Practical Ship Hydrodynamics

64 Practical Ship Hydrodynamics
Schneekluth and Bertram (1998) give several empirical formulae to estimate
w in simple design approaches. All these formulae consider only a few main
parameters, but actually the shape of the ship influences the wake considerably.
Other important parameter like propeller diameter and propeller clearance are
also not explicitly represented in these simple design formulae.
The ratio of the effective power to the thrust power is called the hull efficiency:
H D PE
PT
D RT Ð Vs
T Ð VA
D
1 t
1 w
The hull efficiency can thus be expressed solely by thrust deduction factor t
and wake fraction w. H can be less or greater than 1. It is thus not really an
efficiency which by definition cannot be greater than 100%.
The power delivered at the propeller can be expressed by the torque and
the rpm:
PD D 2 Ð n Ð Q
This power is less than the ‘brake power’ directly at the ship engine PB due
to losses in shaft and bearings. These losses are comprehensively expressed
in the shafting efficiency S: PD D S Ð PB. The ship hydrodynamicist is not
concerned with PB and can consider PD as the input power to all further
considerations of optimizing the ship hydrodynamics. We use here a simplified
definition for the shafting efficiency. Usually marine engineers decompose
S into a shafting efficiency that accounts for the losses in the shafting only and
an additional mechanical efficiency. For the ship hydrodynamicist it suffices
to know that the power losses between engine and delivered power are typically
1.5–2%.
The losses from delivered power PD to thrust power PT are expressed in
the (propeller) efficiency behind ship B: PT D B Ð PD.
The open-water characteristics of the propeller are relatively easy to measure
and compute. The open-water efficiency 0 of the propeller is, however,
different to B. Theoretically, the relative rotative efficiency R accounts for
the differences between the open-water test and the inhomogeneous threedimensional
propeller inflow encountered in propulsion conditions: B D R Ð
0. In reality, the propeller efficiency behind the ship cannot be measured
and all effects not included in the hull efficiency, i.e. wake and thrust deduction
fraction, are included in R. R again is not truly an efficiency. Typical
values for single-screw ships range from 1.02 to 1.06. Schneekluth and Bertram
(1998) give again simple empirical formulae for design purposes.
The various powers and efficiencies can be expressed as follows:
PB >PD >PT >PE
PE D H Ð PT D H Ð B Ð PD D H Ð 0 Ð R Ð PD D H Ð 0 Ð R Ð S Ð PB
D D Ð S Ð PB
The propulsive efficiency D collectively expresses the hydrodynamic efficiencies:
D D H Ð 0 Ð R. Schneekluth and Bertram (1998) again give simple
design estimates for D.