Summary
The general formulae for determining the circulation function for a finite number of blades, as given by Goldstein, has been evaluated for six-and eight-bladed propellers. The values of Bessel functions necessary for this purpose were computed, as the authors were not aware of any known tables listing them.
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Abbreviations
- R :
-
Radius of the propeller blade
- ω:
-
Angular velocity of the blade
- r:
-
Distance of any blade element from the axis of rotation
- r * :
-
=r/R. Dimensionless radius parameter, i.e. 0 <r* < 1
- ν:
-
Velocity of advance of the propeller
- w :
-
Velocity of the vortex screw surface, moving as a rigid body in the
- μ:
-
= ωr/ν;μ 0 = ωR/ν
- λ i :
-
= ν/ωR Advance ratio
- I n (t):
-
Modified Bessel function of the first kind
- K n (t):
-
Modified Bessel function of the second kind
- Z :
-
Number of blades
- Γ :
-
Circulation round any blade element
- K :
-
=ZΓω/2πων Circulation function
References
Goldstein. S., On the vortex theory of screw propellers. Proc. roy. Soc. A123 (1929).
Watson, G. N., A treatise on Bessel functions.
Lock, C. N. H., and D. Yeatman, Tables for use in an improved method of airscrew strip theory calculation. Brit. A.R.C.R. & M. No. 1674 (1935).
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Acharya, Y.V.G., Janakiram, G. Circulation distribution for six- and eight-bladed propellers. Appl. sci. Res. 3, 410–414 (1953). https://doi.org/10.1007/BF03184721
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DOI: https://doi.org/10.1007/BF03184721