Welcome to the Bollard Pull Calculator for Barges - Rev 02
What does this Excel Sheet do?
This Excel sheet helps you calculate the Required Bollard pull of a Tug used for towing a Barge
How is the Excel Sheet Organised?
The Excel Sheet provides four different methods for calculations.
The First Method is based on DNV rules for Marine Operations. This is contained in the sheet named "Bollard Pull - DNV"
The Second Method is using industry standard OPL Guidelines for Barge Transportation Vol 5. This is contained in the sheet named "Bollard Pull - OPL Guideline"
The Third Method is based on Bureau Veritas rules and formulas for Bollard Pull Calculations. This is contained in the sheet named "Bollard Pull - BV"
The Fourth method is using a simple Empirical formula. This is contained in the sheet named "Empirical Formula". It provides Bollard Pull for different weather conditions: Calm, Rough and Extreme
How to use this Excel Sheet
In all the three methods, the user is asked for some inputs to be provided. For example, the Wetted Surface area of Barge, Wind Speed etc. The Input cells are highlighted in blue.
The user has to provide all the inputs highlighted in blue.
For some inputs, Tables and charts are required to be referred. These Tables and charts are provided alongwith for the user to enter these inputs.
Once all inputs are provided, the components of required bollard pull are calculated and added up to give the final Bollard Pull required.
Change log Rev 02
1. DNV Formula - Added Wave Resistance now based on DNV-RP-H103
2. References updated for DNV method
3. OPL method - Wave effect resistance is now being automatically calculated, and user need not input it
4. OPL method - some typo errors rectified
INPUTS
GENERAL
Notation
ρa
ρw
Parameter
Air Density
Sea Water Density
Acc. Due to Gravity
g
BARGE
Notation
Parameter
Length
Breadth
Depth
Draft (Mid)
Type of Bow (1 - Square face, 2 Raked, 3 - Spoon, 4 - Ship Shape)
Freeboard
Hull Windage Area
Hull Underwater Area
Current Drag Coefficient (Hull)
L
B
D
T
REQUIRED BOLLARD PULL CALCULATION FOR BARGES
Value
1.225
1025
9.81
Units
kg/m3
kg/m3
Value
116.00
36.60
7.00
3.00
Units
m
m
m
m
m/s2
Summary: This method calculates the Required Bollard Pull to hold the tow in a given Sea State. The Standard Sea State
used is Hs = 5m, Current = 1 kn and Wind =40 Kn. Directions: The applicability of the method is shown in the box titled
"Applicability Check" on the left. All input cells are in blue. Tug efficiency can be varied. Coefficients Cs and Ch can be
obtained from the Tables on the right.
REQUIRED BOLLARD PULL
4.00
146.40
109.80
1.00
54.37 MT
m
m2
m2
Fc
Cargo Height Hc
Cargo Windage Area AWC= BC X HC
Parameter
Wave Height
Current Speed
Wind Speed
Parameter
Actual Bollard Pull of Tug
Tug Efficiency
Notation
Value
0.00
0.00
1.10
1.00
0.00
Units
m
m
See Table 1
See Table 2
m2
SEA STATE
Notation
HS
VC
VW
Value
5.0
0.5
20.6
Units
m
m/s
m/s
TUG
Notation
BPT
η
Value
60.0
0.75
Units
MT
Bc
Hc
Ch
Cs
AWC = BC X HC
Depth, D
Hull Windage Area AWH= B X f
Hull Underwater Area, ACH = B X T (approx.)
Change Log (Rev 02)
1. DNV Calculation now based on DNV-RP-H-103, the latest document from DNV which replaces the earlier Rules for Marine Operations (2000)
Breadth, B
Sectional View of Barge with Cargo
MT
MT
MT
Cs : Shape Coefficient
Spherical
0.4
Cylindrical
0.5
Large flat surface (hull, deckhouse, smooth under deck areas)
1
Drilling derrick
1.25
Wires
1.2
Exposed beams and girders under deck
1.3
Small parts
1.4
Isolated shapes (cranes, beam, etc)
1.5
Clustered deck houses or similar structures
1.1
Table 1: Shape Coefficient
Reference: ABS, 2016, Rules for Building and Classing Mobile Offshore Drilling Units, Part 3 Chapter 1,
Section 3, ‘Environmental Loadings’, p.11.
