588 



HYDRODYNAMICS IN SHIP DESIGN 



Sec. 70.4 



(IX) Charts of H. H. W. Keith (formerly pro- 

 fessor of naval architecture at MIT). These were 

 carefully drawn to about 7.25 in by 7.25 in, but 

 were never pubUshed. They involve two coeffi- 

 cients: 



Loading coefficient Ku = 



Cn = 



NU° 



Taylor's B^j) 



tto.s 

 Cr, 



(this is identical with D. W. 



DV\ 



where A'' is the rate of rotation in rpm, U is the 

 thrust power in English horses, D is the propeller 

 diameter in ft, and Va is the speed of advance 

 inkt. 



The values of Cn and e (= efficiency rjo) are 

 plotted on a grid of Co and P/D. The latter scale 

 is uniform and exceptionally large. Photostats 

 of these charts are in the TMB library. 

 (X) Charts of J. G. Hill [SNAME, 1951, pp. 

 631-633]. The principal coefficients are; 



_ 2TrQn 

 (_ P — 



vD'V 



where V is the speed of advance {V^ in ITTC nota- 

 tion) and all other symbols are standard. The 

 propeller efficiency ijo (not so marked) is shown by 

 contours on the two sets of diagrams. To render 

 them more compact they are plotted as the square 

 roots of Cp and Cs on a base of J in each case. 



(XI) Charts of C. W. Prohaska. These are log- 

 arithmic-type diagrams based upon the earlier 

 charts of G. Eiffel and W. Schmidt. They embody 

 both the dimensional coefficients of D. W. Taylor 

 and a group of corresponding 0-diml coefficients, 

 with double inclined logarithmic scales. Examples 

 of these charts are given in Figs. 70.A and 70.B 

 to follow, and they are described in Sees. 70.5 

 and 70.6. 



(XII) Charts of F. M. Lewis [SNAME, 1951, 

 pp. 612-615 and 618-620]. The principal coeffi- 

 cients are: 



Thrust coefficient Kt = 



T 



pn'D* 



PD'V} 



Torque coefficient Kq = 



p7l'D 



Efficiency e(= jjo) = jf^'^' 



These charts give contours of the 0-diml co- 

 efficients Kt , Kq , Ku , and e (= efficiency r?o), 

 as listed in the foregoing, on a basis of J and 

 P/D, using data from the Wageningen B.3 and 

 B.4 series of model propellers. A number of 

 examples in the reference cited show how these 

 charts are used. 



(XIII) Charts of W. E. Fermann, formerly of the 

 General Motors Corporation, developed specif- 

 cally for towing and similar situations where the 

 values of the advance coefficient are extremely 

 low. These charts are in four groups: 



Design coefficient So = VA[p<f/PsY^^ as ab- 

 scissas and pitch-diameter ratio a = p/d as 

 ordinates (uniform scale), with contours of pro- 

 peller efficiency ep and advance coefficient 

 J = 101. 3dV a/ {Npd), and a reference line of 

 ei>(Maj) with So constant 



Design coefficient S^ = V a[p/{PsNp)]^''^ as 

 abscissas and pitch-diameter ratio a = p/d as 

 ordinates (uniform scale), with contours of ep and 

 J = 101.33V a/ (Npd), and a line of e^jMaj, with 

 (Sjv constant 



Design coefficient Eo = VA[pd^/PuY^^ as ab- 

 scissas and pitch-diameter ratio a = p/d as 

 ordinates (uniform scale), with contours of Cp 

 and J = 101.33V a/ (Npd) and a line of ep(Mai) 

 with Ej) constant 



Design coefficient E.y = Va[p/{PuNp)Y^^ as 

 abscissas and pitch-diameter ratio a = p/d as 

 ordinates (uniform scale), with contours of ep and 

 J = 101.33V a/ (Npd) and a line of epfu^x) with 

 Etf constant. 



Here Va is the speed of advance in kt, Ps is 

 the shaft power (per shaft) in horses, Np is the 

 propeller rpm, d the propeller diameter in ft, 

 p the propeller pitch in ft, and p the mass density 

 of the water. 



As mentioned previously, Fcrmann's charts are 

 particularly valuable for the design of propellers 

 for tugs and for towing purposes which operate 

 at low speeds of advance and high thrust-load 

 factors. For many of these problems the range of 

 D. W. Taylor's charts is entirely inadequate. 

 The Fermann charts have not been published 

 or circulated but a set is available in the TMB 

 library. 



