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Propeller Dynamics

Essential reading for model aircraft contest fliers. This is the only book on the market explaining propeller theory in non-mathematical terms. A rattling good read, I know, I wrote it.


Words of encouragement from NACA

By Joe Supercool

A letter from Hewitt Philips, Dec/31. 1995

Dear Stuart,

Maynard Hill sent me your book, Propeller Dynamics, along with a copy of your letter in which you asked for my comments. I think the book is very interesting and I am glad to see a book on propellers in language that the average engineer can understand.

My experience with propellers is rather limited as my professional work was in the field of stability and control. I have corresponded with Gene Larrabee for many years. Rather late in his career, when most of the aeronautical industry had just about forgotten about propellers, he made a thorough study of Glauert's excellent article on propellers in the Durand series, and reduced the formulas to a series of calculations that could be carried out on a pocket calculator. About that time, I was interested learning how to program an HP9820 computer, one of the first desk-top sized mini- computers. I used Larrabee's theory as an example. Later, I programmed the same problem on the HP9830 computer, which used the BASIC programming language. I didn't consider that this exercise made me an expert on propellers, but Maynard Hill was quite impressed because when I used the program to design a propellers for his closed-course distance record airplane, it came out with a design almost identical to the one that he had arrived at through his tests and long experience.

I have since done a little more studying on propellers, in connection with high-altitude airplanes and model airplanes. Despite my limited experience, I probably know more about propellers than anyone else in the NASA Langley Research Centre; as all the old propeller experts have either died or retired. ( I am retired, but still keep my office at Langley.)

I found the historical account in your Chapter 2 very interesting. The Wright Brothers are often given a lot of credit for their simplified, but logical propeller design analysis, whereas Maxim, as you point out, used an experimental approach. I have often though that Maxim's propellers were probably more efficient than the Wright's, because of the more efficient airfoil shape used. The Wright's 1903 propeller had a practically trapezoidal airfoil section. This would be a good subject for study by some historically minded engineer.

I must admit that I have not yet read your whole book, though I have looked through the chapters. I think there is one point that has not been emphasized enough in propeller design, particularly for small propellers on models. This is the centrifugal effect on the boundary layer that tends to drain the boundary layer off at the tips. As a result, model propellers show relatively high efficiency even with thick airfoils, whereas if the static data were available on the same airfoils of the appropriate Reynolds Number, it would probably show very poor lift-drag ratio. This effect was first shown up in the old test series of propellers made by Durand at Stanford University in the early '20's. His tests on small propellers showed efficiencies almost as high as those later obtained by Weick on full-scale propellers. The APC propellers favored by pattern fliers and used by Maynard on his recent record flights have relatively thick airfoils. Of course, finding data on theis effect may be difficult. The effect would be expected to be less important on full-scale propellers because of the thinner boundary layers at high Reynolds numbers.

An excellent article on propellers is in the 1995 Symposium Report of the National Free-Flight Society article, by N. Bruce Kramer, an engineer retired from Hughes Microwave Products Division, show an excellent knowledge of the theory. He formulates the problem using Torque and Velocity as inputs. This is something I was trying to do in performance calculations for rubber- powered models.

I will look forward to later reports from you giving more of the analysis. Thank you for letting me see your book. I hope these comments are of some value to you, and wish you a happy New Year.

Yours sincerely
Hewitt Philips

A letter from Hewitt Philips, Jan/27. 1996

Dear Stuart,

Thanks for your letter of Jan. 17, 1996. I will try to answer your question. First I am curious about the propellers that you or your company makes. Are they for full-scale airplanes (home-builts, etc) or for models?

Propeller theory developed in three steps. First, there was momentum developed by Froude. This theory considered the slipstream to be uniform and did not consider losses due to the individual propeller blades. Second, there was the blade element theory. This theory considered the lift and drag forces on a single blade element or on a number of blade elements along the radius, and calculated the resulting thrust, torque and efficiency. This theory was pretty well worked out by the Wright brothers. With the blade element theory, there was always a question as to what effective aspect ratio should be used for the blades.
(blade elements?) Later versions of the theory combined the Froude theory with the blade element analysis to get an idea of the induced velocity at the blade elements. Still, an additional correction for effective aspect ratio was added to make the results agree with experiment.

Some of the expert aerodynamicists realised that the blade element theory was in consistent with wing theory. In wing theory, the airfoils are considered to have their two-dimensional characteristics (infinite aspect ratio). The induced drag is calculated by considering the velocities induced at the wing by the trailing vortex system.. This theory gives very accurate results for unswept wings with aspect ratios greater than about 4.

The result was the vortex theory of propeller, first worked out by Prandtl and Betz in Germany about 1919. The theory was not well known in this country (USA) for a number of years. Weicks' book, published in 1930, does not refer to this theory.

The theory did not become well known until the article by Hermann Glauert was published in the Durand Series (Vol IV, Division L, pp. 169-360).

This article was written just before Glauert's untimely accidental death in 1934, and was deited for the Durand Series by R. McKinnon Wood. This is a most comprehensive article, and I suggest you read it to really understand propellers. Still, I warn you, it is not easy reading.

