|
SHAFT SYSTEM DRAG As can be readily
determined from Kutta-Joukowski &
calculation of The Magnus Effect, removing
the rotational element from a marine shaft
greatly reduces Lift, Drag and the horse
power required to generate them. Enclosing
the shaft in a stationary casing then can be
calculated as straight forward drag based
upon presented area of the appendage. This
can be determined by viewing a standard NACA
Foil or fin section which is the elliptical
result of a cross section through a shaft at
the angle of incidence (shaft angle) of the
fluid stream. A chart of drag factors for
standard NACA foil series is shown below:
NACA Foil Series drag co-efficients
|
NACA Series |
|
Drag Co-efficients
(<
2 Degrees of incidence) |
| 63 |
|
0.0052 |
| 64 |
|
0.0045 |
| 65 |
|
0.0042 |
| 66 |
|
0.0038 |
The total drag on a fin or foil comes
from two major components, induced drag
(drag generated by lift) and profile drag
(drag created by the shape and size of the
foil). These two major drag components can
be thought of as "active" and "passive"
drag. Then, within "passive" or profile
drag, there are two further components, drag
due to the cross-section being presented to
the incident flow, and wetted surface area
drag due to the friction drag of the surface
of the foil.
The passive drag components are present
in both the enclosed as well as conventional
exposed shaft systems. It is worthy of note
however that the Magnus effect is more
detrimental to the performance and power
losses created by a spinning exposed shaft
in a conventional system due to the presence
of both “active”, “passive” and “vortex”
drag, than can be calculated for a
non-rotating enclosed system, which only
exhibits “passive” drag elements.
For every action there exists an equal
and opposite reaction, simply put, the
generation of lift, friction, and drag
requires an equal input of energy to
overcome itself.
Similarly, each cutlass style bearing
within the shaft system adds an additional
3% of lost energy, plus more losses
associated with stuffing boxes and shaft
seals averaging approximately 2%.
Extrapolation of the formulae defining the
Magnus effect in a series, shows an increase
relative to lift and velocity, therefore
total shaft horse power losses can range
from 6% to more than 10% after all the
components are added together. |