Buy now from the bookshop

This is a book about the design and performance of wings: if you intend to design your own airplane, whether full-scale or model, you need this book. There is plenty of Maths which some may find useful: for the non-mathematical, just skip the maths and look at the diagrams, read the text and allow your brain to soak it all in.

A&vD is now hopelessly out of date, being published first in 1949, with a new edition in 1958. However, this is part of its charm. It is still readable, at a level accessible to most, whereas more modern texts have become progressively more mathematical and are pitched to the professional graduate Engineer.
The chapters include discussion on the significance of wing-section characteristics, 2-dimensional flows, theory of wing sections, effects of viscosity, families of wing sections, experimental characteristics of wing sections, high-lift devices and compressibility. At least 50% of the book is comprised of airfoil section coordinates and their aerodynamic polars (lift, drag, pitching moments).

Now I'll skip thru the pages and pull out some gems.

Pages 4 and 5 have graphs showing the effect of Aspect Ratio on wing characteristics. In model pylon race, for many years the models had aspect ratios as low as 5. Modern race models have aspect ratios as high as 9 or higher. I should know, I machined the moulds for the last F3D world Championship winning model and did the area calculations to make sure it fitted the rules. And aspect ratio is simply wingspan-squared divided by area. One glance at figures 2 and 3 is enough to explain the superiority of the new wings.

Page 8, equation (1.6) is

CD = cd + Cl^2/(pi*A)

where CD is the drag coefficient of an elliptical wing of aspect ratio A, cd is the drag coefficient of a wing of infinite aspect ratio, Cl is the lift coefficient and pi is 3.1412 etc.

Don't be tricked by this equation. The total wing drag is quite different from the drag coefficient. The induced drag of the wing does not vary with Cl^2/A, only the coeficient does: that is a different animal altogether. Barnaby Wainfain in Kitplanes some time back pointed out that the total induced drag depends on the span loading, a result that may be derived by substituting eq(1.6) in eq(1.2).

Page 41 throws up a theorem from Fluid Dynamics theory, concerning the superposition of flow fields to obtain a resultant flow field. That is, for a fluid, you add 2 velocity fields together to get the actual flow around an object. I have never been happy with this theorem, and would like to display my ignorance and lack of rigour in this regard. 

E.R Jones has suggested application of this theorem to obtain the flow around a spinner/cowling assembly, with application to the design of propellers. He uses the flow from 2 sources superimposed on the free-field flow. By suitable adjustments of the source strengths, one can obtain a convincing representation of the axial flow velocity into the propeller as a function of propeller radius. The method can be generalised to any number of sources, which suggests perhaps that it could be used to obtain the flow pattern over an airfoil section. This is drawing a long bow, but it lead me to think a bit more carefully about the process.

The flow pattern is a set of streamlines. By definition of a streamline, this means that there is no mass flow across streamlines: hence there is a continuity constraint on the flow between the streamlines. The product of mass times velocity (mass flow) must be constant everywhere within a streamline (near enough, you can make the streamline infinitely thin).

I did the mass flow calculation for a spinner/cowling flow representation and was alarmed to find a huge increase in velocity was required going over the cowling, a figure entirely different from the simple sum of the source and free-field velocities. It is not at all obvious to me that some roll of Bernoulli's dice can sweep this under the proverbial mat. If someone out there has a nice readable explanation for this, I would love to peruse it.

Chapter 4 is about the theory of thin wing sections. As a propeller designer, it's most useful part was on the calculation of the zero-lift angle of an airfoil. While measured section data is really the only reliable way to go here, there are times, when doing computer simulations, that a simple formula for zero-lift angle is most useful. Such a method is given in Section 4.3, involving a summation of terms involving the section coordinates.

I latched right onto this and got results that were OK for high Reynolds numbers. 

