Sec. 57.4 



TOTAL RE.Sl,STy\NCF. OF RODY OR SHIP 



315 



each case is largely frictional. In the high-speed 

 ranges, at and near designed-speed T, values of 

 1.6, 1.7, or more, Rp is only slightly greater 

 than O.Sflr . 



57.4 Methods of Approximating the Total Re- 

 sistance of a Ship. It is sometimes necessary to 

 estimate the total resistance of a ship at a given 

 speed, usually the designed speed, when nothing 

 more is known of it than its principal dimensions 

 and weight displacement. The ship in question 

 ma}' not even be designed or the one making the 

 estimate may never have heard of it before. The 

 ship has not been tested in model scale and there 

 is no opportunity of doing so before the resistance 

 estimate is required. 



A crude approximation of the total resistance, 

 for a speed V, is given directly by the formula 



Rt = Cr(0.5p)SF' 



(57.i) 



where Ct is estimated for the T, or F^ in question 

 by reference to the full-scale values for one or 

 more similar ships of nearly the same size, such 

 as those listed in the SNAME RD Summary 

 Sheets. The wetted area S is taken as the value 

 for the similar ship or is derived by the Cs 

 coefficient of Sec. 45.12. Care is required that the 

 reference ship is of about the same length as the 

 ship for which the total resistance is to be derived, 

 so that for a given T, or F„ the Reynolds number 

 R„ and the specific total friction drag coefiBcient 

 Cp are both nearly the same. 



For example, in the early stages of the ABC 

 design, described in See. 66.9, the total resistance 

 is required to furnish a first approximation of the 

 shaft power. Reference to the SNAME RD 

 Summary Sheets indicates that the destroyer 

 tender of RD sheet 96 closely resembles the ship 

 being designed. The latter sheet indicates that 

 the appendages are limited to a half -rudder only. 



For the tender, at its designed speed of 20 kt, 

 the value of the total specific resistance coefficient 

 Ct is 3.023(10^^) and the wetted surface S is 

 46,509 ftl The designed speed V for the ABC 

 ship is 20.5 kt, or 34.625 ft per sec; the numerical 

 value of V is 1,198.9. Then, for the ABC ship, 

 on the assumption of the same Ct and the same 

 S, and for roughly the same speed, 



Rt = Ct{0.5p)SV^ 



= 3.023(10~')(0.9905)(46,509)(1, 198.9) 



= 166,960 lb. 



This compares well, as a quick approximation, 

 with the value of 171,830 lb derived in Sec. 66.9 

 by the use of the Schoenherr mean friction line 

 and the Gertler reworked data of the Taylor 

 Standard Series described in Sec. 56.5. Actually, 

 for the destroyer tender, the Ct at 20.5 kt would 

 be higher than the figure quoted. 



One may, of course, pick a vessel from the 

 SNAME RD and ERD sheets having proportions, 

 shape, and form coefficients close to those .selected 

 for the vessel being designed. Reference to the 

 appropriate SNAME ERD sheet gives directly 

 the values of total resistance Rt , total resistance 

 per ton of weight Rt/^, and Pb for a geosim 

 vessel having a "standard" length of 100, 200, 400, 

 or 1000 ft, as indicated on the sheet. The total 

 resistance of the geosim ship of the length under 

 design is then determined by correcting for the 

 difference in friction resistance due to the differ- 

 ences in length and in speed between the reference 

 ship and the "design" ship. This scheme, or a 

 modification of it, has the advantage that curves 

 oi Rt and Pe can be constructed for a range of 

 Tj or F„ considerably greater than will be en- 

 coimtered in practice. The full-scale data on the 

 SNAME RD Summary Sheets are for the 

 designed-speed spot only. 



Another rapid method of approximating the 

 total resistance for the designed-speed spot is to 

 pick the value of Kt/A, at the proper T^ , from 

 the meanhne of Fig. 56.M. Multiplying this value 

 by the weight displacement A gives fir at once. 

 For example, the i2j./A value for the ABC ship, 

 at a T, of 0.903, is 10.2 lb. Multiplying by 17,300 

 tons, the displacement at an early stage of the 

 design, gives a total resistance of 176,400 lb. This 

 compares with the 171,830 lb quoted earlier in 

 the section. 



It is customary, if time is available, to estimate 

 separately the friction resistance Rp and the 

 residuary resistance Rr hy the methods of the 

 two sections following, using model-test data 

 from a parent form such as the Taylor Standard 

 Series. They are added to give the total resistance 

 Rt . This method enables the designer to draw 

 curves of estimated Rp , Rt , and Pp for a very 

 large range of Taylor quotient T^ or Froude 

 number F„ . 



Strictly speaking, the use of standard-series or 

 reference data from models or ships of different 

 shape, even though of the same dimensions and 

 proportions and having exactly the same form 

 coefficients, requires the use of a shape-correction 



