Calculator Inputs
Example Data Table
Sample inputs and expected magnitudes. Results vary by beach, wave climate, and calibration.
| Method | Hb (m) | T (s) | αb (deg) | tanβ | d50 (mm) | Approx Q (m³/day) |
|---|---|---|---|---|---|---|
| CERC | 1.8 | 8 | 10 | 0.02 | 0.25 | ~ 2,000 to 10,000 |
| Kamphuis | 1.5 | 7 | 15 | 0.03 | 0.30 | ~ 1,500 to 8,000 |
| CERC | 2.2 | 10 | -12 | 0.015 | 0.20 | ~ -3,000 to -15,000 |
Formula Used
CERC energy-flux transport
This method links transport to the longshore component of wave energy flux at breaking. Breaking depth is computed as hb = Hb / γ, and shallow-water group velocity as Cg = √(g·hb).
Wave energy density is E = (1/8) ρw g Hb², energy flux is P = E·Cg, and the longshore component is Pl = P·sinα·cosα = 0.5·P·sin(2α). Immersed-weight transport rate is I = K·Pl.
Volumetric transport is estimated by Q = I / ((ρs − ρw) g (1 − p)), producing Q in m³/s. The sign of sin(2α) sets direction.
Kamphuis empirical transport
A widely used empirical form relates transport to breaking height, period, slope, and grain size: Q = 2.27·Hb²·T^1.5·(tanβ)^0.75·d50^-0.25·sin(2α). Use d50 in millimeters, and calibrate constants for local conditions when possible.
How to Use This Calculator
- Pick a method that matches your data and project phase.
- Enter breaker wave height, period, and approach angle at breaking.
- Provide beach slope and median grain size for sensitivity checks.
- For CERC, review γ and K values and tune using local monitoring.
- Submit to compute transport rate, daily totals, and annual totals.
- Download CSV or PDF for reports and design documentation.
Professional Article
1) Coastal transport in construction planning
Longshore sediment transport controls how beaches, inlets, and shore protections evolve. During construction, inaccurate transport assumptions can shift erosion hot spots, expose foundations, and overload nourishment volumes. A practical calculator helps teams screen alternatives before committing to surveys, modeling, and permits.
2) What drives longshore transport
Transport is powered by waves that break at an oblique angle. Larger breaking heights raise energy flux sharply, while approach angle controls whether the shoreline gains or loses sand along a project reach. Period affects wave celerity and surf-zone forcing, especially in energy-flux approaches.
3) Why the surf-zone angle matters
The longshore component scales with sin(2α). Small angle changes can flip direction or double magnitude, so engineers should use angles representative of breaking, not offshore headings. When refraction is uncertain, test a range of angles to bracket likely transport.
4) Energy-flux transport for rapid checks
The CERC approach relates transport to the alongshore wave power at breaking. Because the relationship depends on breaker depth and group velocity, a breaker index is used to infer depth from breaking height. Calibration through the K coefficient is common when local measurements exist.
5) Empirical methods for beach-specific behavior
Empirical expressions, such as Kamphuis-style forms, incorporate beach slope and grain size. Steeper slopes can increase transport for similar wave forcing, and finer sand tends to move more readily. These methods are useful when projects need sensitivity to sediment properties across borrow sources.
6) Typical parameter ranges and data sources
For preliminary estimates, use Hb between 0.5 and 3.0 meters, periods from 5 to 14 seconds, and tanβ from 0.01 to 0.10 depending on foreshore steepness. Sand d50 commonly falls between 0.15 and 0.60 mm. Local buoys, hindcasts, and post-storm surveys strengthen input confidence.
7) Interpreting outputs for design decisions
Convert the computed rate into daily and annual volumes to compare against dredging allowances, bypassing capacity, or nourishment placement schedules. If predicted transport is high, groynes and breakwaters may cause rapid updrift accretion and downdrift deficit. Use direction outputs to identify likely deposition and erosion sides.
8) Verification, uncertainty, and documentation
Field verification reduces risk. Combine this calculator with shoreline change mapping, bathymetry, and sediment budgets. Update coefficients after early monitoring, and document assumptions, ranges, and safety factors in design reports. Exported CSV and PDF outputs support consistent internal reviews across project stakeholders and phases.
FAQs
1) Should I use offshore or breaking wave height?
Use breaking wave height at the surf zone. Offshore heights can overestimate or underestimate transport unless transformed with refraction, shoaling, and breaking criteria.
2) Why does the angle use sin(2α)?
Longshore wave power is proportional to sinα·cosα, which equals 0.5·sin(2α). This captures zero transport at normal incidence and peaks near 45 degrees.
3) What value should I pick for the CERC coefficient K?
Start with common planning values around 0.3–0.5, then tune using local transport measurements or sediment budget studies. Site-specific calibration improves reliability.
4) How sensitive are results to grain size?
Empirical methods include grain size explicitly, so finer sand generally yields higher transport. In energy-flux approaches, grain size influences calibration and the volumetric conversion indirectly.
5) Can negative results be “wrong”?
Negative simply indicates the opposite alongshore direction based on your sign convention for α. Confirm your local coordinate system and dominant wave approach seasonally.
6) Is annual transport just 365 times daily transport?
That conversion assumes steady conditions. Real coasts vary by season and storms, so compute transport for representative sea states and sum weighted by occurrence for better annual estimates.
7) When do I need numerical modeling instead?
Use numerical models when geometry is complex, structures cause strong gradients, or permits demand detailed impacts. Models also help with multiple wave directions and time-varying boundary conditions.
Use results wisely, then confirm with site monitoring always.