Calculator
Enter any known values. The tool will compute all available outputs.
Example data table
Sample scenarios for quick validation and training.
| Scenario | Energy (kJ) | Deflection (mm) | Stiffness (kN/m) | Reaction (kN) | Notes |
|---|---|---|---|---|---|
| Rubber fender (linearized) | 120 | 450 | — | 533.33 | R = 2E/δ (η=1, SF=1). |
| Spring model | — | 300 | 1200 | 360.00 | R = kδ, δ=0.30 m. |
| Back-calc energy | — | 400 | — | 650.00 | E = 0.5Rδ → 130 kJ. |
Formula used
- Reaction from stiffness: R = k × δ
- Energy from reaction (linear spring): E = 0.5 × R × δ
- Reaction from energy (linearized): R = 2 × E / δ
- Design energy adjustment: E_design = E × SF / η
- Berthing energy estimate (optional): E = 0.5 × m_eff × v², where m_eff = m × C_added × C_ecc × C_other
Many fenders are non-linear. Use this tool for quick checks or preliminary sizing, then confirm final reaction and energy values using manufacturer performance curves.
How to use this calculator
- Enter deflection distance, or provide height plus deflection percent.
- Add either energy, stiffness, or a known reaction value.
- Set efficiency and safety factor for your design approach.
- Optionally estimate berthing energy from mass and velocity.
- Press Calculate to view results above the form.
- Export CSV for spreadsheets or PDF for submittals.
Professional guide
1) Why fender reaction matters
Fender reaction is the horizontal force transferred from the fender system to the berth, piles, and structural members. It directly affects wall design, bracket sizing, and connection detailing. Quick reaction checks help screen layouts before running full manufacturer-curve verification.
2) Inputs that control the result
This calculator uses deflection (δ), energy (E), stiffness (k), and optional known reaction (R). Enter deflection directly in mm or m, or derive it from height and a working deflection percent. Consistent units reduce conversion errors during tender and construction reviews.
3) Linearized energy–reaction relationship
For preliminary sizing, a linear response is often used: E = 0.5 × R × δ. Rearranging gives R = 2E/δ. This is useful when you have an energy demand and want a reaction estimate at the same working deflection.
4) Stiffness-based reaction modeling
If stiffness is known at the working point, the reaction is computed as R = k × δ. For example, a stiffness of 1200 kN/m at 0.30 m deflection gives about 360 kN reaction. This path is ideal when supplier data provides spring-rate values for a selected deflection.
5) Berthing energy estimate (optional)
When energy is not yet defined, berthing energy can be approximated with E = 0.5 × m_eff × v². Effective mass can include coefficients for added mass, eccentricity, and project factors. Typical berthing velocities are low (often about 0.05 to 0.30 m/s), but small changes in velocity can significantly change energy because of the squared term.
6) Safety factor and efficiency settings
The calculator applies E_design = E × SF / η. Safety factor (SF) increases demand to reflect uncertainty, while efficiency (η) represents how effectively the system absorbs energy. Many preliminary checks use SF in the 1.10–1.50 range and η near 0.80–1.00, depending on project controls.
7) Interpreting results for construction decisions
Use the stiffness-based reaction when k is from reliable performance data at the same deflection. Use the energy-based reaction when energy demand is governing. Compare outputs and document which method was selected. The “Preferred reaction” summary prioritizes stiffness, then energy, then known reaction.
8) Reporting and QA workflow
After calculation, export CSV for design spreadsheets and quantity checks. Export PDF for submittals, internal approvals, and site documentation. Keep assumptions visible: deflection basis, unit set, SF, η, and any berthing coefficients. Final values should be confirmed against manufacturer curves and project criteria.
FAQs
1) What is “fender reaction” in this tool?
It is the horizontal force the fender transfers at the selected deflection. The tool reports reaction from stiffness, reaction from energy, and a preferred summary value for quick comparison.
2) Which method should I trust more, energy or stiffness?
Use stiffness when k comes from supplier data at the same deflection. Use energy when a governing energy demand is specified. For final design, confirm both using manufacturer performance curves.
3) Why does velocity change the berthing energy so much?
Because the estimate uses v². Doubling velocity increases energy by four times, which can raise required reaction and structural demand. Enter realistic berthing velocities based on site operations.
4) What does efficiency (η) represent here?
η scales the design energy demand. If η is less than 1, the tool increases required capacity by dividing by η. Use values aligned with your specification and any system losses.
5) How do I use height and percent to set deflection?
If you do not know δ directly, enter fender height and a working deflection percent. The tool computes δ = height × percent/100 and uses that value throughout the calculations.
6) Can I back-calculate energy from a known reaction?
Yes. Provide a known reaction and deflection. The tool returns energy using E = 0.5 × R × δ under a linearized assumption, which is useful for checking reported supplier points.
7) Is this suitable for final berth structural design?
It is intended for preliminary sizing, comparisons, and documentation. Many fenders are non-linear, so final design should use the manufacturer’s reaction–deflection–energy curves and project standards.