343_add_Added Masses of Ship Structures.pdf - 8.1 Forces and Torques of Inertial Nature Acting on a Propeller 335 Since(8.3 must identically coincide

# 343_add_Added Masses of Ship Structures.pdf - 8.1 Forces...

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8.1 Forces and Torques of Inertial Nature Acting on a Propeller 335 Since ( 8.3 ) must identically coincide with ( 8.1 ), taking into account that the added masses λ ik coincide in both formulas, we get λ 12 = λ 13 = λ 15 = λ 16 = λ 24 = λ 34 = λ 45 = λ 46 = 0 . (8.4) For four-blade propeller, when Z = 4 and β = π/ 2, the formula ( 8.2 ) takes the form 2 T = λ 11 u 2 1 + λ 22 u 2 3 + λ 33 u 2 2 + 2 λ 12 u 1 u 3 2 λ 13 u 1 u 2 2 λ 23 u 2 u 3 + 2 u 1 14 u 4 + λ 15 u 6 λ 16 u 5 ) + 2 u 3 24 u 4 + λ 25 u 6 λ 26 u 5 ) 2 u 2 34 u 4 + λ 35 u 6 λ 36 u 5 ) + λ 44 u 2 4 + λ 55 u 2 6 + λ 66 u 2 5 + 2 λ 45 u 4 u 6 2 λ 46 u 4 u 5 2 λ 56 u 5 u 6 . (8.5) Comparing ( 8.1 ) with ( 8.5 ), we get the following relations between the added masses of a four-blade propeller: λ 22 = λ 33 ; λ 55 = λ 66 ; λ 25 = λ 36 ; λ 26 = − λ 35 ; λ 12 = λ 13 = λ 23 = λ 15 = λ 16 = λ 24 = λ 34 = λ 45 = λ 46 = λ 56 = 0 . (8.6) For a three-blade propeller ( Z = 3), as well as for propellers with higher number of blades ( Z 5) one has to compare the formulas ( 8.1 ) and ( 8.2 ). Coincidence of coefficients in front of pairwise products u i u k for i

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