Current Resistance FC
CARGO
Parameter
Breadth Overall
Height Overall
Height Coefficient
Shape Coefficient
Cargo Windage Area
Wind Resistance, F W = FWH + FWC
FWH = Wind Resistance for Hull
FWH = 1/2 x ρa x VW2 x AWH
FWH
3.88
FWC = Wind Resistance for Cargo
FWC = 1/2 x ρa x VW2 x AWC x Ch x Cs
FWC
0.00
FW = Total Wind Resistance
FW = FWH + FWC
3.88
Cargo Breadth = BC
3
f
AWH = B X f
ACH = B X T
CD
TOW PULL CALCULATION - DNV METHOD
This method is based on DNV Recommended Practice RP-H103 7.2.6 (Applicable for zero towing speed).
Shape and Height coefficients are taken from ABS MODU Rules 2016
Freeboard,
f = D -T
Draft ,T
FC = 1/2 x ρs x CD x VC2 x ACH
1.43
Wave Drift Resistance (FWD)*
FWD = 1/8 x ρs x R2 x B x HS2
Type of Bow (1 - Square face, 2 - Raked,
3
3 - Spoon, 4 - Ship Shape)
Reflection coefficient, R (See Table 3)
0.55
FD
35.46
*Reference: DNV RP-H-103, Sec 7.2.6.4
TOTAL RESISTANCE, F T =
Wind Resistance, F W
Current Resistance, F C
Wave Drift Resistance, F D
Total Resistance, F T
FW + FC + FD
3.88
1.43
35.46
40.78
MT
MT
MT
MT
MT
MT
TUG EFFICIENCY
Tug Efficiency, η**
0.75
**Reference: DNV Rules for Marine Operations Pt2 Ch2, Towing, 3.3.2.6
REQUIRED BOLLARD PULL (BP = F T / η )
BP
54.37
MT
Since Required Bollard Pull < Actual Bollard Pull => OK
Ch: Height Coefficient
Height above sea level (metres)
Over
Not exceeding
0
15.3
15.3
30.5
46
61
76
91.5
106.5
122
137
152.5
167.5
183
198
213.5
228.5
244
259+
30.5
46
61
76
91.5
106.5
122
137
152.5
167.5
183
198
213.5
228.5
244
259
Ch
1
1.1
1.2
1.3
1.37
1.43
1.48
1.52
1.56
1.6
1.63
1.67
1.7
1.72
1.75
1.77
1.79
1.8
R: Reflection Coefficients
Square Face
Condeep base
Vertical Cylinder
Barge with Raked bow
Barge with Spoon bow
Ship bow
Table 3: Reflection Coefficients
Reference, DNV-RP-H103, 2011, Table 7-1
Table 2: Height Coefficient
Use Centre of Area for Above Heights
Reference: ABS, 2016, Rules for Building and Classing Mobile Offshore Drilling Units, Part 3 Chapter 1,
Section 3, ‘Environmental Loadings’, p.11.
1.00
0.97
0.88
0.67
0.55
0.45
CALCULATION OF REQUIRED STATIC BOLLARD PULL FOR BARGE: OPL Guidelines
BARGE NAME
Reference: OPL Oilfield Seamanship Series - Volume 5: Barge Moving
BARGE 1
TOWING SPEED ----->
Actual Bollard Pull of Tug ----->
Towing Efficiency in % (Default value 75%)
Calculation of Frictional Resistance:
RF = f1 (S)(v/6)2 , lbs.
Description
Fouling coefficient(0.4 clean hull, 0.85 fouled hull, usually
f1
0.625)
Wetted Surface of the Hull
S
Still water tow speed in knots
v
Frictional Resistance
RF
Calculation of Wave Forming Resistance:
RWF = 3.42 (f2)(AT)(v)2 , lbs.
Description
Hull Shape Coefficient (0.20 for rake ended barges and bluff
f2
bowed vessels and 0.50 for square bowed vessels)
knots
tonnes
Unit
5.0
60.0
75.0
Value
-
0.63
ft2
knots
tonnes
55553.34
5.0
10.94
Unit
Value
-
0.2
AT
v
RWF
ft2
knots
tonnes
1181
5.0
9.17
Calculation for Wind Resistance:
RW = 0.0034 (AT)(vW+v)2 , lbs.
Description
Height Coefficient for Cargo Exposed to Wind (See Table 1)
Ch
Shape Coefficient for Cargo Exposed to Wind (See Table 2)
Cs
Cargo Transverse Area (Exposed to wind)
AC
Vessel Transverse Area (Exposed to wind)
AH
Total Transverse Area
AT
Wind Velocity
vW
Still water tow speed in knots
v
Wind force
RW
Unit
ft2
ft2
ft2
knots
knots
tonnes
Value
1
1
0.0
1575.0
1575.0
40.0
5.0
4.92
Unit
ft2
knots
tonnes
Value
55553
1.0
0.40
Unit
ft
lbs
tonnes
Value
16
23,400
10.62
Transverse Area(Underwater)
Still water tow speed in knots
Wave Forming Resistance
Wetted Surface of the Hull
Current Speed
Current Effect Resistance
Calculation of Current Effect
RC = 0.016 (S)(vC)2 , lbs.
