Input parameters
Formula used
This calculator provides a practical, screening-level estimate of interior wave conditions. It combines a distance-based attenuation term, a transmission factor for protection, and a capped amplification term for reflection.
| Quantity | Expression |
|---|---|
| Deep-water wavelength | L₀ = g·T² / (2π) |
| Attenuation (geometry + damping) | D = exp( −α · (L/B) ) |
| Reflection amplification (capped) | A = min( 2.50, 1 / max(0.20, 1 − Kᵣ) ) |
| Inside wave height estimate | Hᵢ = H₀ · Kₜ · D · A |
| Tranquility coefficient | Cₜ = Hᵢ / H₀ |
| Target check | Hᵢ ≤ (H_allow / SafetyFactor) |
Notes: The dispersion relation, diffraction hot-spots, and basin resonance are not solved here. For final design, use physical modeling or validated numerical models.
How to use this calculator
- Enter the incident wave height and period representing typical design conditions.
- Define the entrance width and the distance from the entrance to your evaluation point.
- Choose coefficients: lower Kₜ means less wave transmission; higher Kᵣ can amplify waves.
- Adjust α to represent damping from layout, friction, and energy losses.
- Select a vessel type and safety factor, then calculate. Review rating and comfort check.
- Use CSV/PDF downloads to attach results to method statements or reports.
Example data table
Illustrative cases for quick validation and benchmarking.
| Case | H₀ (m) | T (s) | B (m) | L (m) | Kₜ | Kᵣ | α | Hᵢ (m) | Cₜ | Rating |
|---|---|---|---|---|---|---|---|---|---|---|
| A | 1.20 | 8.0 | 120 | 600 | 0.35 | 0.40 | 0.25 | 0.201 | 0.167 | Good |
| B | 1.80 | 10.0 | 160 | 450 | 0.45 | 0.30 | 0.18 | 0.697 | 0.387 | Moderate |
| C | 0.90 | 6.5 | 90 | 800 | 0.25 | 0.55 | 0.30 | 0.035 | 0.039 | Excellent |
Example outputs are generated using the same formulas shown above.
Professional guidance article
1) What harbor tranquility means
Harbor tranquility describes how much incident wave energy is reduced inside a basin so berthing, cargo handling, and mooring remain comfortable. This calculator estimates inside wave height Hᵢ, the tranquility coefficient Cₜ = Hᵢ/H₀, and a pass/fail check against practical vessel limits. It is intended for early design screening, option comparison, and quick reporting.
2) Input data you should prepare
Start with a representative incident wave height H₀ and period T. For screening, use a typical operational sea state or a percentile condition used by your project. Geometry inputs are the entrance width B (m) and the distance inside L (m) to the berth or area of interest. Keep units consistent; small errors in geometry can shift the attenuation term.
3) Transmission and reflection with typical ranges
The transmission coefficient Kₜ represents how much wave height passes through protection. For robust rubble-mound or well-sheltered layouts, screening values often fall around 0.20–0.45. Higher values (e.g., >0.60) may indicate porous structures, overtopping, or direct exposure. The reflection coefficient Kᵣ is commonly screened in the 0.20–0.60 range.
4) Attenuation, distance, and layout effects
The attenuation term D = exp(−α·(L/B)) decreases waves with distance and damping. As a practical guide, when L/B doubles, the decay effect strengthens. The coefficient α is a tuning factor; values around 0.15–0.35 often represent moderate damping for quick comparisons. Use higher α to represent more losses.
5) Comfort limits used in the calculator
The built-in screening limits for allowable inside wave height are: marina small craft 0.30 m, fishing vessels 0.50 m, general cargo berths 1.00 m, and tanker berths 1.50 m. A safety factor reduces these limits to create a conservative target for planning and method statements.
6) Reading the rating bands
This tool classifies tranquility using Cₜ: Excellent (<0.15), Good (0.15–0.30), Moderate (0.30–0.50), and Poor (>0.50). A lower Cₜ means a greater reduction from offshore conditions, usually yielding easier operations.
7) Using results for construction planning
During construction staging, you can evaluate temporary gaps, partial breakwater lengths, or changed alignments by adjusting Kₜ, Kᵣ, B, and L. The CSV export supports quick trend reviews, while the PDF export supports attachment to inspection records and briefs. Use the notes to flag cases where transmission or reflection appear high.
8) Limits and when to upgrade the analysis
The formulas do not solve diffraction hot-spots, resonance, or full dispersion; results should be treated as screening. If the comfort check is marginal, run sensitivity cases (±10% on key inputs) and consider validated numerical modeling or physical testing for final designs and critical berths.
FAQs
1) What does a lower Ct mean?
A lower Ct means smaller inside waves compared to offshore waves. Values below 0.30 typically indicate calm operational conditions for many berths, depending on vessel sensitivity and mooring setup.
2) How should I pick Kt?
Use a screening value based on protection quality. Strong shelter often screens near 0.20–0.45. If waves can pass through gaps, porous structures, or overtopping, Kt can be higher.
3) Why does Kr increase inside waves here?
Higher reflection can support standing-wave amplification within basins. The calculator applies a capped amplification factor to represent this effect in a simple way for early comparisons.
4) Is depth h used in the calculations?
Depth is stored for documentation and reporting. This screening model uses a deep-water wavelength approximation; it does not compute full dispersion with depth. For shallow sites, use a detailed wave model.
5) What safety factor should I use?
Use 1.10–1.30 for typical planning, and higher values when uncertainty is high or operations are critical. The safety factor reduces the allowable inside wave limit to create a conservative target.
6) Can I use this for final design approval?
No. It is a screening tool for option ranking and quick checks. For final design, include diffraction, resonance, and site-specific conditions using validated numerical simulations or physical modeling.
7) What if the result fails the comfort check?
Try reducing Kt (improved protection), increasing attenuation (layout/damping), or increasing distance from the entrance. Run sensitivity checks, then consider detailed modeling if the berth remains critical.