. The blade will start to produce a wake that is more or less helical and, because the blade is stalled, very wide. As the blade continues to rotate the wakes from the two blades will coalesce into one wake that appears as a stream of air flowing from the propeller. If the propeller continues to rotate at steady speed the speed of the air that now flows through it will increase and the angle of attack of every element of the blades will be reduced. This decreases the coefficient of lift and decreases the coefficient of drag and it is possible that the flow over the leading faces of the blades becomes attached again. Ultimately a steady state will be reached but we do not know whether this will be reached when the propeller is stalled or operating aerodynamically, that is un-stalled. Whichever it is the wakes from the blades must be close enough to combine to produce the seemingly continuous stream of air of the diameter of the propeller. This is a new mechanism and it operates at uniform pressure throughout the flow with the exception of the pressure in the immediate vicinity of the blades.
The flow pattern for a stationary propeller must be totally different to that for a propeller in flight. I have to attempt to draw the flow pattern. There are some starting points. It is evident that the rotating propeller is inducing a flow through it. It does this by causing the pressure in front of the blades to fall as one would expect for an aerofoil and the air then flows from every direction towards the propeller gathering kinetic energy in exchange for a drop in pressure energy. Once it is through the propeller the air will move as a steady stream. The work done on the air by the propeller is now in the kinetic energy of the stream of air partly in the net axial velocity and partly in the mixing flow of the stream of air. That stream of air will move at high speed relative to the air surrounding it and the surrounding air will flow to mix with it.
We have seen flow patterns for air entering intakes before but not for the mixing between a free jet of air and the "stationary" air surrounding it. We shall need both in order to draw this new flow pattern.
We need to look at that mixing process and the photographs in figure 21-27a and in figure 21-27b might help. Figure 21-27a is a photograph is of a jet of air emerging vertically from the centre of a round table that forms a flat horizontal surface. The jet was generated by a vacuum cleaner fan used as a blower. It had some residual rotation. The white is smoke generated by burning fumigation pellets intended for use in greenhouses. There are two on either side of the jet and one near the edge of the table. The two near to the jet show that air is entrained from the slowly moving air over the table and carried upwards into a region in which the two flows mix and the mixing region spreads into the jet that is eventually all mixed flow.
Figure 21-23b shows that the smoke going across the table in a long curve indicating that the rotation of the jet affects the flow upstream to produce a slowly rotating vortex. We can see the region of the jet where there is mixing and stray smoke is following a helical path to show that the jet is rotating
We can have this in mind when constructing a flow pattern for the propeller.
I tried to reason out what the flow pattern would be but, in the end found that I needed to experiment. I set up a model propeller and ran it at as high a speed as allowed me to see smoke trails from a smouldering lamp wick and this led me to the flow pattern in figure 21-28. It always surprises me that the air can be drawn forwards to find its way in at the edge of these flows but otherwise it is typical of all intakes. I cannot be certain that there will be the mixing that I have shown shaded but if there is not then it is hard to see what is to happen at the ends of the equi-potential surfaces. It is essentially the same as the free jet for which I have given photographs. As far as I can see this flow pattern fits together. The shape of the flow lines at the tips is consistent with our knowledge of the vector diagrams. I do not know that this diagram will be unchanged at higher speeds of rotation but propellers do not have sudden changes in their behaviour so, whilst we might expect some change, I do not think that it is likely to be major.
The important thing is not whether this is totally accurate but that it is very different to the flow pattern for a propeller in flight.
When an aeroplane takes off this flow pattern must change and much depends on the actions of the pilot. If he just opens the throttle so that the engine speed goes to maximum immediately, the propeller will be stalled, and produce a low thrust and high resistance to rotation. The aeroplane will have a low acceleration. However if the throttle is opened slowly the propeller will continue to operate, probably stalled but only just beyond the point of stalling and produce more thrust and less resistance to rotation. With some practice one can find the best way to take off in the minimum distance.
