Sec. 56.9 



OBSERVED SHIP-RESISTANCE DATA 



307 



residuary resistance of the hull of a model varies 

 with speed in the equation Rr = fc(0.5p)SF". 

 This matter was investigated many years ago by 

 D. Kemp [INA, 1883, pp. 124-125]. He stated 

 that on the steam yacht Oriental the resistance 

 (total in this case) varied as about V^ in the low- 

 speed, range, but increased to about F"* in a T, 

 range of 0.82 to 1.04, F„ of 0.244 to 0.310. It is 

 known from measured .ship-thrust data that 

 Rf for hull surfaces of normal roughne.ss varies 

 as slightly less than the square of the ship speed, 

 probably of the order of the 1.9 or 1.93 power. 

 Although the absolute values of Cf cover a 

 rather wide range, the rates of change of Cf with 

 V, as indicated by a plot of Cf on R„ (with L 

 and j'(nu) constant), are comparatively small. 

 That portion of the hull drag due to deflection of 

 the water, separation, and similar effects is 

 assumed to vary as V~. Unfortunately, since Rr 

 includes these effects plus the drag due to wave- 

 making, it is still difficult to break up what has 

 hitherto been classed as residuary resistance into 

 physical entities. 



Analytic work on pressure drag due to wave- 

 making, described in Chap. 50, indicates that 

 what may be termed the V^ component is only 

 one of those acting. There are components of this 

 drag which vary as the 4th, the 6th, the 8th, and 

 higher powers of V. The expressions for these 

 components are periodic in form, and they produce 

 humps and hollows in the predicted ship-resistance 

 curve, similar to those due to surface-wave inter- 

 ferences in model tests. It is to be expected, 

 therefore, that graphs of pressure drag on a 

 basis of speed will show rather pronounced irregu- 

 larities. 



D. W. Taylor made up graphs of this type for 

 two groups of five models each, representing 

 400-ft ships. The two groups had Cp values of 

 0.56 and 0.64, respectively, and five different 

 displacements, with ship values ranging from 

 1,920 to 11,520 tons. Using the formula Rr = aV" 

 and plotting the velocity exponent n on a basis 

 of ship. speed, he obtained the curves shown in 

 Fig. 54 on page 48 of S and P, 1943. For some of 

 the models the residuary resistance varied at a 

 rate exceeding the 11th power of the speed V. 

 This diagram shows definite, rather narrow lanes 

 embracing all the n values over certain speed 

 ranges, despite the 1 to 6 variation in displace- 

 ment-length quotients. 



To determine whether there are systematic or 

 characteristic patterns in the exponent n of the 



residuary-resistance formula Rjt — kV", for the 

 principal forms of ship hulls, there are plotted in 

 Fig. 56.L the values of n from model test data on 

 nine different vessels, as reported on the SNAME 

 RD sheets listed hereunder: 



RD sheet 39 Passenger ship 



56 Tanker 



74 Tug 



79 Cargo ship 



92 Ore ship 



96 Destroyer tender 



119 Destroyer 



121 Heavy cruiser 



Normandie 

 Tanker E [SNAME, 



1948, pp. 368-369] 

 TCB Design TX-7 

 U. S. Mar. Comm. C-i 



cargo vessel 

 Wilfred Sykes 

 U. S. S. Dixie 

 U. S. S. Hamilton 

 U. S. S. Pensacola 



ABC ship of Part 4 Transom-stern design. 



The residuary resistances for these models were 

 calculated from the formula Rr = Cii{0.5p)SV^, 

 using the values of residuary resistance coefficient 

 lO^Cjj fisted on the RD sheets for a range of 

 speed-length quotients. These were, in turn, 

 calculated from the observed model resistance 

 data and the ATTC 1947 friction formulation, as 

 described in the SNAME Explanatory Notes 

 accompanying the RD sheets. Technical and 

 Research Bulletin 1-13, July 1953. 



The ship wetted surfaces were obtained from 

 the model wetted surfaces by multiplying by 

 X^(lambda). The Rr values were plotted on 

 log-log paper on a basis of T„ and F„ . The velocity 

 exponents n were obtained by measuring the 

 slopes of the Rr curves at even T^ values. This 

 work is facilitated by the use of special log-log 

 plotting sheets, available at the David Taylor 

 Model Basin, which have a supplementary scale 

 of slopes around the margin, to which a slope 

 anywhere on the sheet is transferred by a set of 

 parallel rulers. 



A curve oi Rr increasing with V on Fig. 56. L is 

 associated with a finite positive value of n. If the 

 resistance remains constant with increasing V, 

 then n = 0, whereas if R decreases as V increases, 

 which it does in certain speed ranges for planing 

 and other craft, as shown on Fig. 53. D, n becomes 

 negative. Large circles on the n-curves indicate 

 the T, for the designed speed along the curve for 

 each ship. 



The new velocity-exponent curves indicate that: 



(a) The curves for various ship types by no 

 means follow the same pattern, nor do they fall 

 in lanes, as do D. W. Taylor's earlier data [S and 

 P, 1943, p. 48] 



(b) The n-value for the big ore ship reaches 5.75 



