Chicago, October 12, 1901
I have read with great interest your letter of Oct. 6th and I esteem greatly the experiments which you have lately made. I hope that you will continue them as proposed and advise me of the result.
I have been endeavoring to account for the discrepancy of your results with those of Lilienthal, and I think I have found one possible explanation. I send you a blueprint of Lilienthal's Plate VII in which he has plotted the results of all his experiments.
You will note that those made in "natural wind," from which he derived his coefficients, are greatly in excess of those made with the same surfaces with a whirling apparatus, and that your own recent experiments belong to the latter class, i.e., surfaces driven against still air.
It seems to me that there may be a difference in the result whether the air is impinged upon by a moving body, or whether the wind impinges upon the same body at rest. In the latter case each molecule, being driven from behind, tends to transfer more of its energy to the body than in the former case when the body meets each molecule successively before it has time to react on its neighbours. This conjecture seems to be sustained by an examination which I have just made into the methods by which the coefficients of air pressures have been found to vary from 0.00492 to 0.0033 by various experimenters. Those who have found the higher coefficients seem to have experimented with natural wind (Roux, Smeaton, Duchemin), and those who got the lower coefficients (Hazer, Dines, Langley) seem to have experimented with whirling tables. I have believed for years, however, that some discrepancy was due to the fact that the formula for direct pressure (P = KV2S) may not be in proper form to represent both the pressure and the rarefaction; that it should consist of two terms, as explained in the enclosed old clipping of mine.
You will find in Engineering News, March 14, 1895, a paper by Lieut. W. H. Bixby giving the various coefficients which have been found. I think that Langley's is too small, and note by the way that 0.005 in miles per hour corresponds to 0.12 in meters per second (not 0.13).
Please notice that in the diagram curve 1 represents the values found by Lilienthal in experimenting in natural wind, measuring the angle with the horizon; but as he had found an ascending trend of the wind on the plain where he made his experiments, of about 3 1/2°, he corrected his results to curve 2, from which I believe he got his coefficients. Both these curves are way outside of your results. I have put down three of the latter by a pencil point surrounded by a circle 0, and these seem to indicate that you obtain results analogous to those of Lilienthal in still air. It remains to be seen what you would get in natural wind, curve 3 being obtained with the same surface as curve 2.
I have plotted in a pencil line the coefficient for the Duchemin formula. Please note how much they differ from Lilienthal's curve for the plane.
It is possible, however, that Lilienthal's method for measurements in the wind was at fault. I enclose a paper by Obermayer, which please be sure to return, in which he claims that Lilienthal so hung his surfaces that the resultant of the pressures was forward of the point of attachment and thus exhibited a propelling component which did not exist. As Obermayer, however, starts with the assumption that the resistance of the air is proportional to the first or second power of the sine, while we know that for planes it is proportional to (2 sin a) ÷ (1 + sin2 a), I have not accepted Obermayer's conclusions, but I would like to have your own opinion about it. He admits the greater carrying power of arched surfaces, does not say how much, but denies the tangential component. I hope that it has been reserved to you to settle this intricate question by experiment. I would like you to insert a table of the coefficients you are about to obtain, for various angles, in your paper before the Western Society of Engineers. We would then print some separate copies and send them abroad to those who are interested in the question.
When sending you the translations from the Revue de l'Aéronautique I had forgotten that substantially the same data are given by Lilienthal in the Zeitschrift für Luftschiffahrt which is translated in my book, see pages 288-289. See also Pilcher's statement, page 146, Aeronautical Annual of 1897, that a speed of 25 miles an hour & 30 pounds pull will float 220 lbs. This seems to confirm Herring's statement, page 69, that a pull of 32.19 pounds and a speed of 22 miles an hour will float 178 pounds on a surface of 134 square feet.
Reply from Wilbur to Chanute, October 16, 1901