84 



in OROm \ \MI(.S 1\ SHIP DESIGN 



Sec. H.13 



If rnkc or .xwoop-lmck is lu'Ci-ssjiry or licsirahlc 

 in the leading edpe of a hydrofoil, and if the trailing 

 edge is raked in the opposite direction so that the 

 hydrofoil has a taper ratio less than 1.0, the 

 behavior and characteristics may be estimated on 

 the basis of a number of chordwisc eiomcnts 

 liaving small spans Sh and varying chord lengths. 

 If the raked or swept-back hydrofoil has ajjpioxi- 

 mately constant chord over the span, it.s per- 

 formance may be predicted on a basis of (1) a 

 span normal to the relative-flow direction cc|ual 

 to the diagonal length of the hydrofoil, and (2) a 

 rciativc-flow velocitj" equal to the dircction-of- 

 motion speed times the cosine of the angle of 

 sweep-back. This corresponds to the situation 

 depicted in diagram 1 of Fig. 17. D on page 2G5 

 of \'olume I. 



The appropriate chapters of Part 5 in ^'olu^le 

 III describe and illustrate the manner in which 

 ship hulls themselves act as low-aspcct-ratio 

 hydrofoils. Of still smaller aspect ratio are the 

 fbced roll-resisting keels whose design is discussed 

 in Sees. 73.15 and 73. IG, especially the forward 

 portions which run at varying angles of attack 

 as the ship pitches and rolls. 



The ma.ximum section thickness /.v and thick- 

 ness ratios /.v/c arc, more often than not, fi.xed by 

 requirements for strength and stiflne.ss. Xevcr- 

 theles.s, it is well for the designer to know some- 

 thing of the effect of thickness ratio upon hydro- 

 foil drag. Fig. 44.J, adapted from "Modern 

 Developments in Fluid Dynamics," edited by S. 

 Goldstein (Fig. 137 on page 402 of Volume II), 

 indicates the variation in drag coefficient with 

 thickness ratio to be expected on a Joukowski 

 type of airfoil section at low /?, values. Fig. 44. K, 



vOOl 



Data Are for Joukowshc Airfoil Sections 

 ot a Reynolds Number Uc/k of 4 (lO*) 

 Drag Coefficients ore Based on Chord 

 Lenqth per Unit Span 



''ioniinor Flow on o Fiol Plote 



Jifl2 



m 55 — r — 35 



Thici<ne»» Rolio -^ 



Fifi. 'll-J Vaiiiatiom in ReHiDUARY-Diun Cokkkiciknt 

 ov J0UKOW8K1 Aiiiron. Skctionh With Tiiickncss IIatio 



Fio. 44. K Variation OF Total-Drao, Friction- 

 Drag, AND Residuary-Drag CkjEKKiciENTs of a 



JorKOWSKI .\lRFOIL WiTII THICKNESS RaTIO 



adapted from Fig. 138 on page 138 of Volume II 

 of the referenced book, gives representative 

 values for the total-drag, friction-drag, and 

 rcsiduary-tlrag coefficients, on a base of thickness 

 ratio, for Joukowski airfoil siH'tioiis. 



44.13 Quantitative Data on Cascade and In- 

 terference Effects. On the basis that interference 

 effects ill) exist between the flows around hydro- 

 foils placed abreast or in cascade, despite the 

 qualifying statement in the last paragraph of 

 Sec. 14.15 on page 228 of Volume I, the matter of 

 allowing for or predicting these effects poses 

 many difficulties. So far as known, there are no 

 reasonably simple or straightforward rules or 

 procedures by which the marine architect may 

 execute a proper new design or even estimate the 

 behavior of an existing design involving two or 

 more hydrofoils approximately abreast each other. 



In every screw propeller, even though it has 

 only two blades, there arc some small radii where 

 the stagger between blade sections is small with 

 respect to the gap. However, the interference 

 effects here, in the case of an analytic design 

 based upon the circulation or vortex theory, are 

 taken care of by other portions of the design 

 procedure, as described in Chap. 70. It is not 

 easy to transfer the correction procedure to 

 another problem, such as to that of twin or triple 

 steering rudders, side by side. 



Problems involving the use of ratlier closely 

 spaced hydrofoils in cascade are of common 

 occurrence in the design of pumps for handling 

 fluitls of all kinds. Allliough there is an extensive 

 literature in this field, the symbols, methods of 

 analysis, and design procedures for hydraulic 

 machinery' are so different from those customary 

 in marine proi>ulsion and relateii fieUls that they 

 are not in a form readily usjible by naval architects 

 and marine engineers. 



