THE DESIGN OF WING SECTIONS Published in "Radio Control Model News" Issue Number 8 Winter 93 Aerofoil section design has advanced a great deal since great pioneers like Horatio Phillips experimented with wind tunnels. Phillips invented the double surfaced, cambered wing section in 1884 when most other people at his time had been working with single thicknesses of fabric stretched over light frames. Having found that a pointed leading edge tended to cause flow separation on the under side of his sections, Phillips introduced a carefully shaped bulge on the under side which guided the flow round this critical area. He called this the Phillips Entry. It was patented in 1891. It is astonishing that some model fliers still talk about the Phillips Entry, not realising that they are a full century out of date! Moreover, the original Phillips Entry was quite different from the feature that is usually intended now. It is time the term 'Phillips Entry' made its final exit! One of the important things that has been proved since Phillips' time, is that we cannot treat the airflow over and under a wing as entirely separate. In a flow of air, just like a flow of water, a disturbance in one place spreads its influence out in all directions, upstream, downstream and sideways. Any alteration, anywhere on a wing section, affects the whole. Changing the shape of the underside has some effect on the upper surface flow, and vice versa. An alteration at the trailing edge has some effect at the leading edge and even further forward, ahead of the wing altogether. It is not possible to alter one pan without changing everything else to some extent. The profile has to be taken as a whole. Aerofoil section design is now done by a repetitive mathematical process of iteration. The total variations of air pressure and flow speed around the entire profile are calculated. Each tiny bit of the wing surface is taken in turn, working out how it affects the flown not only over itself but also over the next adjacent segment downstream. From an approximation at the beginning for one small panel, the result is applied to the next panel in sequence and so on, all the way over and around both surfaces until the iteration arrives back at the place it started from. This produces different figures for the first panel from the approximate ones used to start the process. Hence the first panel has to be recalculated and so does the next and the next and the next and so on. The iteration goes all round the profile a second, third, fourth time or more, however many times it takes. When all the answers on the 'nth' time, everywhere round the profile, come out the same as the last time, the iteration stops. Such work would be impossibly lengthy without a computer. For full sized aircraft, the results are very good. For models, although a good deal has been done, the full scale formulae do not apply with very great accuracy. Progress has been made but the final answers to our problems are not yet known. There is still much to be learned about the vital boundary layer, the thin zone in the air flow closest to the skin of the wing, at very low flight speeds with small wings. MODEL SECTIONS While we cannot afford to ignore the modern research, experience remains the most important teacher. This is all the more true when actual wings constructed by modellers are compared with exact section ordinates. Not many of us work to the fine limits required to reproduce a section with mathematical accuracy. If the model has a wavy skin, as when covered with plastic film or fabric over an open frame, or if a foam cored wing is slightly wobbly, or the wing has a badly shaped leading or trailing edge, or if there are blobs of paint or small steps where a paint trim line or a piece of decorative tape has been stuck on, these alter the character of the section. (Not all such variations are necessarily bad. As will be explained, turbulator strips correctly placed can sometimes improve a wing.) It is still fair to say that two fundamental things about wing sections should be understood: camber and thickness. Nothing much can go wrong if we get the camber and thickness right. We shall now look at camber and thickness separately, but bear in mind that any change will change everything else to some extent.
CAMBER In an earlier article (RCM News No. 5, page 6-7) it was explained that a slightly arched or cambered piece of card or thin wood, held in an air stream like a wing, will develop lift if it is held at an appropriate angle of attack. Some diagrams from that article are repeated here (Figure 1). If the angle is too large the wing will stall, if too negative (equivalent to upside down in flight), it will stall in the negative sense. These are the practical limits for normal flying. Somewhere between the positive and negative stalling angles there is an angle of no lift, called the aerodynamic zero. If the section is perfectly symmetrical or un cambered this aerodynamic zero coincides with the geometric zero angle of attack. With a cambered surface, aerodynamic zero appears at a negative geometric angle. Some model airplanes and gliders are flown with wing sections which are virtually cambered surfaces of almost no thickness. For example, the best indoor models have very flimsy wing frames covered with the thinnest possible membranes of microfilm. Radio controlled models require some depth in the wing to provide strength and stiffness for flight in the ordinary, turbulent atmosphere. (There are other reasons why a thickened section is often preferable to the thin sheet wing, but discussion of this will be left on one side for the present.) The model flier may think of any aerofoil section as an arched or cambered line buried within the thickness. It may be imagined as the skeleton of the profile. Some of the main features of the wing are determined by the shape of the skeleton just as bone structure determines important human bodily features. The flesh, or thickness of the wing, may be imagined as grown around the camber line, equally on both upper and lower sides. FINDING THE CAMBER The camber line of a profile may be found by plotting a row of points midway between the top and bottom surfaces. For the most accurate results this should be done by the method shown in Figure 2. With a large drawing of the section on plain white paper, fit circles into the outline at as many points as possible. Mark the centres of the circles and join them with a smooth curve. The result is the section camber line. The easiest way of doing this in practice is to draw a whole lot of circles of differing sizes on a piece of tracing paper, using simple school compasses. Slide the tracing paper about over the section drawing to a places where a circle fits, just touching the top and bottom surfaces. Prick through the centre. Move the tracing to another position and find another fit, and prick through, repeating with different circles until there is a long curved row of prick marks, which should be joined up to show the camber line. It is not necessary to do this every time a new section is examined. It is useful as an occasional exercise. A rough idea of the camber can be found quickly by measuring, with a ruler or dividers, a few points equidistant between the top and bottom lines, and sketching the curve. Computer programs are available now which do a better job in much less time, once the section ordinates are put into the data bank. Often, information about the camber line is given in some form by the section designer. All these methods lead to the same point. Whatever the external appearance of the section, there is a camber line inside it. The shape of this inner skeleton has fundamental influence on the behavior of the wing in flight. Sections which look superficially alike may differ a good deal in camber. A symmetrical wing section has an un cambered skeleton, a straight line, surrounded by a thickness form which gives exactly the same shape on the top and bottom surfaces of the wing.
