Course Teacher: Dr. Md. Mashud Karim, Associate Professor, Dept. of NAME, BUET
Course #: NAME 324
Assignment # B.3: Approximate Calculation of Ship Resistance
Hotrop and Mennen’s Method
The total resistance of a ship can be
subdivided into:
R
T
=R
F
(1+k
1
)+R
APP
+R
W
+R
B
+R
TR
+R
A
Where,
R
F
Frictional resistance according to
the ITTC 1957 friction formula
= 0.5.ρV
2
SC
F
.
C
F
= 0.075/(Log
10
Re-2)
2
Re Reynold’s
No.=
ρVL /µ
1+k
1
Form factor describing the viscous
resistance of the hull form in relation
to R
F
R
APP
Appendage resistance
R
W
Wave-making and wave-breaking
resistance
R
B
Additional pressure resistance due
to bulbous bow near the water
surface
R
TR
Additional pressure resistance of
immersed transom stern
R
A
Model-ship correlation resistance
The form factor of the hull can be predicted
by:
}
)
0225
.
0
1
(
)
95
.
0
(
)
/
(
93
.
0
{
1
6906
.
0
521448
.
0
92497
.
0
12
13
1
lcb
C
C
L
B
c
c
k
P
P
R
+
−
−
+
=
+
−
In this formula, C
P
is the prismatic coefficient
based on the waterline length, L and lcb is
the longitudinal centre of buoyancy forward
of 0.5L as a percentage of L. Here, L
R
is a
parameter reflecting the length of the run
according to:
L
R
/L=1-C
P
+0.06C
P
lcb(4C
P
-1)
C
12
=(T/L)
0.2228446
if T/L > 0.05
=48.20(T/L-0.02)
2.078
+0.479948 if
0.02<T/L<0.05
=0.479948 if T/L<0.02
Where T is the average moulded draught.
C
13
=1+0.003C
stern
C
stern
will be -10, 0 and +10 if the afterbody
form is of V-shaped, Normal and U shaped
sections respectively.
The wetted area of the hull can be
approximated by:
B
BT
WP
M
B
M
C
A
C
T
B
C
C
C
B
T
L
S
/
38
.
2
)
3696
.
0
/
003467
.
0
2862
.
0
4425
.
0
453
.
0
(
)
2
(
+
+
−
−
+
+
=
where A
BT
is the transverse sectional area of
the bulb at the position where the still-water
surface intersects the stem.
The appendage resistance can be
determined from
R
APP
=0.5ρV
2
S
APP
(1+k
2
)
eq
C
F
Where S
APP
the wetted area of the
appendages,
1+k
2
the appendage
resistance factor
Approximate 1+k
2
values
Rudder behind skeg 1.5~2.0
Rudder behind stern 1.3~1.5
Twin-screw balance rudders 2.8
Shaft brackets 3.0
Skeg
1.5~2.0
Strut bossings 3.0
Hull bossings 2.0
Shafts 2.0~4.0
Stabilizer fins 2.8
Dome 2.7
Bilge keels 1.4
The equivalent 1+k
2
value for a combination
of appendages is determined from:
(1+k
2
)
eq
=
∑
∑
+
APP
APP
S
S
k )
1
(
2
The wave resistance is determined from:
{
}
)
cos(
exp
2
2
1
5
2
1
−
+
∇
=
n
d
n
W
F
m
F
m
g
c
c
c
R
λ
ρ
with
37565
.
1
07961
.
1
78613
.
3
7
1
)
90
(
)
/
(
2223105
−
−
=
E
i
B
T
c
c
33333
.
0
7
)
/
(
229577
.
0
L
B
c
=
if B/L<0.11
= B/L if 0.11<B/L<0.25
= 0.5-0.0625 L/B if B/L>0.25
3
2
89
.