Glauert used Betz's approximation to the calculation of induced velocity at the blades. This approximation assumes that the advance ratio is small so that the successive vortex sheets in the slipstream can be considered to be in planes normal to the axis, instead of being sections of a helical surface. Still, it is a very good approximation.

Later, S. Goldstein in England calculated the induced velocity more exactly, taking account the helical shape of the vortex sheets.

In this country, Theodorsen made similar studies of various kinds of propellers (high pitch, contra-rotating, etc.) Theodorsen used an electric analogy to obtain his results. In recent years, Ribner has checked Theodorsens results using modern computer techniques and found they were very accurate.

I should emphasize the point that if vortex theory is used, it is logical to use the airfoil characteristics for infinite aspect ratio.

It should be realised, however, that none of these theories are exact models of the actual operation of a propeller. They mostly assume lightly loaded propellers, so that the induced velocities are small. In addition, the blade is handled by a lifting line theory, which considers the blade vorticity to be at the quarter chord line. A more exact theory would be similar to lifting surface theory for airfoils, in which the distribution of lift, and vorticity over the surface is considered.

Finally, the complete theory would use computational fluid dynamics (CFD) to include the effects of the boundary layer. I believe some efforts have been made to work out a complete theory, but I am not familiar with them. The need for such complete theories, is not very apparent, since results accurate enough for practical purposes can be obtained by simpler theories.

I hope this discussion will clarify the question that you asked. I wish you success with your propeller operations.

Yours sincerely,

Addendum by Supercool:

Much study has followed the encouragement given by Hewitt. The following texts entered my library subsequently and are of use.
Journey in Aeronautical Research. 1998 W. Hewitt Phillips (biography)
Theoretical Aerodynamics. 1958 L. M. Milne Thomson
Airplane Propeller Principles. 1944 Wilbur C. Nelson
Aircraft Propeller Design. 1939 Fred E. Weick
From the Ground Up. 1988 Fred E. Weick and James Hansen (biography)
Critical Mach Number. 2012 Joe Supercool
Aerodynamic Drag. 1951 Sighard F. Hoerner
Fluid-Dynamic Lift. 1975 S.F Hoerner and H.V Borst
Airfoils at Low Speed. 1989 M. S. Selig J. F. Donovan and D.B. Fraser
Soartech 8. H.A. Stokely, publisher.
Cooling of Aircraft Engines. 1935 F.W. Meredith
Propeller Dynamics. 1994 Stuart L. Sherlock
Report No. 777, 778 NACA. 1944 The Theory of Propellers: Theodore
Theodorsen, with application formulae.
Report No. 924 NACA. 1948 Application of Theodorsen's Theory to Propeller Design. John L.Crigler On the Vortex theory of screw propellers. 1929 Sydney Goldstein
Modern Propeller and Duct Design 1993. Martin Hollmann and Mark Bettosini
Propeller Design and Analysis program. 1991 E.R. Jones (program not included)

The above collection, complete only, is available for sale on the offer of an obscene amount > USD5000, inclusive of shipping. Failed bids will not be replied to. Offers to Supercoolprops@gmail.com


It is now the year 2023. The words of Hewitt Philips above resonate in my 80 year old mind. Fortunately, age has not dimmed my intellect, the intellect passed on to me from my great-grandfather, so nobly recorded into history by Conan Doyle.

My efforts in propeller design, from Larrabee on, my ventures into Fluid Dynamics and CFD, have served only to convince me that theoretical analysis is a blind alley. At least, with the small propellers used in model racing aircraft, F3D, F2A and F2C, a different approach was required.

Something crude was in order. The framework was provided by professor Milne Thomson, as listed above in Theoretical Aerodynamics. Applied into the blade element concept, this reduced the design problem to guessing the lift and drag coefficients at each station along the blade.

If this seems simplistic, that is because it is simplistic. At first glance, the idea of designing a propeller to absorb 4 HP at 32000 RPM and 200 MPH in a diameter of only 15cm. (7) is quite bizarre. For a start, the tip velocity is close to Mach 1, definitely in the region of compressibility and shock waves: i.e. the unknown!!

So where to go? One solution is to make a propeller for all possible values of lift and drag coefficients, then test them.

Testing them would seem to be straightforward, but finding model pilots prepared to make possibly hundreds of flights is remote, but not impossible.

Making the propellers also would be impossible, were it not for computer controlled milling machines. Controlling for lift and drag coefficients is possible by constructing mathematical models of the propellers, then machining moulds for them from bar-stock aluminium.

My first efforts were to CNC an F3D wing mould. This required a way of generating the airfoils: such was given in Abbott and Von Doenhoffs Theory of wing Sections. Stuart Maxwell provided all this.

The first efforts were immediately successful, winning both F3D and F2C World Championships. Subsequent wins were an anticlimax, as the propeller performance was more down to the precision machining of the moulds than a real knowledge of the lift and drag coefficients.

To cut a long story short, here in post-covid 2023 I have 9 F2A and 9 F3D prop moulds and no takers for testing them.

But this is a requiem. Not for the loss of intellectual or pilot input, but the ageing of my Bridgeport Interact 1 series 2 CNC mill. Having given good service for nigh on 40 years, the electronics in this machine are giving up the ghost and replacements parts are hard to find.

So if anyone out there has a Heidenhein TNC151 controller they could gift to me, then they could know it was going to a good home! For those who came in late,