292 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 55.6 



As an example of the application of these data, 

 one may estimate the drag of the extensible 

 sound-dome assembly shown in diagram 1 of 

 Fig. 55. D in Sec. 55.7. This is on the basis of no 

 hydrodynamic interference between neck and 

 hull or between neck and head, and the absence 

 of alternating cu'culation effects due to the 

 vortex trail. It may be assumed that the ship 

 speed is 12.3 kt, that the water is salt, at 59 deg F, 

 and that no account is taken of variations in 

 velocity across the boundary-layer thickness of 

 the hull. 



(1) For the neck, assume a diameter of 1.22 ft 

 and a length below the hull of 3.22 ft. The L/D 

 ratio is about 2.64 and the c?-Reynolds number 

 for 12.3 kt, or 20.77 ft per sec, is Ud/v = (20.77) 

 (1.22)(10')/1.2817 = 1.98 niilhon. This is greater 

 than the value of 5(10'"') in the lower portion of 

 the box of Fig. 55.B, devoted to the circular 

 cyhnder, with its axis normal to the flow. For 

 this situation Co = 0.35, hence 



D (for neck) = 0.35^^^^ [(3.22)(1.22)](20.77)- 



= 590.1 lb. 



(2) For the head, assume a diameter of 2.11 ft 

 and a length of 1.72 ft. The L/D ratio is about 

 1.23 and the Reynolds number is (20.77)(2.11) 

 (10')/1.2817 = 3.419 million. This is greater than 

 the 5(10^) referred to in the foregoing but much 

 less than infinity. Hence 



1 9905 

 D (for head) = 0.35 ^^^^ [(1.72)(2.11)](20.77)' 



= 545.3 lb. 



The total predicted drag is then 590.1 + 545.3 = 

 1,135.4 lb. 



A word may be said here about the drag of 

 some of the bodies represented on Figs. 55. B and 

 55. C after the cavitating range has been reached. 

 The drag coefficient Cd„ for a cavitation number 

 o-(sigma) is found to be related in fairly simple 

 fashion to the non-cavitating drag coefficient, as 

 described by P. Eisenberg [TMB Rep. 842, pp. 

 19-20], who gives values of the variables for a 

 few well-known forms. 



55.6 Allowances for Wake Velocities on 

 Appendage Drag. With friction drag varying as 

 a power of F in the range of 1.8 to 2.0, and pres- 

 sure drag — excluding that from wavemaking — 

 varying as V, it is important that a reasonably 

 correct value be used for the relative water 



velocity in the prediction of appendage resistance. 

 This means that it is necessary to estimate the 

 probable actual velocity past the appendage 

 (or its several parts) from the known or estimated 

 flow pattern around the ship, considering wakes 

 of all the kinds listed in Sec. 11.2 of Volume I 

 and in Chap. 52. For instance, in the example 

 concluding Sec. 55.5, if the shape of the ship and 

 the sound-dome position in the ship were given, 

 it could be estimated that for the 3.22-ft length 

 of the neck the local velocity in the boundary 

 layer would average only 0.78 of the ship speed. 

 For the head, it could be predicted that, because 

 of potential flow outside the boundary-layer 

 cloak, the average velocity past the head would 

 be 1.04 times the ship speed. 



The modified drag, not calculated here, might 

 not differ greatly from that derived in Sec. 55.5 

 but the moment of the drag, taken about the 

 point of support at the hull, would be considerably 

 greater. This is because the drag at various 

 ^/-distances is proportional to the square of the 

 local velocity U, which increases with the' y-dis- 

 tance from the hull. 



Some appendages Ijdng abaft propulsion devices 

 are acted upon by augmented velocities, to 

 develop thrust-deduction forces. Because of the 

 V^ effect, the percentage increase in drag for a 

 given condition is at least twice the percentage 

 augment of velocity. 



Those appendages (or parts of them) lying 

 within separation zones might have drag values 

 of the order of zero. 



55.7 Shadowing Allowances for Appendages 

 in Tandem. The shadowing allowance(s) for the 

 downstream unit(s) of a system of similar append- 

 ages in tandem, like the fins or portions of a 

 discontinuous roll-resisting keel, diagrammed in 

 Fig. 36. M on page 553 of Volume I, or for any 

 appendage lying downstream from another, 

 indicated in diagram 2 of Fig. 55. D, depends upon: 



(a) Whether or not the after unit is actually 

 downstream from the leading one, having in 

 mind the local direction of flow rather than the 

 overall direction of motion. If directly in the 

 wake of the upstream unit, th« following one 

 may benefit from positive wake velocities due to 

 viscous flow or separation. If slightly to one side 

 or the other it may suffer increased drag because 

 of the augmented velocity -\-AU left in the water 

 that passed around the leading unit. 



(b) The shape of the bodies, particularly their 



