CHAPTER V. THE FRICTIONAL RESISTANCE OF AIR It is well known, from the investigations of Froude and others, that the frictional resistance of a body in water was great. By analogy it would seem as if the friction of the air would also be considerable. Many prominent experimenters and investigators, however, have stated that the tangential resistance of air is negligible. Langley implicitly assumed the effect of friction at the speeds he used, to be negligible, and did not investigate the problem to any extent.1 Clerk Maxwell conducted experiments on the viscosity of the air, i. e., the internal friction of the fluid, and gave the coefficient of viscosity of air as u= 0.0001878 (1+0.0027 6), 6 and being taken as defined in his paper. By this formula the actual tangential force on a plane of one square foot area moving horizontally at 100 feet per second is less than 1/50 of 1 per cent of the pressure on the same plane when moved normally at this speed. Maxim, Dines, and Kress considered the friction negligible throughout their experiments." Armengaud and Lanchester, who have thoroughly investigated the subject, take the opposite view and consider skin friction a very appreciable factor in the resistance of an aeroplane.* Lanchester gives the total friction on both ends of a plane as 0.015 of the normal pressure. Thus the frictional resistance F of a flat plane 200 square feet in area, moving at 50 miles an hour, and set at an angle of 20 deg., would be F 0.015 (0.003 X 200 X 2500) X (0.59) = In 1882 Dr. Pole investigated the skin frictional resistance of the dirigible balloon of M. Dupuy de Lome and found it to be 0.0000477 dlv2 where d is the diameter, the length, and v the velocity. This gave a very appreciable value to the frictional resistance. W. Odell in 1903 conducted experiments for the purpose of determining the friction of the air on rotating parts of machines and arrived at the conclusion that the energy dissipated per second = c w3 v5 where c is a constant, w the angular velocity of the disks with which he experimented, and v the radius of the disk.® The friction was found to be considerable, although the character of his experiments precludes their being applied directly to aeroplanes. Canovetti found the skin friction on surfaces equal to a constant times the square of the velocity, the constant taking the value 0.00012 when the metric system of units was employed.' The most thorough experiments in this line were conducted by Prof. Zahm in 1903. The results of his experiments showed conclusively that the friction of the air on surfaces was a very considerable factor, and he expressed its general value in the formula: f=0.0000158 70.07 v where f the frictional drag in pounds per square foot, l=the length of the surface in the direction of motion in feet, and the velocity of the air past the surface in miles per hour. = 1.85 The friction was found approximately the same for all smooth surfaces, but 10 to 15 per cent greater with extremely rough surfaces such as coarse buckram. The table on page 58 gives Zahm's values for f as obtained by experiment and from the above formula. The frictional drag for any intermediate velocity or length of surface may readily be found by interpolation. The frictional resistance of a flat or arched aeroplane surface of area S is F2Xfx S the factor 2 being introduced because the value of ƒ refers to a single surface of a plane, while a plane in free flight has, of course, two sides exposed to frictional resistance. To illustrate the practical application of these results on air friction, the actual frictional resistance F of a biplane consisting of two surfaces, 30 feet wide and 4 feet deep, moving at 60 miles. an hour is computed, S=240 square feet. From the table on page 58 the value of f = 0.0279. :. F = 2 X 0.0279 × 240 This value is very much less than what would be obtained by using Lanchester's method. The frictional resistance of air as determined by Zahm bears a striking resemblance to that of water as determined by Froude." Froude found the friction to vary very nearly as 185, and a comparison of the results indicates that the resistances are proportional in some way to the densities of the two media. If it is true that the air stream never touches an aeroplane surface but only comes in contact with the air film surrounding it, then the frictional resistance would be the same for all reasonably smooth surfaces, but would be higher for surfaces so rough that the fibers themselves cause regions of discontinuity. This appears to be borne out in the results of the experiments of Prof. Zahm. Curve 6 shows the variation of the skin friction on a unit surface with speed as plotted from Prof. Zahm's tables. It is now generally accepted that skin friction is an appreciable factor in the resistance of an aeroplane, and amounts in an average sized machine to from 10 to 25 pounds. 1 Langley, S. P., "Exp. in Aerodynamics," p. 9. Bader.-Powell, Aeronautics (Brit.), v. 1, p. 117. * Lanchester, F. W., "Aerodynamics"; Armengaud, "Prob 5 Pole, William, Ecl. Eng. Mag., v. 27, p. 1, 1882. Canovetti, "Sur la Resistance de l'Air," Paris, Acad. Sci., Zahm, A. F., "Atmospheric Friction," Bulletin, Phil. Soc. of Wash., v. 14, p. 247. 9 Froude, Brit. Assoc. Report, 1872. |