Correspondence with the Journal of Aeronautical History

The Editor welcomes letters from readers and below you will find the latest corespondence between members, the Editorial Board of the Journal of Aeronautical History and authors.

The following letter was received on 6th February 2014 but held until the first paper of 2014 was ready for publication.


My good friend, Gordon Bruce, intrigued by my suggestion concerning the origin of the Spitfire’s wing planform(1), has provided additional evidence supporting that suggestion. In order to understand Gordon’s line of enquiry it is necessary to be reminded of the following facts. In the design evolution of the Spitfire, its distinctive double-ellipse wing planform first appeared in a Supermarine drawing of December 1934. A geometrically identical shape had appeared in Prandtl’s Göttingen Report of 1918 which initiated modern wing theory. This planform reappeared in the German-language textbook by Prandtl & Tietjens of 1931 and in its English translation of 1934, both of which included an explanation of this planform’s advantages. The Canadian aerodynamicist, Beverley Shenstone, who had joined Mitchell’s Supermarine design team in 1932, had previously worked in Germany. Shenstone was competent in technical German and, according to Cole(2) , had met Prandtl whilst in Germany. The suggestion made in Ref. 1 was that, either through direct contact with Prandtl or more likely from the latter’s 1931/34 textbooks, Shenstone learned of the double-ellipse planform and recommended it to Mitchell.

Gordon Bruce decided to explore further the possibility of Shenstone’s use of the English translation of Prandtl & Tietjens (3) . He tells me that this was published by McGraw-Hill not only in New York but also in London in 1934 and that Cambridge University Library obtained its copy as a compulsory deposit on 23 April of that year. This date provides an indication of when the book became available in Britain. Gordon adds that an anonymous review of the book appeared in this Society’s Journal in June 1934(4) . This is highly complimentary, stating that “The chapter dealing with aerofoil theory …is one of the best in the book…” and concludes with the following:

“The book is strongly recommended as being much the best book on the subject for the technician that has so far appeared.”

As to the question of whether or not Shenstone had read this review and then studied the book, there can be no answer, of course. However, Gordon points out that in the preceding month of May 1934 the Journal carried Shenstone’s paper(5) on wing theory. It thus seems likely that Shenstone, by then an Associate Fellow of the Society, would have the Journal on his reading list.

Shenstone’s purpose in publishing his paper on wing theory(5) is to introduce the English-speaking world to Lotz’s method(6) . The latter neatly avoids the mathematical difficulties of earlier methods based on Prandtl’s lifting-line model of wing flow. Not only is the spanwise vortex distribution expressed as a Fourier series but so too are the chord and twist distributions. The method is versatile, capable of handling discontinuities such as those of shape introduced by deflected control surfaces. Solutions to the resulting series expansions in Fourier coefficients are achieved with predictable accuracy by successive approximation. Shenstone provides a schematic Journal of Aeronautical History 2014 2 layout for the final calculations which require only basic arithmetic skills. From these, lift, induced drag, pitching and rolling moments are obtained. He gives a single example of the method’s use, that of a wing having straight taper and a non-linear twist creating 6° washout at the tip. Interestingly, he cites three German references in which the Lotz method had been used, a further indication that he kept a close eye on German literature in aerodynamics. Shenstone acknowledges the help of Raymond Howland, Professor of Mathematics at the then University College of Southampton, in preparing the paper. In 1936 Howland and Shenstone published a further paper on wing theory(7) . The “inverse method” of this paper’s title is that in which planform shape and spanwise lift coefficient distribution are assumed, from which wing twist is determined together with the consequent induced drag. Densely mathematical, the paper considers examples of straight taper and the simple ellipse, and discusses how twist affects stalling characteristics. Thus neither of these papers touches on the double-ellipse planform adopted for the Spitfire. Although both papers’ methods could have been applied to that case, presumably commercial confidentiality would have deterred the publication of results.

Irmgard Lotz (Flügge-Lotz subsequent to her marriage in 1938 to Wilhelm Flügge, a civil engineer) (1903-1974) was an accomplished mathematician who joined Prandtl’s Göttingen team in the late 1920s. Her paper on wing theory(6) gained her rapid promotion at Göttingen. Having moved with her husband to Stanford University in 1948, Dr Lotz became the first female Professor of Engineering there. Although the Lotz method(6) was considered a significant breakthrough at its publication, in 1938 it became superseded by Multhopp’s method(8) which has since stood the test of time.

