Berthing Energy and Fender Selection
Vessel kinetic energy factored for virtual mass, eccentricity, softness, and berth configuration.
Example
You enter
- Vessel displacement (short tons; long tons x 1.12) 22000
- Approach velocity normal to berth (ft/s) 0.5
- Virtual mass factor Cm 1.5
- Eccentricity factor Ce 0.5
- Softness factor Cs 1
- Berth configuration factor Cc 0.95
- Fender rated energy absorption (ft-lb) 150000
- Alternative approach velocity (ft/s) 1
You get
- Vessel mass 1,366,460 slugs
- Kinetic energy 170,807 ft-lb before the factors
- Design berthing energy 121,700 ft-lb at a combined factor of 0.7125
- Against the fender rating less 10% tolerance 11% of margin on 135,000 ft-lb
- At the alternative velocity 486801
- Alternative energy ratio 4
- The fender at that velocity 3.60594
- A square berthing 243401
Checked against published worked examples from: Civil Engineering and Development Department, Hong Kong SAR Government.
Details, formula, and sources
ScopeAgainst the fender's rated absorption. The worked berthing has 11% of margin on the rating less its 10% tolerance at 0.5 ft/s and is 3.6 times it at 1.0 ft/s, because the velocity term is squared. Published berthing guidance governs.
Formula or tableE = 0.5 M V^2 with M = displacement / g and V normal to the berth; design energy = E x Cm x Ce x Cs x Cc against the fender's rated absorption at its design deflection.
Source and editionPublished berthing-energy guidance, with virtual mass 1.3 to 1.8, eccentricity 0.4 to 0.7 for a normal quarter-point berthing, softness 0.9 to 1.0, and configuration 0.8 to 1.0. The fender manufacturer's energy curves and the berth designer govern.
Free accessThe kinetic-energy relation is public; the coefficient bands come from published design guidance.
What governsVessel master governs. Verify against the stability letter and USCG-approved loading manual.
API field namesdisplacement_tons, approach_velocity_fps, virtual_mass_factor, eccentricity_factor, softness_factor, configuration_factor, fender_rating_ftlb, alternative_velocity_fps, vessel_mass_slugs, kinetic_energy_ftlb, design_energy_ftlb, fender_margin_pct, alternative_design_energy_ftlb, alternative_energy_ratio, alternative_fender_utilization, square_berthing_energy_ftlb
- Tolerance and accidental case normal berthing is checked against 90% of the rating (fender curves carry +/-10%); the accidental case is at least 50% more energy, absorbed by the system at or near failureUFC 4-152-01, 5-1.5.2 and 5-1.5.3
- Approach velocity an assumption about seamanship on a day nobody can specify; design guidance gives wide bands by vessel size and berthing conditionberth designer
- Eccentricity a barge pushed square onto a face has Ce near 1.0 and delivers about twice the usual assumption -- an easily overlooked second design casespec-v1833 method