402 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 61.9 



TABLE 61.C — Calculation of Ship Friction Resistance For Case l.c 

 The data marked with asterisks (*) are from SNAME RD sheet 2. 



Example 61.11. The vessel selected is a tanker of 

 20,584 long tons displacement, 487.5 ft in length by 68 ft 

 beam by 29.87 ft draft, forming the subject of SNAME RD 

 sheet 2. It was tested as TMB model 3617. It is designed 

 to run at a speed of 16.5 kt in deep water. If the curve of 

 total resistance on ship speed, as determined by trials run 

 in unrestricted (unlimited) shallow water having an 

 average depth of 64 ft, is given by the curve through the 

 points C31 and C3 of Fig. 61.1, find the corresponding curve 

 for deep water. The trials were conducted in standard 

 salt water, at sea level, having a temperature of 59 deg F. 



From data on the SNAME RD sheet, the value of Cx 

 is 0.9803. Hence Ax = 0.9803(68)29.87 = 1,991.15 ft^. 

 Using the model Ax of 3.353 ft^ times X^ (= 594.14), this 

 comes out as 1,992.15 ft^. The square draft \/a.\- is 44.63 

 ft, whence VJ^/h is 44.63/64 = 0.6973. The wetted 

 surface S is, from the SNAME RD Summary Sheets, 

 51,047 ft^ 



The method of calculating the ship friction resistance 

 Rf for three selected values of Fn from SNAME ERD 

 sheet 2 follows that previously listed in Table 61. a, except 

 that the total-resistance calculation of the latter is omitted. 

 Plotting the Rp values on a basis of V/\/qk gives the 

 long-dash curve through the points F3 and E3 of Fig. 61.1. 



The solid curve through C31 and C3 is plotted from the 

 Rrh and the Vi, data observed on the trial. Although 

 designed for only 16.5 kt in deep water the vessel in question 

 had sufficient margin of power to make 16.5 kt in shallow 

 water, at a total resistance of 158,900 lb, corresponding to 

 point C3 . It is desired to know the deep-water speed Vco 

 which would be achieved at a total resistance Rtco equal 

 to the measured Rn at the speed Vu in shallow water. 



Better, it is desired to plot a (Rtoi — Im) curve for a 

 range of normal operating speeds from the (Rth — Vh) 

 data observed on the trials. 



Starting first with the 16.5-kt point at C3 , the value of 

 Vh/\/^gh is 0.6143. The position of the ordinate of the 

 point B3 , opposite C3 and at the same value of Rn , is 

 determined from the Yily/gh ratio. This is found by 

 entering the graph of Fig. 61. G with the known ratio of 

 square draft to water depth, where for this ship y/ Axl^ 

 is derived in the upper lines of Table 61. d. The Vh/Vi 

 ratio is found to be 0.958, whereupon Vj/y/gh is 

 {Vk/Vgh)/{Vh/Vi) or 0.6143/0.958 = 0.6412. The point 

 B3 is plotted upon this ordinate and a horizontal broken 

 line drawn from C3 to B3 on Fig. 61.1. 



The method of arriving at a correct value of V^Z-^/gh, 

 as described earlier in this section, is illustrated by the 

 steps listed in the lower portion of Table 61. d. Erecting 

 an ordinate at Vca/\/gh = 0.6467 and drawing a broken 

 line through B3 parallel to that portion of the friction- 

 resistance curve directly below it produces the intersection 

 A3 . This is one point on the desired (Rto, — Va,) curve. 

 The data for another point are derived in the right-hand 

 column of Table 61. d. 



The speed Fa, which would have been made in deep 

 water at the same total resistance Rti, as in shallow water 

 is found by extending the horizontal line C3B3 in Fig. 

 61.1 until it intersects the (Rrm — Vco) curve at the point 

 M3 . With a value of Vco/ \/gh = 0.6451 at this point, 

 Table 61.d indicates that the deep-water speed sought is 

 17.33 kt. This is 0.83 kt more than the speed made in 

 shallow water. 