As the flow pattern changes with airspeed the wakes separate and the mixing between wakes lessens until the propeller operates normally. It is an interesting transition.
However there are applications of the propeller where the forward speed is low Hovercraft move at much lower speeds than light aeroplanes. Then the flow pattern must be intermediate between that for flight and that for a stationary propeller.
The rotor of a helicopter is really a propeller that changes its blade angle cyclically as it rotates. The rotor moves in its plane of rotation so the flow pattern will be very complex.
The problems of the fixed pitch propeller can be overcome by using propellers of variable pitch. Given that the centre 40% of the diameter makes so little contribution to the thrust there is plenty of space to fit a hub so that the blades are free to rotate about their radial axes and to fit a spinner to cover the hub and any operating mechanism. We have seen that for the working part of the blades the twist is small and this lends itself to this simple method of changing pitch. The engine/propeller combination can then have a management system that matches the pitch to the engine speed and the airspeed.
It is important to realise that all that I have said is only for a propeller without any other solid boundaries. It would be the flow pattern for the propeller of a swamp buggy with a mesh guard but not one fitted with a ring or any other ducting. It would be the flow pattern of a helicopter rotor when it is hovering well clear of the ground but not for the rotor near to the ground or in forward motion.
I cannot leave the propeller without giving some thought to ground effect. All this chapter has been about propellers in which air flows without obstruction through the propeller disc and the propeller is the only solid boundary. However propellers are used where there is another solid boundary, the ground. The fact that the propeller in near to the ground will ensure that the wakes from the blades will coalesce to form a stream of air that flows downwards from the propeller.
Again I tried to construct a flow pattern but decided that it was too complicated to predict and to find out what happen by experiment. I set up a propeller in the middle of a flat square board. It is shown in figure 21-29. the speed could be controlled up to about 4,000 rpm.
I fully expected the flow to be in two parts. I expected an inner core that might extend to about 40% of the maximum radius in which the air flowed downwards through the propeller and inwards as it approached the board. I expected an outer annulus that flowed downwards through the propeller and then outwards. Beyond this I could offer no detail. I searched the flow with a wand made up of a piece of aluminium tubing of one millimetre outer diameter with a piece of cotton in its end.
It was easy to find the radius at which the split between the two flows occurred and the radius increased with speed to a maximum of about 40% of the maximum radius. The flow from the outer part of the propeller appeared to be smooth and steady.
The flow in the core was inevitably more complicated. After all the flow may start off by flowing inwards but it must then go upwards in some way. I made little progress except to determine that the flow rotated and became very confused.
In figures 21-30a, b and c I used a wand with two short lengths of cotton separated by about 10 mm. In 21-30a both cottons are pointing outwards. In 21-30b one is pointing outwards but the other is pointing inwards and indicating rotating flow. The split is between these two cottons. In 21-30c both are pointing inwards and indicating rotation.
The pattern appears to be repeatable but it does vary with the distance between the propeller and the board. Other than the fact that the flow splits I think the message is that there is more to be found out about this flow pattern. There is a split so that some of the flow goes outwards and some inwards. Momentum tells us that at the split equal and opposite forces must drive the two flows. However if the air flows inwards it must turn upwards towards the hub. I do not know whether it t actually flows "through" the hub
I looked at the approach flow to the propeller and it generally behaves like the approach flow pattern in figure 21-28 but it seems to me as though the air was preparing to flow round an obstruction in the centre of the propeller and above the hub. It is as if there is a torroidal vortex above the hub. It would not be a surprise to find that the flows above and below the non-functional hub of the propeller are separated by the hub.
