Yamazaki 



0.15 



10'Kfi 

 10'Kmx 

 10 "Kh* 



0.05- 



/^"Kmi — ■ 



0.70 



0.85 



1.00 



1.15 



Fig. 5 - Magnitudes of the vibrating parts 

 of the bearing forces of propeller M 



AKp.. AKi 



AKi 



AK,^,^, AK,^^ and AK,^,^, increase with increase of j, or with de- 



^Fx> ""^Fyj ^^^Fz) "'''■MX5 ""My> <*"" ""Mz 



crease of the mean thrust coefficient -K 



Fx' 



The mean values and the magnitudes of the vibrating parts of the bearing 



forces of propellers Mjj, M22, M32, M52, 

 shown respectively in Figs. 6 through 13. 



M43, M21 and M23 versus J are 



Let us examine the effect of skew on the bearing forces. It is found from 

 Figs. 6, 7, 8, 4, and 9 that the mean values of the bearing forces of the propel- 

 lers with a blade area ratio of 0.5748 have almost the same value for each J in- 

 dependent of the skews. Let us compare the magnitudes of the vibrating parts 

 of the bearing forces for each J. The values of AK^^, AKp^, AKp^., AK^,^, AK,^,y, 

 and AK,^j^ versus a for J - 0.85 and 1.00 are taken from Figs. 6, 7, 8, 5, and 9 

 and are shown in Fig. 14. It is found in Fig. 14 that all the magnitudes of the 

 vibrating parts of the bearing forces of the propellers with a constant blade area 

 ratio decrease with increase of backward skew. Similar results are obtained in 

 the cases of propellers Mji and M^j and in the cases of propellers M23 and M43. 



We will next examine the effect of the blade area ratio on the bearing forces. 

 To compare propellers M^j, M, and M43 on the basis of idea of thrust identity, 

 we use Figs. 10, 4, 5, and 11 and we calculate the ratios Rpy, Rp^ , R,^^^ , R^ , 

 ^MzJ ^^Fx, ARpy, ARpz, AR^^, AR^,y, and AR^,^ of propellers M^^ and M43 to propel- 

 ler M as shown in Fig. 15. Similarly we calculate the ratios of propellers Mji 

 and M23 to propeller M22 as shown in Fig. 16. It is found from Figs. 15 and 16 

 that the mean values and the magnitudes of the vibrating parts of the bearing 

 forces vary within 10% for blade area ratios between 0.43 and 0.72, excepting 

 Rp and ARp^, which vary about 15%. 



Finally let us consider the amplitudes of the bearing forces for the frequency 

 mn^N. The amplitudes Ap^^, Apy^, Ap^^, A^^^, A^,y^, and A^^^ of propeller M for 

 m > are shown in Table 5. Since the harmonic numbers n of the inflow velocity 

 are ±8 at most as shown in Eqs. (132) and Table 3, the amplitudes of the bearing 

 forces for m = 3 and 4 are negligibly small compared with those for m = 1 and 2. 

 The characteristics of the amplitudes versus J for m = 1 and 2 are similar in 

 tendency to the characteristics of the magnitudes of the vibrating parts versus J. 



70 