1
exp(
c
c
−
=
c
5
= 1-0.48A
T
/(BTC
M
)
λ = 1.446C
P
-0.03 L/B if L/B < 12
= 1.446C
P
-0.36 if L/B>12
Course Teacher: Dr. Md. Mashud Karim, Associate Professor, Dept. of NAME, BUET
16
3
/
1
1
/
79323
.
4
/
75254
.
1
/
0140407
.
0
c
L
B
L
T
L
m
−
−
∇
−
=
3
2
16
984388
.
6
8673
.
13
07981
.
8
P
P
P
C
C
C
c
+
−
=
if C
P
<0.8
= 1.73014-0.7067C
P
if C
P
> 0.8
)
1
.
0
exp(
2
2
15
2
−
−
=
n
P
F
C
c
m
c
15
= -1.69385 for L
3
/▼<512
= 0 for L
3
/▼>1727
=-1.69385+(L/▼
1/3
-8.0)/2.36
if 512<L
3
/▼<1727
d=-0.9
}
)
/
100
(
)
/
(
)
0225
.
0
1
(
)
1
(
)
/
(
exp{
89
1
16302
.
0
3
34574
.
0
6367
.
0
30484
.
0
80856
.
0
L
B
L
lcb
C
C
B
L
i
R
P
WP
E
∇
−
−
−
−
+
=
)}
31
.
0
(
/{
56
.
0
5
.
1
3
B
F
BT
BT
h
T
A
BT
A
c
−
+
=
where h
B
is the position of the centre of the
transverse area A
BT
above the keel line and
T
F
is the forward draught of the ship.
)
1
/(
)
3
exp(
11
.
0
2
5
.
1
3
2
ni
BT
ni
B
B
F
g
A
F
P
R
+
−
=
−
ρ
)
5
.
1
/(
56
.
0
B
F
BT
B
h
T
A
P
−
=
2
15
.
0
)
25
.
0
(
/
V
A
h
T
g
V
F
BT
B
F
ni
+
−
−
=
6
2
5
.
0
c
A
V
R
T
TR
ρ
=
)
2
.
0
1
(
2
.
0
6
nT
F
c
−
=
if F
nT
<5
= 0 if F
nT
≥5
)
/(
2
/
WP
T
nT
BC
B
gA
V
F
+
=
A
A
SC
V
R
2
2
1
ρ
=
)
04
.
0
(
5
.
7
/
003
.
0
00205
.
0
)
100
(
006
.
0
4
2
4
16
.
0
c
c
C
L
L
C
B
A
−
+
−
+
=
−
c
4
= T
F
/L when T
F
/L ≤ 0.04
c
4
= 0.04 when T
F
/L>0.04
Problem:
The characteristics of a ship is as
follows:
L.O.W L=205.00 m
L.B.P. L
PP
= 200.00 m
Breadth moulded B = 32.00 m
Draught moulded on F.P, T
F
=10.00 m
Draught moulded on A. P. T
A
=10.00 m
Displacement volume moulded,▼=37500 m
3
Longitudinal centre of buoyancy 2.02% aft of
1/2L
PP
Transverse bulb area A
BT
= 20.0 m
2
Centre of bulb area above keel line h
B
= 4.0 m
Midship section coefficient C
M
= 0.98
Waterplane area coefficient C
WP
= 0.75
Transom area A
T
= 16.0 m
2
Wetted area appendages S
APP
= 50.0 m
2
Stern shape parameter, C
stern
= 10.0
Propeller diameter, D = 8.0 m
Number of propeller blades Z = 4
Clearance of propeller with keel line 0.20 m
Ship speed V=25.0 knos
Density, ρ = 1025.87
Kinematic Viscosity,
υ
= 1.18831e-006
Find R
F
, R
APP
,R
W
, R
B
, R
TR
, R
A
, R
total
.
Reference:
J. Holtrop and G.G. J. Mennen,
1982: An Approximate Power Prediction
Method
, International Shipbuilding Progress,
Vol. 29, No. 335.
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