Sec. 57.7 



TOTAL RESISTANCE OF BODY OR SHIP 



319 



XIV-XVII. These plates contain several of the 

 Telfer extrapolation diagrams. 



(4) Horn, F., "Die Weiterentwicklung des Modellver- 



suchsverfahrens zur Ermittlung des Schiffswider- 

 standes (The Further Development of Model Test 

 Methods to Obtain Ship Resistance)," Schiffbau, 

 16 Nov 1927, pp. 504-510, esp. Fig. 1 on p. 507 



(5) Telfer, E. V., "Frictional Resistance and Ship Re- 



sistance Similarity," NECI, 1928-1929, Vol. XLV, 

 pp. 115-184 



(6) SNAME, 1932, Fig. 13, p. 89, for three models of the 



U. S. S. North Carolina (old) series 



(7) Van Lammeren, W. P. A., "Propulsion Scale Effect," 



NECI, 1939-1940, Vol. 51, p. 115ff 



(8) Van Lammeren, W. P. A., Troost, L., and Koning, 



J. G., RPSS, 1948, pp. 39-40 and Fig. 13 



(9) Telfer extrapolation diagrams have been prepared for 



the Lucy Ashton family of models; see the references 

 hsted under (7) in Sec. 56.12, esp. INA, 1953, 

 Fig. 20 opp. p. 372 and Fig. 23 opp. p. 378; also 

 INA, Apr 1955, Figs. 12 and 13 opp. p. 122 



(10) Birkhoff, G., Korvin-Kroukovsky, B. V., and Kotik, 



J., "Theory of the Wave Resistance of Ships," 

 SNAME, 1954, pp. 359-396, esp. Fig. 1 on p. 361 



(11) Acevedo, M. L., Comments on Skin Friction and 



Turbulence Stimulation, 7th ICSH, 1954, SSPA 

 Rep. 34, 1955, pp. 110-117, esp. p. 115 



(12) Van Lammeren, W. P. A., van Manen, J. D., and 



Lap, A. J., "Scale Effect Experiments on Victory 

 Ships and Models. Part I — Analysis of the Resist- 

 ance and Thrust-Measurements on a Model Family 

 and on the Model Boat D. C. Endert, Jr.," INA, 

 Apr 1955, Vol. 97, Figs. 21 and 22 on pp. 184-185 

 and Fig. 25B on p. 232 



(13) Sund, E., "On the Effects of Different Turbulence- 



Exciters on B.S.R.A. 0.75-Block Models Made to 

 Various Scales," Norwegian Model Basin Rep. 11, 

 Aug 1951. Figs. 1 through 11 on pp. 19-22 embody 

 specific total resistance values, plotted on Reynolds 

 number, for four models having scale ratios of 15, 

 22.5, 30, and 45. 



(14) Pavlenko, G. E., "Soprotivleniye Vody Dvizheniyu 



Sudov (The Resistance of Water to the Movement 

 of Ships)," Moscow, 1953, Fig. 154, p. 250. The 

 diagram given is not exactly that of Telfer but the 

 graphic method is the same, including the addition 

 of a roughness allowance to the friction resistance 

 for the ship. 



The graphic procedure has several definite 

 advantages. First, it is easy to visualize the 

 agreement (or otherwise) of the several spots for 

 model tests at a given T^ or F„ with the inclined 

 extrapolation line for that speed-length ratio. 

 The analysis is made still easier by plotting R„ 

 on a log scale and Ct on a uniform scale because 

 the extrapolation hues are then all straight (or 

 very nearly so) and parallel, depending upon the 

 friction formulation used. Indeed, analysis by 

 any method other than a graphic one might be 

 intricate and laborious. Second, as pointed out by 



G. Birkhoff, B. V. Korvin-Kroukovsky, and J. 

 Kotik [SNAME, 1954, p. 361], it affords a plau- 

 sible separation of the total specific resistance 

 coefficient Ct into components, as well as an 

 excellent visual representation of those com- 

 ponents. Further, it visualizes the ship roughness 

 allowance and illustrates rather forcibly the 

 discrepancies which still exist because of inade- 

 quate model-testing techniques, lack of complete 

 knowledge of scale effects, and similar factors. 



The diagram of Fig. 57. C, deliberately drawn 

 in schematic fashion, illustrates most of the fea- 

 tures mentioned. The formula for the smooth, 

 flat-plate, turbulent-flow friction line is assumed 

 for simplicity to be an explicit function of Cf and 

 log Rn , so the Cf line is straight when plotted on 

 those coordinates. The horizontal gap between 

 the model range and the ship range is deliberately 

 closed to enable the features to be shown to 

 better advantage. It is assumed that the average 

 roughness allowance to be added to the friction 

 line representing hydrodynamic smoothness is 

 practically zero at the point Bi and increases as 

 indicated by the long-dash line B1B2 , correspond- 

 ing to the line CC on Fig. 45.E. 



The vertical distance between Ci and Ai , or 

 between C2 and Bj , is a measure of that portion 

 of the total specific resistance Ct which corre- 

 sponds to the separation drag, at speeds below 

 which there is practically no wavemaking drag. 

 However, as i2„ increases toward the ship range, 

 the hne C1C2 is not extended straight to C3 , but 

 beyond C2 becomes parallel to B1B2 , occupying 

 the short-dash position C2C4 . 



At small values of R„ , in the small-model range, 

 the boundary-layer thickness 5 (delta) increases 

 rapidly as the absolute model size diminishes. 

 Even though stimulating devices on the small 

 models render the flow completely turbulent the 

 boundary-layer thickness is so large in proportion 

 that the transverse velocity gradient at a given 

 point along the run is smaller than it is at the 

 corresponding point on the full-size ship or even 

 on a model of normal size. This means, by refer- 

 ence to Fig. 7.B on page 124 of Volume I, that 

 the port and starboard separation points on the 

 small model are farther forward than on the large 

 model or on the ship. The separation zone is thus 

 wider and the separation drag is larger. Further, 

 on the small model, there is a curvature effect, 

 transverse in particular, which adds to the specific 

 friction resistance Cp to be expected at that R„ . 

 As a third item, listed on Fig. 57. C, the small 



