Bollard Pull Calculator Suite

Based on DNV Rules, OPL Guidelines & Empirical Formulas

Developed by Hrithin

DNV Rules

OPL Guidelines

Empirical Formula

Vessel Particulars (DNV Rules)

DNV Rules for Marine Operations Pt.2, Ch.2

This calculator determines the required bollard pull for towing operations based on DNV standards, considering wind, current, and wave resistances.

Length, L (m)

Breadth, B (m)

Depth, D (m)

Draft, T (m)

Hull drag coefficient

Typical values: 0.08-1.0 depending on hull shape

Cargo Particulars

Breadth overall, BC (m)

Height overall, HC (m)

Height coefficient, Ch

Shape coefficient, CS

Environmental Conditions

Wave height, HS (m)

Current speed, VC (m/s)

Wind speed, VW (m/s)

Tug Particulars

Actual bollard pull of tug, BPT (MT)

Towing efficiency, η

Typical range: 0.7-0.85

DNV Rule Calculation Results

Wind Resistance

Parameter	Value	Unit
Hull windage area, AW	45.00	m²
Cargo windage area, AWC	0.00	m²
Wind resistance of hull, FWH	11.03	kN
Wind resistance of cargo, FWC	0.00	kN
Total wind resistance, FW	11.03	kN

Current Resistance

Hull submerged area, AC	157.50	m²
Current resistance, FC	1.97	kN

Wave Drift Resistance

Wave drift resistance, FD

64.26

Total Resistance

Total resistance, TR

77.26

Required Bollard Pull

Required bollard pull, BPR	103.01	kN
Required bollard pull	10.51	MT
Actual bollard pull, BPT	80.00	MT
Status	PASS
Condition	Since required bollard pull is less than the actual bollard pull of tug, the condition is satisfactory.

Key Formulas (DNV Rules):
1. Wind resistance: FWH = 0.5 × ρa × AW × VW² / 10000 (kN)
2. Current resistance: FC = 0.5 × ρw × AC × VC² × CD / 1000 (kN)
3. Wave drift: FD = 1/8 × ρw × g × (Hs/2)² × L × Cd (kN)
4. Required BP: BPR = TR / η (kN)

Note: Based on DNV Rules for Marine Operations Pt.2, Ch.2

Applicability: L/T > 6 and L/D > 3 for zero towing speed

1 MT (Metric Ton) = 9.80665 kN

Vessel Particulars (OPL Guidelines)

Outside Port Limits (OPL) Guidelines

This calculator determines required bollard pull based on OPL guidelines using imperial units, considering frictional, wave forming, wind, and current resistances.

Length, L (ft)

Breadth, B (ft)

Depth, D (ft)

Draft, T (ft)

Towing Speed, VT (knots)

Resistance Coefficients

Fouling coefficient, f1

Hull shape coefficient, f2

Height coefficient, Ch

Shape coefficient, CS

Environmental Conditions

Wave height, HS (ft)

Current velocity, VC (knots)

Wind velocity, VW (knots)

Tug Particulars

Actual bollard pull of tug, BPT (tonnes)

Towing efficiency, η (%)

Typical range: 70-85%

Cargo & Hull Areas

Cargo transverse area, AC (ft²)

Exposed hull transverse area, AH (ft²)

OPL Guidelines Calculation Results

Frictional Resistance

Parameter	Value	Unit
Hull wetted surface area, S	23034.70	ft²
Frictional resistance, RF	17.41	tonnes

Wave Forming Resistance

Transverse underwater area, ST	1695.46	ft²
Wave forming resistance, RWF	21.10	tonnes

Wind Resistance

Total transverse area, AT	2056.98	ft²
Wind resistance, RW	5.70	tonnes

Current Resistance

Current resistance, RC

8.23

tonnes

Wave Effect Resistance

Wave resistance, RWH

3.64

tonnes

Total Resistance

Hawser resistance, RH	3.85	tonnes
Total resistance, TR	59.93	tonnes

Required Bollard Pull

Required bollard pull, BPR	79.91	tonnes
Actual bollard pull, BPT	40.00	tonnes
Status	FAIL
Condition	Since required bollard pull is more than the actual bollard pull of tug, the condition is not satisfactory.

Key Formulas (OPL Guidelines):
1. Frictional: RF = f1 × S × (VT/6)² × 0.000454 (tonnes)
2. Wave forming: RWF = 3.42 × f2 × ST × VT² × 0.000454 (tonnes)
3. Wind: RW = 0.0034 × AT × (VW+VT)² × Ch × Cs × 0.000454 (tonnes)
4. Current: RC = 0.016 × S × VC² × 0.000454 (tonnes)
5. Hawser: RH = 0.1 × (RF + RWF) (tonnes)
6. Required BP: BPR = TR / (η/100) (tonnes)

Note: Based on Outside Port Limits (OPL) Guidelines

All calculations in imperial units (feet, pounds, knots)

Conversion: 1 lb = 0.000454 tonnes

Vessel Particulars (Empirical Formula)

Empirical Formula

This calculator uses empirical formulas for quick estimation of required bollard pull under different weather conditions and towing speeds.

Length, L (m)

Breadth, B (m)

Depth, D (m)

Draft, T (m)

Cargo height, H (m)

Displacement, Δ (tonnes)

Is it tow by stern?

If tow by stern, multiply result by 1.2

Tug Particulars

Actual bollard pull of tug, BPT (tonnes)

Tug efficiency, η (%)

Weather Conditions

Calm

Rough

Extreme

Towing speed, v (knots)

Weather factor, K

Weather Factor Guidelines:

• Exposed tows: K = 1-3

• Sheltered tows: K = 0.75-2

• Protected tows: K = 0.5-1.5

Empirical Formula Results

Current Weather Condition: Calm

Parameter	Value	Unit
Exposed height, D1	5.35	m
Required bollard pull, BPR	22.29	tonnes
Bollard pull considering tug efficiency	29.72	tonnes
Actual bollard pull, BPT	40.00	tonnes
Status	PASS

All Weather Conditions

Weather Condition	Towing Speed (knots)	Weather Factor, K	Required BP (tonnes)	Status
Calm	5	1	22.29	PASS
Rough	4	2	33.10	PASS
Extreme	1	3	10.15	PASS

Empirical Formula:
BPR = ((Δ^(2/3) × (v³/(120×60))) + (0.06 × B × D1)) × K
If tow by stern: Multiply result by 1.2

Note: Empirical formula for barge towing calculations

This formula provides quick estimates and should be verified with more detailed methods

Displacement (Δ) in tonnes, Breadth (B) in meters, Speed (v) in knots