Other uses of propellers
The development of piston engines produced engines that produced more power than could be absorbed by one propeller. This led to the design of the contra-rotating propeller typified by figure 21-31 of a Rolls Royce propeller. At first sight one might think that the second propeller is working in a stream of air that is hopelessly disturbed by the first with no blades to tidy it up but, as the first propeller is screwing its way along and only producing three quite compact wakes, the second propeller is working in substantially undisturbed air. Such a propeller is complex with a gearbox to make the reversal and this gearbox has to be maintained to aircraft standards. As a result the contra-rotating propeller is not all that common and high power piston engines have given way to much lighter gas turbine engines that, for some applications, use a propeller.
There are several recreational uses of propellers on hovercraft and ultra-light aeroplanes including paramotors. It seems to me that if an ordinary propeller can be used to power a paraglider where the conditions under which it works are totally unsuitable then it can be used for an untold number of other applications where conditions are nothing like as adverse.
The paraglider relies on the use of an inflated parawing for lift as shown top left in fig 21-32. The front view is shown in top right. Lower right shows the pilot sitting in front of the propeller and upstream conditions for the propeller are not at all what aerodynamicists would choose. But it works as a recreational device. Lower left shows the power unit from behind and, in effect most of the area swept by the propeller from 40% of the propeller diameter outwards is not directly obstructed. We have seen that this is the area that does most of the work.
By comparison the propellers on most ultra light aeroplanes work in much better conditions.
When I started to write this chapter I had used propellers on model aeroplanes for many years and had formed a view on how they worked and how they behaved. That view was coloured by the fact that the only opportunity to see a propeller at work close up was when it was on the ground when the flow from the propeller flattened the grass as if it was a much wider wake than the diameter of the propeller. If you then add my acquired knowledge of the mode of operation of rotodynamic water pumps where the wake rotates it was no surprise that I vaguely supposed the propeller in flight to produce a "solid" flow of air that rotated. Yet I had seen vapour trails from the tips of propeller blades in flight at air shows that said otherwise. These two are contradictory.
I have found over a long life in engineering that devices that involve the flow of fluid work best when the flow is smooth and free from swirls and eddies and for that to happen the flow must be guided at all times. The engineer cannot just let the fluid flow as it "wants to". Here we have a very simple device that is just a twisted wing yet it appears to function very successfully without any guidance of the flow into it or away from it. It will work with flow through only a part of its frontal area, the rest being obstructed in some way. It can be shaped on the basis of the helix or on the basis the helix plus an angle of attack and it is hard to find any difference in the way that it performs.
I had to change my mental model of the propeller to one where each blade produces a relatively thin wake that corkscrews away behind the propeller affecting very little of the air flowing through the propeller arc. Similar wakes are produced by wind turbines producing a very objectionable pulsing sound downstream.
In both the model world and the full size world propellers seem to be used in the most outrageous ways especially in recreational applications but generally the propeller proves to be a flexible device. As far as I can see the worst thing that can be done to a propeller is to fit a shroud round it or to try to use it in a pipe. Then the propeller is called upon to produce a rise in pressure as the air flows through its circle of rotation and this it cannot do except at a very, very low efficiency. The propeller becomes excessively noisy and there can be no doubt that the flow breaks down because the centre part of the propeller cannot produce a pressure rise to keep the flow going in one direction as we have seen with ground effect. One must change to using a fan with the centre blocked by a hub and six, eight or ten blades and that is a device that functions in a different way to the propeller.
 I shall use knots for airspeed. It can easily be converted to metres/second by multiplying be 0.515 or a half.
 Piston engines such as those used in light aeroplanes have their maximum efficiency at about 75% of the maximum permitted speed of rotation. (The maximum speed is on no load and it comes when the engine disintegrates.)
 This angle is really an angle of incidence because the angle of attack of the air flowing over it could take any value that is physically possible. Generally angle of attack is loosely used for both cases.
 Some gliders have power pods that are normally retracted for soaring flight. When they are needed the power pod lifts up from the fuselage, the folding propeller opens and spins up to start the engine.
 These pellets are not intended for this purpose. We set them off, hurriedly took a dozen photographs, and closed the lab whilst the extractor fans cleared the poisonous smoke.