where D = turning diameter (m)
LWL = length of waterline of ship (m)
CS = water salinity coefficient (saline = 1,
x = reamer width relative to midbody
brackish = 0.85 and fresh = 0.75)
length (%).
CH = hull condition factor (Inerta = 1, new
bare steel = 1.33 and old bare steel = 2)
For rounded vessels with fully effective rud-
B = ship beam (m)
ders, and in level ice of thickness equal to 60%
L = waterline length of ship (m)
of the icebreaking capability at 1m/s
T = draft of ship (m)
H = ice thickness, taken to be ice thickness
D/LWL = 0.022 (PMB)1.75 + 3
plus half the snow depth (m)
t = ice surface or air temperature (C)
where PMB is the percentage of waterline length
σf = flexural strength of ice (kPa)
representing a parallel midbody (%).
ψ = average flare angle in bow region ()
For rounded vessels with partially effective rud-
ϕ = average buttock angle in bow region
ders, and in level ice of thickness equal to 60% of
().
the icebreaking capability at 1 m/s
D/LWL = 0.14 (PMB)1.5 + 3.
For rounded-shoulder ships, an expression (us-
ing the same symbols) for the ice resistance at a
Open water resistance
speed of 1 m/s is given as
For chined vessels, open water resistance is ex-
pressed in terms of Froude number
R1 = 0.015 CS CH B0.7 L0.2 T0.1 H1.5
{1 0.0083 (t + 30)} {0.63 + 0.00074 σf}
R/Disp = 1.1 Fn1.64
ψ)1.6}
{1 + 0.003 (ϕ
5)1.5}.
{1 + 0.0018 (90
where R = open water resistance (kN)
Energy to penetrate an
Disp = ship displacement (tons)
unconsolidated ridge
Fn = Froude number v/ gL
Based on the full-scale data, an expression for
v = ship velocity
the energy to penetrate an unconsolidated ridge is
L = ship length between perpendiculars.
given as
For vessels of rounded shapes, open water re-
ER = 0.25 AC AR CS CH {1 0.0083 (t + 30)}
sistance is expressed in terms of Froude number
{1 + 0.012 (90 ψ)}
R/Disp = 0.4 Fn1.68.
where ER = energy for ridge penetration (MJ)
Propulsive performance
AC = largest cross-sectional area of vessel
Propulsive performance is defined as the ratio
(m2)
of net thrust to the shaft power (or specific net
AR = ridge depth ridge profile length
thrust). Keinonen et al. (1991) compared the pro-
(rubble only) (m2)
pulsive performance of different icebreakers at full
CS = water salinity coefficient (saline = 1,
power. The data are shown in Figure 24a for dif-
brackish = 0.85 and fresh = 0.75)
ferent speeds for ships having ducted propellers,
CH = hull condition factor (Inerta = 1, new
whereas similar data for ships with open propel-
bare steel = 1.33 and old bare steel = 2)
lers are shown in Figure 24b. A comparison of the
t = ice surface or air temperature (C)
data for the single-screw, ducted, controllable-pitch
ψ = average flare angle in bow region ().
system of Kigoriak and Arctic with that of twin-
screw, open, controllable-pitch system of Terry Fox
Turning circle diameter
shows that the net propulsive performance of the
For vertical-sided chined vessels, and in level
ducted systems has an advantage of 27% over the
ice of thickness equal to 60% of the icebreaking
open system at low speeds. However, this advan-
capability at 1 m/s
tage decreases at higher speed until both systems
have the same specific net thrusts.
D/LWL = 38 0.56x
27
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