Sec. 45.23 



FRICTION RESISTANCE CALCULATIONS 



127 



There follows an example of the procedure 

 described, applicable to the 20.5-kt or trial-speed 

 point for the ABC design of Part 4. The basic 

 data are as follows: 



(a) Ship length (wetted length on 



waterline) 510 ft 



(b) Speed (to be achieved with clean 



bottom) 20.5 kt 



equivalent to 34.62 ft per 



sec 



(c) Wetted surface, with all append- 



ages, from Sec. 45.13 47,875 ft' 



(d) Plating has lapped riveted seams 



and flush butts 



(e) Coating is "commercial" anti- 



fouling, with self-leveling 

 properties 



(f) Mass density p, for the salt water 



in the 20-deg latitude of item 

 (16) of Table 64.c, at 68 deg 

 F, from Table X3.e (involves 

 no correction for latitude, as 

 described in Sec. X3.3) 1.9882 slugs 



per ft' 



(g) Kinematic viscosity ;', for tem- 



perature of 68 deg F, from 



Table X3.h 1.1372(10"') 



ft' per sec 

 (h) Time out of dock 12 days 



(i) Ocean water salt 



(j) Average sea-water temperature, 



from item (18) of Table 64.c, 68 deg F. 



The Reynolds number E„ , based on the water- 

 line or wetted length, is 



Rn = 



LV ^ (510)(34.62)(10') 

 V 1.1372 



= 1,552.6 million 



From Table 45. d the value of Cp , considering 

 the ship wetted surface as a flat, smooth plate of 

 ship length L in turbulent flow, is 1.451(10"'). 



Data are not available (1955) for determining 

 the allowances for longitudinal and transverse 

 curvature in the forms A^Cp and AjCp , respec- 

 tively, of Eq. (45. ii) in Sec. 45.7. However, in 

 Sec. 45.14 the value of ARp due to curvature in 

 the hull of the ABC ship has been calculated by 

 F. Horn's method and found to be 0.0606. 



Considering the plating roughness ApCp , a 

 reasonable value for the ship, when new, is 

 0.02(10"'), from Table 45.f of Sec. 45.18. Similarly, 

 a liberal value of the structural roughness AsCp is, 

 from the same table, 0.08(10"'). As the vessel is to 



be coated with an anti-fouling paint that has 

 selfrleveling properties, a conservative value of 

 AcCp is the highest one listed in Table 45.f, or 

 0.12(10"'). For 12 days out of dock, or 0.4 month, 

 the fouling allowance ApCp from the dasshed-line 

 curve of Fig. 45. L, applying to the ABC ship, is 

 about 0.04(10"'). Adding all these, SACp is 

 (0.02 + 0.08 + 0.12 + 0.04) (10"') = 0.26(10"'). 

 Then {Cp + SAC;,) = (1.451 -|- 0.26) (10"') = 

 1.711(10"'). 



It will be noted that, in the preliminary-design 

 stage of Sec. 66.9, ACp (actually SACp) was taken 

 as 0.4(10"'). When instructions were prepared to 

 test the models of the ABC ship, quoted in Sec. 

 78.6, the corresponding ACp value was taken as 

 0.3(10"'). These compare with the final estimate 

 of 0.26(10"'). 



The ARp value of F. Horn is equivalent to a 

 Cf. addition of 0.0606(1.711)(10"') = 0.104(10"'). 

 Taking account of this curvature correction, the 

 revised {Cp + SAC^) value is (1.711 + 0.104) 

 (10"') = 1.815(10"'). 



Then, by Eq. (45.ii), 



Rp = qS{Cp + ACp) = I V'SiCp + ACp) 



1.9882 



(34.62)'(47,875)(1.815)(10-') 



= 103,531 lb. 



As a matter of interest the {Cp + SAC,?) 

 values taken by inspection from Fig. 45. E, using 

 only the R„ value derived here, are: 



(1) Taking account of the ATTC 1947 allowance 

 for clean, new vessels, from curve B-B, 1.85(10"') 



(2) Considering the roughness allowance proposed 

 by L. A. Baier, from curve D-D, 1.85(10"') 



(3) Considering the roughness allowance proposed 

 by J. M. Ferguson, from curve C-C, 1.81(10"'). 

 These compare with the value 1.815(10"') derived 

 in the foregoing. 



45.23 Allowances for Friction Drag on Straight- 

 Element and Discontinuous-Section Hulls. The 



transverse curvature at an unrounded chine is 

 always sharp. It may be severe if the chine angle 

 (defined in diagram 3 of Fig. 27. A) is of the order 

 of 80 or 90 deg, as on short sailboats and motor- 

 boats, especially those which run at low F„ or T, 

 values. The Reynolds number is then low, the 

 Cp high, and the added friction due to convex 

 curvature is also relatively large. Coves or regions 

 of concave transverse curvature are rarely to be 