Any wing which is not absolutely symmetrical has camber. It thus makes no sense whatsoever to speak of a section as 'semi symmetrical', for example. A section which is not perfectly symmetrical is a cambered section and what matters then is the shape of the camber line. A section cannot be semi-cambered any more than someone can be semi-pregnant. Either one is pregnant or one is not. Either a wing is cambered, or it is symmetrical. Knowing the difference, in either case, is important! Some examples are shown in Figure 3. The wing sections here are cambered. The shape of the camber line is indicated in each case. Figure 4 shows another important point. Four sections here, all from the famous NACA four digit series, have the same camber exactly. When a camber line, of a certain shape and amount of curvature, is buried in a thick wing, the external appearance of the profile often produces a section which is biconvex, like the
4415. If the same camber line is buried inside a thinner section, very possibly the under surface of the wing will come out flat, or nearly so, like the 4412. If the wing is thinner again, the under surface may be partly concave or under cambered, as with the 4410 and even more with the 4409. Further thinning approaches the membrane or film type of section. Thickening or thinning a section certainly does make a difference to the way the wing flies, but since the camber is the same in all these examples, those aspects of the wing which are chiefly affected by camber, will be the same. From this it follows that terming a wing section 'flat bottomed', 'bi-convex', under cambered, etc., does not mean a great deal in aerodynamic terms. It is true that flat bottomed wings are slightly easier to build than any other form. For this reason, but only for this reason, there is some value in mentioning this feature. Under cambered wings require slightly more care in covering or skinning, bi-convex wings may need special jigging or propping up during assembly. Using the external appearance of the wing to describe its aerodynamic qualities, is almost always misleading.
THE EFFECTS OF CAMBER IN FLIGHT Imagine a wing with a symmetrical section being held at different angles in a steady airflow of constant speed. Such a flow might come from a simple fan. (The situation is artificial, since changing the angle of attack of a real wing brings with it changes in the speed of flight. For the moment ignore this complication.) At zero angle of attack, aerodynamic zero, the symmetrical section creates no lift. As the angle of attack increases the amount of lift it gives also increases. If the angle decreases, the lift decreases. If the angle of attack is negative the lift reverses in direction. (This allows an aircraft to fly upside down.)
Over the normal operating range, the relationship of lift to angle of attack is usually proportional. That is, a small angle of attack yields a small lift force, a larger angle produces a larger lift and so on, until the wing begins to stall. Different wing sections stall in different ways, but over a certain range of angles used in normal flight, they all tend to behave very much alike. So long as the flow does not begin to stall the amount of lift is proportional to the angle of attack, above or below the zero lift angle. It is customary and helpful to represent the variations of lift with angle of attack, by drawing a very simple chart, as in Figure 5. Here, the angle of attack is represented along the horizontal line or X axis, and the lift by the vertical or Y axis. The exact units used do not matter at this stage but it is usual to count the angle of attack in degrees. The lift is plotted as the section coefficient of lift or cl. (Small c, small 1, because CL in capital letters usually means something different.) The line showing the relationship between angle of attack and the lift, is called the lift curve. The usual convention is to draw the chart with the lift curve sloping up from left to right. If the model is being flown very close to the stall, the way in which the lift curve behaves at top and bottom becomes important. Some sections stall gradually as the airflow begins to separate from the trailing edge of the wing. In other cases the flow suddenly breaks away from the leading edge and this produces a very sharp stall. Something more will be said about this later. For the moment, it is important to notice that, between the flow separation limits, the chart of lift against angle of attack is practically a straight line. Paradoxically, the part of the lift curve that is interesting to us is not a curve, but a straight line. This neat state of affairs, perfect proportionality between angle of attack and lift, giving a straight lift curve on the chart, is not always exactly true but departures from the straight lift line are usually small and for most practical purposes can be ignored. INTRODUCING CAMBER Now imagine that the symmetrical section shown on the first chart, is bent round as a whole to give it a little camber. Nothing else is changed. (Figure 6). The aerodynamic zero of the cambered section is found at a negative geometric angle, as expected. On varying the angle and few degrees either way, still in the same steady flow, the chart shows the same kind of straight lift line. Not only is the proportionality preserved, but the actual slope of the line is the same. This means that if the angle of attack of the symmetrical section is increased one degree above aerodynamic zero, it will give just the same amount of lift as the cambered section if its angle is also one degree above aerodynamic zero. If we measure all angles from the aerodynamic zero of a wing section, within certain limits, all wing sections are very much alike. The slope of all the lift curves is about the same. (As before, this is not perfectly true in all circumstances but it is very close to correct in practical flying situations.) wing section, within certain limits, all wing sections are very much alike. The slope of all the lift curves is about the same. (As before, this is not perfectly true in all circumstances but it is very close to correct in practical flying situations.)
There is a change in upper and lower limits. In the positive direction, the cambered section reaches a higher point on the chart before it stalls. It can produce more lift than the symmetrical profile. Viewing the chart as a whole, we now see the effect of camber on lift more clearly. The lift curve, all the way from negative stall to positive stall, moves up and to the left on the chart. The more pronounced the section camber, as shown by its camber line, the more the lift curve moves to the left and upward. The general shape of the curve as a whole changes very little. This geometrical feature should not be allowed to obscure the fact that the range of angles between aerodynamic zero and the positive stall, is larger for the cambered section and so the total lift is greater. At angles of attack below aerodynamic zero, things are the other way round. Flying upside down with a cambered section, less lift is available.