Description
S
vC
RC
Calculation of Wave Effect
From Table 3
Description
Wave Height
Force at 16 feet wave - See Table 3
Wave Effect Resistance
FWR
RWH
Directions:
1. Fill the input cells which are in blue.
2. The outputs will show in the bottom as the final Bollard Pull required.
3. Use Table 1 for calculating the Height coefficient for Wind
4. Use Table 2 for finding the Shape Coefficient for wind
5. Use Table 3 to calculate the Wave Effect Resistance which depends on the wave height.
In case the value of Wave Height falls in between two values given in the table, interpolation is to be used
Factor Ch (Height coefficient for wind calculations)
Height
0-50
50-100
Unit
feet
feet
100-150
150-200
200-250
250-300
300-350
feet
feet
feet
feet
feet
Frictional Resistance
Wave Forming Resistance
Hawser Resistance
1.2
1.3
1.4
1.5
1.6
Factor Cs (Shape coefficient for wind calculations)
Shape
Cs
Cylinder
0.5
Flat Perpendicular Surface
1
Isolated Structure – Beam-channel angle braces
1.5
Exposed Beams
1.3
Derrick (latticed structures)
1.25
Sphere
0.4
Table 2: Carge Shape Coefficient for Wind Calculations
Unit
tonnes
tonnes
tonnes
Value
10.9
9.2
2.01
tonnes
tonnes
tonnes
tonnes
tonnes
tonnes
tonnes
10.94
9.17
4.92
0.40
10.62
2.01
38.1
75.0
50.74
60.00
Yes
OUTPUTS
Calculation of Total Resistance:
RT = RF + RWF + RW + RC + RWH + RH
Frictional Resistance
RF
Wave Forming Resistance
RWF
Wind Resistance
RWH
Current Effect Resistance
RC
Wave Effect Resistance
RWH
Hawser Resistance
RH
Total Resistance
RT
Tug Efficiency in percentage(Default value 75%)
η
Required Bollard Pull = (RT/η)*100
BP
Actual Tug Bollard Pull
Satisfied/Not Satisfied?
1
1.1
Table 1: Cargo Height Coefficient for Wind Calculations
Wave Height Effect – For wave Force on Hull:
Significant Wave Height
Added Resistance
5
feet
2000
lbs
10
feet
12000
lbs
15
feet
22000
lbs
20
feet
29000
lbs
25
feet
30000
lbs
30
feet
33000
lbs
Table 3: Wave Effect Resistance Table
Calculation of Hawser Resistance:
RH = 0.10 (RF + RWF)
Description
RF
RWF
RH
Factor
TONNES
TONNES
CALCULATION OF REQUIRED STATIC BOLLARD PULL FOR BARGE: BV Rules and Formulas
BARGE NAME:
