Sec. 55.9 



APPENDAGE-RESISTANCE CALCULATIONS 



293 



^^^^^H^ 



kh^i 



Center-to -Centar DistanC' 



%^ 



/struts for Guord-Skeq- _t____^ \ !^^ 



Supp ort I ^^'II;:^*^—^^— ^^__ _j- 



Offset from (^ ^ -»^ 



' Length u_ 



FISH-EYE VIEW 



Fig. 55. D Definition Sketches for Appendages 



IN Varying Flow, Appendages in Tandem, and 



Appendages Abreast 



section shape if they are long and slender, with 

 their axes roughly parallel. A leading unit of 

 circular section generates a long separation zone 

 abaft it, in which the drag of the follo\ving unit is 

 diminished. On the other hand, a streamlined 

 leading unit leaves in its wake a trail of aug- 

 mented velocities, in which the drag of the 

 following unit is increased. 



(c) Whether the wake velocities from the leading 

 unit, positive or negative as the case may be, are 

 largely dissipated by the time the following unit 

 comes along. This is, as a rule, a function of the 

 ratio between the thickness and bluntness of the 



leading unit and the fore-and-aft distance to the 

 following unit. For well-streamlined sections, 

 normal to the flow, it may be the ratio between 

 the section length and the fore-and-aft center- 

 to-Center spacing. 



(d) Whether the traihng unit is so close to the 

 leading unit as to modify the flow around the 

 latter, over and above what it would be by itself 

 in an infinite stream, and to change the drag of the 

 leading unit. When placed close enough behind to 

 lie in the separation zone of the leading unit, the 

 follomng one may have negative drag, as dis- 

 covered by G. Eiffel [Hoerner, S. F., AD, 1951, 

 Fig. 7.1, p. 93]. 



Quantitative indications of what may be 

 expected when the two appendages or units are 

 in the form of struts are given by D. Biermann 

 and W. H. Herrnstein, Jr., in NACA Report 468 

 of 1933, entitled "The Interference Between 

 Struts in Various Combinations." Their conclu- 

 sions, to be found on page 522, indicate that 

 interference effects are to be expected if the 

 leading and following units are closer than 5 

 section lengths to each other, center to center. 



S. F. Hoerner also gives a considerable amount 

 of interference drag data for airfoUs (or hydro- 

 foils), flat discs, strut sections, and cyhnders in 

 tandem [AD, 1951, pp. 83-84, 93-94]. A. Borden, 

 D. B. Young, and W. M. Ellsworth, Jr., discuss 

 the drag situation in "Hydrodynamic Induced 

 Vibrations of Cylinders Towed in Various Combi- 

 nations," TMB Report C-452, September 1951. 



55.8 Modifications in Drag for Appendages 

 Abreast. The general situation relative to ad- 

 jacent appendages which must, to fulfill some 

 special design requirement, be placed abreast 

 each other, is depicted in diagram 3 of Fig. 55. D. 

 Graphs indicating the single and combined drag 

 of two 2-diml circular rods and of two 2-diml 

 streamlined strut sections, placed abreast, are 

 pubUshed by S. F. Hoerner [AD, 1951, Fig. 7.4, 

 p. 95]. These show that, whenever practicable, 

 the center-to-center transverse spread should 

 be at least 4 times the maximum transverse 

 section thickness tx ■ For a spread of 2tx (or 2D) 

 between the centers of a pair of circular cylinders 

 of infinite length, the drag coefficient Co of each 

 cyhnder is increased from its normal value of 

 1.2 to about 1.54. 



55.9 The Drag of Exposed Rotating Shafts. 

 An exposed rotating shaft, such as that driving 

 a screw propeller, generates two kinds of friction 



