whereLis the length of the tow, the maximum drift angle, bthe width of
the tow, cthe clearance between the tow and channel bank and cthe
clearance between the passing tows; suffix ‘d’ refers to a downbound and
‘u’ to an upbound tow. The result of computations using equation (11.3)
can be checked against equation (11.1).
11.6 Resistance of ships
The interaction of a ship with the surrounding body of water is a compli-
cated one, particularly in a constricted waterway where, furthermore, the
interaction of the flow and waves generated by navigation with the banks
and bed of the waterway has to be taken into account. These factors,
together with the power and speed requirements of the tow, determine the
design of the navigation fairway, which also has to take into account the
various bottlenecks encountered, e.g. fixed and movable bridges, off- and
intakes, harbour entrances and exits, navigation locks, river and canal
crossings, ferries, bypasses, crossing of lakes used for recreation, etc.
As a vessel moves along a waterway a backflow of water occurs,
filling the space vacated by the submerged volume. In a restricted space
the velocities of the backflow can be considerable. Furthermore, the water
level along the vessel is depressed, with the greatest depression occurring
near midship. The bank protection required on constricted waterways has
to withstand these velocities, as well as the effect of waves generated by
the movement of the vessels. Effective bank drainage is essential.
The maximum flow velocity for upstream navigation to be economic-
ally viable is about 2.5 m s^1. The speed of vessels and tows is limited by
RESISTANCE OF SHIPS 473
Fig. 11.5 Bends and tow drift on a waterway (Novak, 1994)