However, R.T. Jones in his book Modern Subsonic Aerodynamics (which is no more more "Modern" than A&vD) gives an analysis which provides an extremely simple way of obtaining the zero-lift angle. It is just the angle between the chord-line and a line joining the trailing edge to the camber-line high-point.
Calculation by both methods suggests that there is no difference between the two, for all practical purposes. Hence I ended up using R.T.'s method, but mainly because he was such a cool guy at high Mach numbers! I believe he was the first American to appreciate the joys of swept-back wings.

Moving right along, Chapter 6 introduces the method the old NACA used to generate their families of wing sections. This is pure gold! I have only used the equations for the 4-digit sections. Because my work invariably involves low Reynolds numbers, I have felt that more advanced sections have little to offer me. I have been thru Herk Stokeley's Soartech 8 sections, but always return to NACA 4-digit for ease of use and high-performance in turbulent flows. Sections such as NACA6409 and NACA4407 have given me good results. 6409 is the Dixielander section, and I have used 4407 in F1C at the suggestion of Peter Nash.

My CNC machined propeller moulds are nearly all NACA 4-digit sections, so some pause here may be justified.

The most famous wing section of all-time must be Clark-Y. Many people may not be aware that the thickness form of Clark-Y is the basis of the NACA 4-digit sections. All NACA appears to have done is recognise the good performance of Clark-Y, and fitted their parameters of camber, camber-line high-point and thickness to chord ratio to this section. Thus NACA 4412 is very close to Clark-Y. Clark-Y has 11.72% t/c and camber 3.55%, compared to 4412's 12% t/c and 4% camber. The camber line high-point is close for both, at about 40% of x/c.

Variations on 4412 can be expected to have good performance as well. Just by thinning 4412 to say 4409, one gains considerably in L/D.
Moving the high-point forward inceases the max L/D for better acceleration at low speed. Thus the 4-digit sections can be tailored to suit the design constraints. This is all very nice.

Chapter 9 is about airfoil characteristics at high Mach numbers. This is the region, nowadays known as the transonic region, where the compressibility of air and the formation of shock waves start to dominate the airfoil section performance. At the time this book was written, aerodynamicists were not up to speed on these problems. A lot has happened since then. But let us look at the transonic data in A&vD and check them out with 20/20 vision, ie, lots of hind-sight!!

There are graphs of lift-coefficient and drag-coefficent versus Mach Number and angle of attack for NACA 4-digit sections 2306, 2309, 2312 and 2315. Remember, the notation for 4-digit sections tells us that the only difference in these sections is their thickness-to-chord ratio. Blind Freddie can see that the thicker the sections, the worse the high-Mach number performance.
Hence the drive to make propeller tip section as thin as possible, to the point where they need to be impractically thin. About the only time when high Mach-number problems do not occur in propellers is the rubber and human powered types.

Now for the hind-sight, which is the most fun. Modern super-critical airfoil sections are basically like the old sort, but turned upside down! Yes, most curvature is on the bottom of the wing, a situation not unlike negative camber!
So let us now do something novel, and turn A&vD's book upside down and again read the airfoil data. Looking for example at Figure 163, we see that NACA2309 has lousy performance below Mach .7, and works wonderfully well at Mach .9 !

It was 20 years after A&vD's work that supercritical airfoils were discovered. If only they had turned the book upside down, we would have had Jumbo jets in 1955!!

Well by now you have a taste for the delights of this book. I want to finish on one last point.

I said earlier that the NACA 4-digit sections can be adapted to many needs. From immediately above, we can see that they can work at high-Mach numbers. For some time I tried to use Mark Drela's Xfoil code to analyse my own supercritical sections, without success. The code would just hang up. It would only run reliably on the 4-digit sections ! So I set out to optimise the 4-digit sections for Reynolds number and Mach number. I found that the sections needed to be thin, with a rearward high-point and could only be run at a few degrees angle of attack. Anyone out there with the time, how about doing this exercise again, but with negative camber?

I'm too busy trying to stay in the black, so its up to you, dear reader.

Oh, and buy the book, you can't go wrong.