Yamazaki 



1 N 



+ V*g{sin[5^,(^) + SJ 1. [sin^(^) - ^(^) cos ^(^)] '■•■ 



- cos [0^,(^) + S^][i.0^,(^) + ^e] sin^(^)}) ^d^, '- 



KmzD = - ^ f E Cpd[1 + iv/^f] Vt,(V*, cos [0^(O + K] ^ sin ^(^) 



+ V*^{cos [%(^) + S^] V [sin ^(^) - e{^) cos ^(^)] y -v \ 



+ sin [0m(^) + S^] [ve^{^) + ^e] sin^(^)}) ^ d<f . ^24) 



From Eqs. (56) we get the thrust coefficient c^ and torque coefficient Cq: 



Ct = - Kp^ , Cq= k^,^ . (125) 



Further, denoting the components of Kp^ , Kp^, etc., for a harmonic number c by 

 K^^^, K^y-*, etc., respectively, assuming that Cp^ is a constant independent of k 

 and s instead of the expression in Eqs. (122), and using the formula 



N fNe-imNs _ for £ ^ mN , 



Y^ e'''^ A (126) 



k=i , for E 7= mN , 



then Eqs. (122) and (123) are reduced to 



_ V vCniN) -imNs „ _ .r-, „ ( mN ) -imNs „ _ yh ^r(mN) - imNs 

 %x " /_, '^Fx ^ ' '^Fy - 2_, Fy ^ ' ^Fz " 2_, F 



'Fz 



(127) 



T, _ V"" v(mN) -imNs „ _ V"' Tr(mN) -imNs ^ _ v-" „(mN) -imNs 



•^Mx - Z. ^Mx ^ • '^My - Z^ *^My ^ • *^Mz " 2_. '^Mz ^ 



where 



(mN) _ (mN) (mN) (mN) _ (mN) (mN) (mN) _ (mN) (mN) 



^Fx - %xO + %xD • %y - %yO ■*" '^FyD ' %z " %zO "^ %zD 



''Mx " ''MxO ^ '"MxD ' "^My ' '^MyO "*" ''MyD ' *^Mz " '^MzO ^ ''MzD 



60 



(128) 



