Sec. 4 5. S FRICTION-RESISTANCE CALCULATIONS 



(b) Cp = 0.0725(log,„ Rn - 2)-' 



(c) C^^ = 0.370(log,o /?.)"'■''' 

 (4) Prandtl-Schlichting [PNA, 1939, Vol. II, p. 82] 



Cp = 0.455(log,oi2„)"'-" 



103 



application to fresh water [SNAME, 1951, pp. 

 373-374]: 



Rr 



[''■'- + (^t)]-' 



For the local specific friction drag Cip or shearing- 

 stress coefficient C,. , H. Schhchting gives [Ing. 

 Archiv, 1936, Vol. 7, p. 29] 



C,^^ = C. = (2 log.oiJ. - 0.65)-'-' 



(5) Von Karman, based on the 1/7-power law of 

 velocity distribution [PNA, 1939, Vol. II, p. 80]; 

 see Sec. 5.10 of Volume I of the present book: 



(a) Cf. = 0.072(E„)~'" 



This is also given as [Rouse, H., EH, 1950, p. 106] 



(b) Cr = 0.074(i?„)"°' 



(6) Gebers [INA, 1925, pp. 110-111] 



(a) Rf = hSV\R„)-''-''' 



where /c2 is a rather complicated term defined in 

 the reference. 



(b) [PNA, 1939, Vol. II, p. 80] 



Cp = 0.02058(i?„)"°''' 



where Rp is in lb for salt water of specific gravity 

 1.026 at 59 deg F, 15 deg C, L is in ft, S is in ft', 

 V is in kt [2nd ICSTS, Paris, 1935; Todd, F. H., 

 SNAME, 1951, pp. 317-318] 



(f) For fresh water the formula corresponding 

 to (e) is as follows [Baier, L. A., SNAME, 1951, 

 p. 365]: 



R[ 



.[«. 



00846 + 



0.0516 

 i.8 + L 



)] 



SV 



where the units are as given for the preceding 

 formula (e) 



(g) The following Froude formula corresponds 

 to (f) preceding, for use with metric units and for 



where i2p is in kg 



L is in meters 



S is in square meters 

 V is in meters per sec. 



When the temperature differs from 15 deg C, the 

 value of Rf given by (g) preceding is multipHed 

 by the factor [1 + 0.0043(15 - T)], where T is 

 the water temperature in deg C. 



(h) As an aid in correlating Froude's "0" 

 friction values with the specific friction resistance 

 coefficients presently used, A. M. Robb has 

 prepared and published tabular and graphic pre- 

 sentations in his paper "An Examination of the 

 Records of the Greyhound Experiments" [SBSR, 

 5 Jun 1947, pp. 568-571]. Page 570 of the reference 

 contains: 



(i) A table headed "Association of Froude's '0' 

 Values and Specific Resistance Coefficients on 

 Basis of Reynolds Number" 



(ii) A graph entitled "Froude's '0' Values in Cp 

 CoeflRcients." This has ordinates of Cf = 

 Rp/iO-BpSV^) and abscissas of Reynolds number 

 i?„ , extending from 1 to 10,000 million (10' to 10'°) . 



(8) Tideman 



Rf = kTSV, where Rf is in lb 



/ct is a coefficient given as / 

 in the first two references cited as (a) and (b) 

 hereunder 



S is in ft' 



V is in kt. 



When, as is the case here, n has a value differing 

 from 2, and p is omitted, this formula is dimen- 

 sional. 



The coefficient and exponent values of the 

 Tideman formulation, hsted in the following 

 references, are not given here: 



(a) Peabody, C. H., NA, 1904, p. 405, for ship 

 lengths of 10 through 500 ft 



(b) Taylor, D. W., S and P, 1910, 

 Vol. I, p. 63; notes only 



Vol. II, Table VI, for ship lengths of 10 



through 500 ft 

 1933, Table V, p. 32 

 1943, Table V, p. 34, with explanatory 



notes, for ship lengths of 10 through 



1,200 ft 



