Berthing Velocity Calculator

Calculate approach velocity for safer quay operations. Use standard coefficients for angle, mass, and contact. Download tables, compare scenarios, and brief your crew today.

Inputs

3 columns on large screens, 2 on smaller, 1 on mobile.

Used in the report and history table.
Enter a short identifier for your scenario.
Enter displacement in metric tonnes (t).
Hydrodynamic added mass as a percent of displacement.
Energy capacity of the fender system for the scenario.
Reduces the displayed velocity for conservatism.
Accounts for off-center contact and approach conditions.
Represents energy distribution between vessel and fender.
Adjusts for contact arrangement and berthing layout.
Reset CSV PDF
Notes: Units must be consistent. Energy in kJ, displacement in tonnes. Coefficients vary by project guidance; keep a record of assumptions in the report.

Formula used

The calculator rearranges the standard berthing energy relationship into velocity form:

E = 0.5 × M × Cm × V² × (Ce × Cs × Cc)
V = √( 2E / ( M × Cm × (Ce × Cs × Cc) ) ) ÷ SF
  • E = available berthing energy (J). (Input is kJ; converted internally.)
  • M = vessel displacement mass (kg). (Input is tonnes; converted internally.)
  • Cm = 1 + added mass (%)/100, to represent hydrodynamic added mass.
  • Ce, Cs, Cc = project coefficients for approach, response, and configuration.
  • SF = safety factor; divides the computed velocity for conservatism.

Engineering note: This is a planning tool. Always confirm coefficient definitions with your governing standard or client specification.

How to use this calculator

  1. Enter vessel displacement and an added mass percentage for the berthing condition.
  2. Set available energy to your fender or system capacity for the case.
  3. Input coefficients (Ce, Cs, Cc) based on your design guidance.
  4. Choose a safety factor to keep the velocity conservative.
  5. Press Calculate to view velocity in m/s, knots, and km/h.
  6. Use the CSV/PDF buttons to export the history and brief stakeholders.

Example data table

Illustrative scenarios
Scenario Disp. (t) Added (%) Energy (kJ) Ce Cs Cc SF Velocity (m/s)
Harbor tug 450 15 60 0.90 0.95 1.00 1.10 0.427
Coaster vessel 6,000 10 240 0.85 0.90 1.00 1.10 0.265
Bulk carrier (mid-size) 25,000 10 600 0.85 0.90 1.00 1.10 0.229

Example velocities are computed using the same formula, shown for reference. Replace with your site-specific coefficients and verified fender capacity.

Calculation history

Saved in your browser session (up to 25 entries).

No saved entries yet. Run a calculation to create exportable history.

CSV exports full details, including the energy check value. PDF provides a compact summary for sharing.

Technical article

Approx. 400 words

1) Why berthing velocity matters

Berthing impacts are typically evaluated by energy, but crews feel the outcome as speed. A small change in approach velocity can create a large change in impact energy because energy varies with velocity squared. For example, a 20% speed increase raises energy by about 44%. This calculator converts an available energy value into a recommended velocity so operational targets match design capacity.

2) Inputs that drive the result

The three biggest drivers are displacement, available energy, and the combined coefficient (Ce × Cs × Cc). Displacement is entered in tonnes and converted to kilograms internally. Energy is entered in kJ and converted to joules. Typical planning values often use added mass between 0–30%, depending on hull form and water depth conditions.

3) Added mass and hydrodynamic effects

Added mass represents extra water accelerated with the vessel during contact. The calculator uses Cm = 1 + (added mass % / 100). If displacement is 25,000 t and added mass is 10%, effective mass increases by 10% for the energy balance. This is useful when comparing calm-water berthing against more constrained or shallow-water cases.

4) Coefficients and practical ranges

Coefficients allow you to reflect approach condition, system response, and contact layout without changing the core physics. Many projects keep Ce, Cs, and Cc within about 0.7–1.2 for screening studies, then refine per specification. If your combined coefficient decreases, the allowable velocity decreases because the same energy is absorbed less effectively.

5) Safety factor and operational conservatism

The safety factor (SF) divides the calculated velocity to build margin. Values around 1.05–1.30 are common for conservative operational limits, while higher factors may be used for uncertainty. The history table stores SF with each run so you can demonstrate how a limit was selected during reviews.

6) Unit checks and conversions

Output is shown in m/s, knots, and km/h to match marine practice. This tool uses 1 knot = 0.514444 m/s and km/h = m/s × 3.6. Always confirm that the energy input reflects the same condition as the coefficients, such as the same berth face and fender arrangement.

7) Scenario comparison using history

The calculator keeps up to 25 recent scenarios in session history. This supports quick comparison such as “same vessel, different fender energy” or “same berth, different added mass.” Export to CSV for spreadsheets or share a compact PDF summary during toolbox talks and design coordination meetings.

8) Good practice notes for project records

Record the assumption set: displacement basis (loaded or ballast), the source of available energy, and the meaning of each coefficient. For operational limits, add environmental qualifiers such as wind/current thresholds and tug assistance. Treat the result as a planning target and confirm with governing standards and site procedures before field use.

FAQs

1) What does “available berthing energy” mean here?

It is the energy capacity you are willing to allocate for the case, typically based on the fender system rating for the berth configuration and vessel class.

2) Why does velocity change so strongly with energy?

The relationship is quadratic: E ∝ V². Doubling velocity requires four times the energy capacity, assuming the same mass and coefficients.

3) How should I choose added mass percentage?

Use project guidance if available. For screening, many teams test 0%, 10%, and 20% to understand sensitivity before selecting a design value.

4) What if my coefficients are uncertain?

Run a range. Compare conservative and optimistic combinations (for example, 0.8 to 1.1). Use the history export to document the envelope.

5) Is the safety factor the same as a structural factor?

No. Here it is an operational conservatism factor applied to velocity. Structural checks should follow the relevant design code and specification.

6) Can I use this for different vessel sizes?

Yes. Enter the displacement and scenario coefficients for each vessel. Keep energy consistent with the berth’s fender system and arrangement.

7) Why does the PDF look simple?

The PDF exporter is intentionally lightweight and dependency-free. It produces a one-page summary suitable for quick sharing and recordkeeping.

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