398 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 61.7 



STEPS 1 Colculote or Deten 

 for Deep Woter 



2. Calculate V;j„//SR Values Cornespondinc^ 

 and Plot Groph af Rjm °" Mao/i^ 



i Calculate CRfo„-V„) Values ond Plot 

 on F?T and Veo /y^h" Scales 



4. Fix Ag ot Selected V„/y^ Ratio 



5. Determine Vi/v,^ from Fiq. 61-E 



ond Draw Ordinate for Vj/y^fi 

 6. Prow AgB;^ Porollel to EgF^ 



0.5a 0.54 0.56 QSa 0.60 0.6E 0,64 066 0.68 0.70 0.7Z 0.74 0.76 0.78 

 Cnticol Wave-Speed Ratio -^- 



03Z Q84 0.86 088 Q90 



Fig. 61 .H Diagram Illustrating Construction op a Shallow- Water Resistance-Speed Curve From a 



Deep-Water Curve 



square draft '\/Ax is 33.34 ft, whence \/Ax/h is, by- 

 calculation or from Fig. 61. D, 1.389. Even with a bed 

 clearance of 24 — 17.5 = 6.5 ft, the square draft is much 

 larger than the actual water depth. 



The value of the critical-speed ratio Va,-\/gh for a 

 speed of 13 kt, or 21.96 ft per sec, and a depth of 24 ft, is 

 found from Fig. 61. F, or by calculation, to be 0.790. In 

 this case a range of Vco'\/gk of 0.60 to 0.90 appears to be 

 ample for the abscissas of the points corresponding to 

 Ai and Ei in Fig. 61. B. Instead of using a horizontal scale 

 of ship speed V, as in Fig. 61.B, the abscissas of the new 

 diagram for this case, reproduced as Fig 61.H, are plotted 

 on a base of VatyTgh, to facilitate entry into the VjlYa> 

 curves of Fig. 61. E. 



It is again pointed out that when the water depth h 

 and the ship length L are fixed, as in this case, the Kpco 

 and Rrm curves, whether plotted on a base of Ya, , of 

 Vm/y/gh, or of Va>/\/gL, have e.xactly the same shape, 



provided the horizontal scales are consistent. The hori- 

 zontal scale to be used is therefore strictly a matter of 

 convenience, provided it is based on a velocity. 



The first step in the solution is to find the full-scale 

 ship values of Rrm and Rpa, for the range of values of 

 Va>/\/gh from 0.60 through 0.90, so that the deep-water 

 curves may be plotted. This is possible by using the 

 values of {IOsjCr for a series of values of F„ for the speed 

 range in question, available on SNAME ERD sheet 9 

 for a 400-ft ship. These particular values apply to a geo- 

 metrically similar ship of any length. 



The Cfl values for a range of F„ from 0.1637 to 0.2233 

 are set down as the first line of entries in Table 61.a. A 

 short calculation, as listed in the upper part of that table, 

 indicates that this range of f„ gives a range of critical- 

 speed ratio Vo,/Vyk of from 0.6425 to 0.8765 for the 

 given estuary depth of 24 ft. The method of working out 

 the friction and the total deep-water resistances Rf^o and 