Finally, my thanks go to Gordon Bruce for his ever-meticulous research, and to Brian Riddle and Christine Woodward of the NAL, Farnborough, for supplying copies of the Shenstone papers.

J. A. D. Ackroyd FRAeS
Timperley, Cheshire


1. ACKROYD, J. A. D. The Spitfire wing: a suggestion, J. Aero. Hist, 2013, 3, (2), 121- 135.
2. COLE, L. Secrets of the Spitfire: The Story of Beverley Shenstone, the Man Who Perfected the Elliptical Wing, Pen & Sword Books Ltd., Barnsley, 2012.
3. PRANDTL, L. & TIETJENS, O. G. Applied Hydro- and Aeromechanics, McGraw-Hill, New York & London, 1934.
4. ANON. Review of Applied Hydro- and Aeromechanics, JRAeS, 1934, 38, 562.
5. SHENSTONE, B. S. The Lotz method for calculating the aerodynamic characteristics of wings, JRAeS, 1934, 38, 432-444.
6. LOTZ, I. Berechung der Auftriebsverteilung beliebig geformter Flügel, Zeit. für Flugtechnik und Motorluftschiffahrt, 1931, 22, (7), 189-195.
7. HOWLAND, R. C. K. & SHENSTONE, B. S. The inverse method for tapered and twisted wings, Phil. Mag. Series 7, 1936, 22, 1-29.
8. MULTHOPP, H. Die Berechnung der Auftriebsverteilung von Tragflügeln, Luftfahrtforsch. 1938, 15, 153-169.

Letter to the editor of The Journal of Aeronautical History, 4 December 2011 


First may I congratulate you on the launch of The Journal of Aeronautical History, which I hope might help compensate for the lamentable lack of historical papers in the Society’s other learned journals. Sadly, the RAeS has always seemed unaware that properly researched history is just as demanding a discipline as any of the scientific and technical disciplines that aeronautics entails.

Professor T.J.M. Boyd’s tribute to the work of Professor G.H. Bryan (Paper No. 2011/4) is welcome, as greater recognition of Bryan’s pioneering work on stability was long overdue. However, there is a significant omission regarding the early influences on Bryan’s interest in aviation. Bryan was evidently quite closely associated with Britain’s disciple of Otto Lilienthal, Percy Pilcher, who experimented with Lilienthal- and Chanute-inspired hang gliders from 1895 to 1899, yet Pilcher’s name does not appear at all in the paper.

On Monday November 30, 1896, the then Dr G.H. Bryan presented a lecture at the Imperial Institute in London on ‘Flight, Natural and Artificial’. Not only did Pilcher assist Bryan, but his newly completed Hawk glider was suspended over the audience. During the proceedings it was lowered, and Pilcher explained its operation and demonstrated his technique for flying it. At the end of the lecture Pilcher proposed the vote of thanks.

Moreover, Bryan alluded specifically to Pilcher’s work, and quoted him, in his article ‘Artificial Flight’ (not ‘Report on Artificial Flight’), in the October 1897 issue of Science Progress. The article contains a perceptive comment by Bryan regarding the interrelated problems of stability, control, size and weight in relation to powered flight, in which he states, in part: ‘If any experimenter can so thoroughly master the control of a machine sailing downhill under gravity as to increase the size of the machine and make it large enough to carry a light motor, and if, further, this motor can be made of sufficient horse-power, combined with lightness, to convert a downward into a horizontal or upward motion, the problem of flight will be solved.’ This essential realisation that it was necessary to master control before the application of power was truly groundbreaking at the time. He also said: ‘Another promising direction for success lies in an elaborate and exhaustive [mathematical] investigation of balance and stability, such as would allow the safe use of motor-driven machines too large to be controlled by mere athletic agility [i.e. body-swinging]’. Thus he laid out the basic path to powered flight, though sadly too many pioneers failed to comprehend the significance of his remarks.

Given this evidently close relationship, there can surely be little doubt that Pilcher’s tragic death as a result of a crash in his Hawk on September 30, 1899, would have further fired Bryan’s determination to apply his mathematical skills to the problem of stability. Finally, I think Professor Boyd is being rather unfair when he credits the Wright brothers with ‘. . . little need for — or understanding of — mathematics’. While the Wrights might not have been as mathematically gifted as the likes of Bryan, and initially neglected Journal of Aeronautical History 2011 128 stability in their quest to achieve control, their abilities in this respect were certainly above average, as their extensive 1901 windtunnel data tables, and their calculations of propeller efficiency, testify.

