Sec. 45.13 



FRICTION-RESISTANCE CALCULATIONS 



109 



troughs, but this is largely compensated for by 

 the bodily sinkage of the ship while in motion, 

 described in Sec. 29.2. The reduction in wetted 

 surface becomes appreciable, of course, when a fast 

 or high-speed boat approaches or reaches the 

 planing range. 



Often it is definitely known that a separation 

 region exists along some part of the wetted surface, 

 such as that behind a transom stern or inside a 

 sizable rudder recess, or the extent of the zone 

 can be estimated with reasonable certainty. The 

 wetted area next to the separation zone is then 

 subtracted from that of the rest of the ship, 

 considering the extent of the zone constant at all 

 speeds [Horn, F., 3rd ICSTS, 1937, p. 22; Acevedo, 

 M. L., "Skin Friction Resistance," Madrid, 

 1948, p. 14]. 



When a fixed appendage covers a part of the 

 main ship hull, such as a roll-resisting keel of 

 V-section, the area so covered is subtracted from 

 the calculated wetted area of the hull. 



Although all hull and appendage wetted areas 

 are frequently lumped together, and although 

 there is some justification for adding an allowance 

 for appendages to the wetted surface S in the 

 early stages of a design, before the appendages 

 are laid out, it is preferable to make separate 

 wetted-surface calculations for the appendages. 

 This gives the designer an idea of what is being 

 added to the S value of the ship. 



Summarizing, the calculation of the wetted 

 surface of a ship, when the shape and size of the 

 hull and the underwater appendages are known, 

 takes the following form: 



(1) If the lines are not yet drawn, estimate the 

 wetted surface by the use of the wetted-surface 

 coefficient Cg from Fig. 45. H, then combine it 

 with the underwater volume ¥ and the waterline 

 length L in the formula S = Cs 'V'VL. Add a 

 percentage or an area allowance for the contem- 

 plated appendages, if it can be estimated at this 

 stage and if it is considered necessary. 



(2) With ship lines available, measure the girths 

 from designed waterline to designed waterline at 

 21 or more equally spaced stations along the 

 waterhne length, including the FP. Compute the 

 mean girth from Simpson's first rule [PNA, 1939, 

 Vol. I, p. 16] or the equivalent, and multiply the 

 mean girth by the waterline length. When measur- 

 ing the girths, include large bossings or skegs and 

 discontinuities in the sections where the ship 

 plating is carried continuously around them. Be 



generous in measuring girths to include the shell 

 plating outside the molded lines. 



(3) For large appendages, especially those long 

 enough to have an a;-Reynolds number exceeding 

 15 million, calculate the wetted girth as for (2) pre- 

 ceding and multiply by the length projected on 

 the centerplane 



(4) For small, short appendages, excluding rotat- 

 ing shafts and the like and the propulsion devices 

 proper, if their resistance is primarily frictional, 

 calculate the wetted surface by any convenient 

 method 



(5) Make no allowance or correction for actual 

 wetted surface between the at-rest WL and the 

 wave profile when the ship is in motion except 

 for F„ > 0.6, Tj > 2.0, or for unusual cases 



(6) Estimate the wetted surfaces of zones of 

 separation, if it is practically certain that they will 

 exist at the speeds for which resistance and power 

 estimates are wanted. Otherwise, neglect them. 



(7) Calculate the hull area covered by the attach- 

 ments of fixed appendages of appreciable size 



(8) Add the areas of (2), (3), (4), and (5), and 

 subtract the areas (6) and (7). The result is the 

 value of wetted surface S for the design. 



45.13 Wetted-Surface and Boundary-Layer 

 Calculations for the Transom-Stem ABC Ship of 

 Part 4. The wetted-surface calculation for the 

 preliminary design of the transom-stern ABC ship 

 designed in Part 4 of this volume is made by 

 using Eq. (45.vii), namely S = CsvVL. When 

 the hull lines are available this is checked by a 

 calculation embodying the measured girths at 21 

 stations, plus those at four half-stations near the 

 ends, namely 0.5, 1.5, 18.5, and 19.5. 



At the stage corresponding to the first estimate 

 of wetted surface the pertinent parameters are: 

 Bx/Hx = 2.808; Cx = 0.956; V = 574,000 ft'. 

 The latter is derived from an estimated weight 

 displacement of 16,400 t and a round-number 

 volume density of 35 ft'' per ton. Entering the 

 0-diml wetted-surface coefficient contours of Fig. 

 45. H with the first two parameters, the value of 

 Cs by inspection is 2.616. The location of this 

 point is shown on the diagram by the distinctive 

 double circle with its black lower half, used in 

 this volume for the ABC design. Substituting 

 these values in Eq. (45.vii), 



S = CsVVL = 2.616 \/(574,000)510 

 = 44,759 ft'. 