BARGE 1
1. Fill the input cells which are in blue.
2. The output will show in the bottom as the final Bollard Pull required.
3. Use Appendix 1 for calculating the coefficients Cx and Ch
4. Use Graph 1 below for finding the value of Rv/D
INPUTS
Symbol
Value
L=
B=
T=
V=
Vc =
D=
S=
d=
l=
Z=
P=
N=
Vfr =
rsw =
rair =
n=
Vw =
BPt =
116.00
36.60
3.00
5
1
11463
146.4
65
700
1
900
150
18
1.025
1.22
1.2E-06
40
60
Directions:
Unit
m
m
m
Kn
Kn
t
m^2
mm
m
m
m
days
Kn
t/m^3
kg/m^3
m^2/s
Kn
Tonnes
Description
Waterline Length
Breadth
Draft
Vessel Speed (Towing Speed)
Assumed Current Speed
Displacement
Windage Area
Tow Line Diameter
Tow Line Immersed Length
Sag of Tow Line
Tug to Towed Vessel Distance
Number of Days Elapsed Since last Dry Docking
Maximum Towing Vessel Speed in Free Run
Sea Water Specific Gravity (default value 1.025)
Air Specific Gravity (default value 1.22)
Viscosity (default value 1.2 10^-6)
Wind Speed (default value 40)
Actual Bollard Pull of Tug
APPENDIX 1: Tables for Cx and Ch
RESULTS
Symbol
Value
Frictional Resistance Rf
R = 298375200
Cf =
0.001789
DCf =
0.002147
Cft =
0.004336
Sw =
4485.44
Rf =
94961
Wave Resistance Rv
L/B =
3.17
B/T =
12.20
V/(L)^0.5 =
0.29
Rv / D =
12.00
Rv =
137556
Total Hydrodynamic Resistance Rh
Rh =
232517
Aerodynamic Resistance Ra
Cx =
1
Ch =
1
Ra =
37815
Tow Line Resistance Rr
Rr =
1994
Total Resistance of Towed Vessel
Rtot =
272325
Bollard Pull Coefficients
(V+Vc)/Vfr =
0.33
Cef =
0.67
Unit
2
m^2
N
Rf = ½ Cf (rsw)(Sw)(v)
Reynolds Number, R = vL / ν
Friction Coefficient, Cf = 0.075 / [log10 R)-2]2
Addition to Friction Coefficient due to Hull Fouling, DCf = 0.008 (N)(Cf)
Total Friction Coefficient, Cft = Cf + DCf +0.0004
Wetted Surface Area
Frictional Resistance
N
(To be taken from the Graph 1 on the right)
Wave Resistance
N
N
N
Total Hydrodynamic Resistance
Ra = ½ Cx * Ch * (rair)(S)(Vw)2
Drag Coefficient(To be taken from the Appendix1 on the right)
Height Coefficient(To be taken from the Appendix1 on the right)
Aerodynamic Resistance
-3
2
Rr = 4.6 x10 (d)(v) ( l + (71.6 Z/P)) , in Newton
Tow Line Resistance
N
Graph1: Graph for Values of Rv/D
Percentage of Static Bollard Pull = (1 - (V+Vc)/Vfr)
Total Required Static Bollard Pull for Tug, Rt
Rt =
41.6
Actual Bollard Pull for Tug, BPt
BPt =
60.0
Satisfied/Not Satisfied
Yes
Description
T
T
CALCULATION OF REQUIRED STATIC BOLLARD PULL FOR BARGE: Empirical Formula
FORMULA USED
INPUTS: Please input the following
Description
BARGE NAME
Length, L
Breadth, B
Displacement, ∆
Depth, D
Draft, d
Cargo Height, H
Tug Efficiency in percentage(default 75%)
Is it Tow by Stern?
Actual TUG Bollard Pull
Using Empirical Formula for towing guide by Port Authorities
Unit
m
m
tonnes
m
m
m
Yes/No
tonnes
Value
BARGE 1
116.00
36.60
11463.00
7.00
3.00
0.00
75.00
No
60.00
⅔
Where:
=
=
=
=
full displacement of towed vessel, in tonnes
v
B
D1
BP
K
=
=
Required bollard pull, in tonnes
the factor depending on the likely condition to be met. This factor is
intended to reflect desired weather margins.
∆
Note: For tow by the stern, then the Bollard Pull requirement is to be increased by 20%
OUTPUTS: CALCULATED BOLLARD PULL WITH VARIOUS WEATHER CONDITIONS & TOWING SPEEDS
Description
Length, L
Towing Speed, V
Breadth, B
Displacement, ∆
Depth, D
Draft, d
Cargo Height, H
Exposed Height, D1
Weather Factor, K
Required Bollard Pull as per formula, Rt
Tug Efficiency in percentage(Default 75%), η
Bollard Pull considering Tug Efficiency =
(RT/η)*100
Tow by Stern?
Final Bollard Pull, BP (in tonnes)
Actual TUG Bollard Pull
3
BP = { [ (∆ · (v / (120 · 60)) ] + (0.06B · D1) } · K (tonnes)
Good
116.00
5.00
36.60
11463.00
7.00
3.00
0.00
4.00
1.00
17.89
75.00
Rough
116.00
4.00
36.60
11463.00
7.00
3.00
0.00
4.00
2.00
26.89
75.00
Extreme
116.00
3.00
36.60
11463.00
7.00
3.00
0.00
4.00
3.00
32.25
75.00
23.85
35.86
43.00
No
23.85
60.00
SATISFIED
No
35.86
60.00
SATISFIED
No
43.00
60.00
SATISFIED
In General:
tow speed, in knots
breadth of the vessel, in meters
depth of exposed transverse section of the vessel including
deck cargo above the water line, in meters
• for exposed tows, K = 1.0 - 3.0
• for sheltered tows, K = 0.75 - 2.0
• for protected tows, K = 0.50 - 1.5
<---- Please input the different speeds considered for the three weather conditions
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