Philip Jarrett AMRAeS

Reply to letter from Philip Jarrett, 20 December 2011


Until I read Philip Jarrett's letter I was unaware of any link between Bryan and Percy Pilcher. With hindsight it is hardly surprising, given Bryan's contacts with Maxim, Langley and Chanute. Prompted by Mr. Jarrett's reference to Bryan's lecture on Flight, Natural and Artificial at the Imperial Institute in November, 1896, I found the following resumé in Natural Science; A Monthly Review of Scientific Progress, vol. X, p.66, 1897:

"An interesting lecture on "Flight, Natural and Artificial" was delivered by Dr. G. H. Bryan, F.R.S. in the Imperial Institute on November 30. The advantage of a screw propeller over a flapping method was illustrated by some little models which were thrown up and floated in a very bird-like manner. Lantern slides of various old and new machines were exhibited, and Mr. P. S. Pilcher's machine which was displayed in the hall, was explained by the inventor."

Pilcher's machine, incorporating aspects of Lilienthal's design and using data from his extensive research on lift, may well have been the only glider Bryan ever saw at first hand.
Lilienthal's fatal accident the previous August had prompted Bryan to question the stability of his design. Increasingly he would come to equate stability with safety. Writing some years later, in one of his annual reports to the College Council at Bangor he blamed departmental burdens for setbacks in his campaign on stability:

"…..It is a pity that such has been the case as it is certain that some at least of the fatalities….could have been prevented if the results could have been sooner placed in the hands of those developing the problem on the experimental side."

But Pilcher's accident at the end of September, 1899 was not one of those, as it was due to a structural failure of the tail of his glider and not to any loss of equilibrium through onset of the pitching instability. That apart, the death of a valued associate, the leading exponent of gliding in the country, could only have added to Bryan's resolve to tackle the problem of glider stability, as Mr. Jarrett suggests.

However other concerns were uppermost in Bryan's mind on his return to Bangor that autumn, after recuperating at Cambridge from his nervous breakdown earlier in the year. He would have been only too aware that Principal Reichel had lost confidence in his ability to run the mathematics department and wanted rid of him. In a real sense he was on probation, needing to devote most of his energies to teaching and examining duties. At the same time, Journal of Aeronautical History 2011 129 his visit to Boltzmann in Vienna in the summer of 1899 had rekindled his deep interest in thermodynamics and as I have argued, the invitation from Sommerfeld to write the article on thermodynamics for the Enzyklopädie für Mathematischen Wissenschaften may well have come at Boltzmann's prompting. So over the next two years, what spare time he had was given to thermodynamics rather than to problems in aerodynamics. More insistently, the stability of the Bangor Mathematics department took precedence over the stability of gliders.

Had I simply cast the Wrights as having ".....little need for - or understanding of - mathematics", Mr. Jarrett would have been right to take me to task. But what I wrote was:

"They (the Wrights) solved their control problems by trial and error, with little need for - or understanding of - mathematics …."

By mathematics I did not mean just numeracy - the Wrights had that without question, as Philip Jarrett points out. What I had in mind was that in common with engineers and practical men and women of the day, they knew virtually nothing of the mathematics needed to describe the stability of dynamical systems, in their case, gliders in flight. In the words of a mantra Bryan never tired repeating:

"…. with very few exceptions those who experiment with aeroplanes do not possess a large amount of mathematical knowledge …. Few of the experimenters know what a biquadratic equation is and the sooner they do, the better it will be for them."

The biquadratic analysis had been worked out by Routh in 1877 and it took someone like Bryan, steeped in the stability of systems early in his career, to see what was needed.

The true genius of the Wrights lay in other directions. James Lighthill, doyen of theoretical aerodynamicists, said of them in his lecture Mathematics in Control, (J.Inst.Math.App., 4, 1- 19, 1968):
"the famous brothers themselves used no significant quantity of mathematics in solving the control problems required for …. the first powered flight in December, 1903."

Culick, Vincenti and others have gone further, arguing that the Wrights could not really understand stability. That we do is because Bryan could, and did.

Centre for Physics University of Essex