Sec. 45.26 



FRICTION-RESISTANCE CALCULATIONS 



129 



The reader's attention is invited to the fact 

 that the references hsted in this bibliography do 

 not duplicate those hsted in Sec. 45.21, relating 

 to fouling as affecting ship propulsion. There is 

 available in the Library of Congress at Wash- 

 ington a long and comprehensive bibUography 

 entitled "Skin Friction and Boundary Flow," 

 prepared by Dr. A. F. Zahm [SNAME, 1932, p. 

 309]. 



The titles in the present selected bibliography 

 are divided into three groups, described briefly as: 



I. Classical and historical 



II. Development of friction-resistance formula- 

 tions 



III. References of modern application. 



I. Classical and Historical 



There are hsted in this group a number of the 

 papers which form landmarks, as it were, in the 

 early development of the theory of friction resist- 

 ance, as applied to bodies and ships moving in 

 both air and water. Included are a number of 

 references which describe the development of the 

 theory, and its practical applications, in much 

 more detail than can be given here. 



(1) Stokes, G. G., "On the Steady Motion of an Incom- 



pressible Fluid," Trans. Camb. Phil. Soc, 1842 



(2) Bazin, H., "R6cherohes hydrauliques (Research in 



Hydrauhcs)," Mem. divers savants, Sci. Math, et 

 Phys., Paris, 1865, Vol. 19 



(3a) Froude, W., "On Some Difficulties in the Received 

 View of Fluid Friction," Brit. Assn. Rep. for 1869 

 (publ. in 1870), pp. 211-214. On pages 212-213 

 Froude gives an amazingly clear and straight- 

 forward exposition of the physical phenomena of 

 fluid friction, as it was known at that time. Much 

 of his statement applies to the knowledge of the 

 physics of fluid friction, as known 85 years later. 



(3b) Froude, W., "E.xperiments on Surface Friction," 

 British Association Reports, 1872 and 1874 



(4) Froude, W., "On Experiments with HMS Greyhound," 



INA, 1874, pp. 36-73 and Pis. Ill through XIII 



(5) Tideman, B. J., "Memoriaal van de Marine II. 



Afdeeling 9e Aflevering," 1876-1880. The paper 

 carries the title "Uitkomsten van proeven op den 

 Wederstand van Scheepsmodellen (Results of 

 Resistance Tests with Ship Models)." There 

 appears to be no Enghsh translation of it but a 

 note at the bottom of page 374 of Volume III 

 of PoUard and Dudebout's "Theorie du Navire," 

 1892, states that Tideman's paper was translated 

 (into French) by M. Dislere, Ingenieur de la 

 Marine, in the Memoires du Genie Maritime, 6th 

 Book, 1877. 



(6) Reynolds, Osborne, "An Experimental Investigation 



of the Circumstances which Determine whether 

 the Motion of Water Shall be Direct or Sinuous, 



and of the Law of Resistance in Parallel Channels," 

 Phil. Trans. Roy. Soc, London, 1883, Vol. 174, 

 Part III, pp. 935-982 



(7) Prandtl, L., "Uber Flussigkeitsbewegung bei sehr 



kleiner Reibung (On Fluid Motion with Very Small 

 Friction)," Verhandlungen des III Internationalen 

 Mathematiker-Kongresses, Heidelberg, 1904 (Pro- 

 ceedings of the 3rd International Mathematics 

 Congress, Heidelberg, 1904)," Leipzig, 1905, pp. 

 484-491; reprinted in "Vier Abhandlungen zur 

 Hydrodynamik und Aerodynamik," by L. Prandtl 

 and A. Betz, Gottingen, 1927. These contain 

 Prandtl's original statement of the boundary-layer 

 theory. 



(8) Blasius, H., "Grenzschichten in Flussugkeiten mit 



kleiner Reibung (Boundary Layers in Liquids of 

 Small Friction)," Zeit. fiir Math, und Phys., 1908, 

 Vol. 56, p. Iff 



(9) Stanton, T. E., MarshaU, D., and Bryant, C. N., "On 



the Conditions at the Boundary of a Fluid in 

 Turbulent Motion," ARC, R and M 720, 1919- 

 1920, Vol. I, pp. 51-67 



(10) Stanton, T. E., "Friction," London, 1923 



(11) Bruckhoff, "Reibungskoeffizienten (Friction-Resist- 



ance Coefficients)," WRH, 22 Aug 1923, pp. 

 435-438 



(12) Shigemitsu, A., "Skin Friction Resistance and Law 



of Comparison," INA, 1924; abstracted in SBSR, 

 17 Apr 1924, pp. 454-455 



(13) Burgers, J. M., and van der Hegge Zijnen, B. G., 



"Preliminary Measurements of the Distribution of 

 the Velocity of a Fluid in the Immediate Neighbor- 

 hood of a Plane, Smooth Surface," Verh. d. Kon. 

 Akad. v. Wetenschappen, Amsterdam, 1924 



(14) "Skin Friction Committee's Report," INA, 1925, 



pp. 108-123, esp. pp. 115-116 



(15) Hansen, M., "Velocity Distribution in the Boundary 



Layer of a Flat Plate," NACA Tech. Memo 585, 

 Oct 1930 



(16) Millikan, C. B., "The Boundary Layer and Skin 



Friction for a Figure of Revolution," ASME, 

 APM-54-3, 1931, p. 33 



(17) "The Prediction of Speed and Power of Ships by 



Methods in Use at the Experimental Model Basin, 

 Washington," Bu C and R Bull. 7, 1933. Pages 

 18-20 describe the modified Gebers formula in use 

 at the Experimental Model Basin, Washington, in 

 the period 1923-1947. 



(18) Payne, M. P., "Historical Note on the Derivation of 



Froude's Skin Friction Constants," INA, 1936, 

 pp. 93-109 



(19) Lackenby, H., "Re-Analysis of WiUiam Froude's 



Experiments on Surface Friction and Their Exten- 

 sion in the Light of Recent Developments," INA, 

 1937, pp. 120-158. On pp. 136-137 there is a list 

 of 16 references. 



(20) Millikan, C. B., "A Critical Discussion of Turbulent 



Flows in Channels and Circular Tubes," Proc. 

 Fifth Int. Congr. for Appl. Mech., Sep 1938; 

 published by Wiley, New York, 1939 



(21) Davidson, K. S. M., PNA, 1939, Vol. II, pp. 76-82 



and Figs. 22-23 



(22) Taylor, D. W., S and P, 1943, pp. 31-35 



