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Hudson Formula Breakwater Armor Rock Weight Calculator

Size rubble mound breakwater armor rock mass (W), nominal diameter Dn50, layer thickness, and placement packing density using Hudson’s coastal stability formula.

Design significant or maximum wave height arriving at the breakwater toe.

Specific gravity of armor stone (typically 2.60 - 2.70 for granite/basalt, 2.30 - 2.50 for limestone).

Cotangent of structure seaside slope angle (e.g. 1.5 for 1:1.5, 2.0 for 1:2 slope).

Stability coefficient KD (typically 4.0 for rough angular quarrystone trunk, 3.2 for head).

Breaking wave condition applies an empirical safety derating to the stability coefficient.

Calculated Result
1.18 Tonnes

Armor Stone Minimum Weight (W)

Weight in Kilograms

1180 kg

Nominal Armor Diameter (D_n50)

0.76 m

Total Layer Thickness (2 layers)

1.51 m

Placement Density

2.2 units/m²

Calculation Breakdown

  1. Rock Submerged Relative DensityΔ = (S_r - 1) = (2.65 - 1) = 1.65; Rock Density = 2716 kg/m³
  2. Hudson Formula Weight DeterminationW = (γ_r · H³) / [K_D · (S_r - 1)³ · cot θ] = 1.18 Metric Tons (1180 kg)
  3. Nominal Dimension & Double-Layer BlanketNominal Diameter D_n50 = (W / ρ_r)^(1/3) = 0.76 m; 2-Layer Thickness = 1.51 m

Breakwater Armor Rock Properties

Interactive visualization based on your current inputs

Value
0.02.75.58.211Stone Mass (t)Dn50 (m)Layer Depth (m)Units / 10m²ParameterValue

What Is the Hudson Formula Breakwater Armor Rock Weight Calculator?

Size rubble mound breakwater armor rock mass (W), nominal diameter Dn50, layer thickness, and placement packing density using Hudson’s coastal stability formula.

The Hudson Formula Breakwater Armor Rock Weight Calculator is an analytical tool in the construction domain designed to evaluate Design Wave Height (H), Rock Specific Gravity (S_r), Seaward Slope cot(θ), Stability Coefficient (K_D), Wave Breaking Condition using verified mathematical equations. It provides reproducible, deterministic calculations for academic, professional, and practical applications.

How Does the Hudson Formula Breakwater Armor Rock Weight Calculator Work?

This calculator computes results by taking input values for Design Wave Height (H), Rock Specific Gravity (S_r), Seaward Slope cot(θ), Stability Coefficient (K_D), Wave Breaking Condition and applying the governing equation: USACE Hudson equation balancing armor stone gravitational submerged weight against hydrodynamic wave drag and lift forces.. Values are checked for dimensional consistency and processed through standard arithmetic routines.

Hudson Formula Breakwater Armor Rock Weight Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

W=γr⋅H3KD⋅(Sr−1)3⋅cot⁡θ,Dn50=(Wρr)1/3W = \frac{\gamma_r \cdot H^3}{K_D \cdot (S_r - 1)^3 \cdot \cot\theta}, \quad D_{n50} = \left(\frac{W}{\rho_r}\right)^{1/3}

USACE Hudson equation balancing armor stone gravitational submerged weight against hydrodynamic wave drag and lift forces.

How to Use the Hudson Formula Breakwater Armor Rock Weight Calculator

  1. Enter your value for Design Wave Height (H) in m.
  2. Enter your value for Rock Specific Gravity (S_r) in dim.
  3. Enter your value for Seaward Slope cot(θ) in H:1V.
  4. Enter your value for Stability Coefficient (K_D) in dim.
  5. Enter your value for Wave Breaking Condition.
  6. Verify your input parameters to ensure they match your design or problem specifications.
  7. Review the calculated results, intermediate mathematical steps, and graphical visualization below.

Step-by-Step Example Calculation

Harbor Trunk Breakwater (H = 2.5 m, 1:2 Slope)

Input Values:

designWaveHeightHM:2.5
armorRockSpecificGravity:2.65
structureSlopeCotTheta:2.0
stabilityCoefficientKD:4.0
isBreakingWave:false
Worked Steps: Requires minimum 1.18 tonne rock armor units (Dn50 ≈ 0.76 m) placed in a 1.52 m double layer.

Understanding Your Result

The calculated output gives the primary solution for Hudson Formula Breakwater Armor Rock Weight under the specified conditions. Use this value to compare against standard design tolerances, benchmarks, or reference ranges in construction.

Factors That Affect the Result

  • Input precision and measurement accuracy of Design Wave Height (H), Rock Specific Gravity (S_r), Seaward Slope cot(θ), Stability Coefficient (K_D), Wave Breaking Condition.
  • Operating conditions, environmental parameters, and specific construction tolerances.
  • Boundary constraints and deviations from nominal theoretical model assumptions.

When Should You Use This Calculator?

  • When performing technical analysis or dimensioning related to Hudson Formula Breakwater Armor Rock Weight.
  • To cross-verify manual calculations or theoretical models in construction.
  • For preliminary estimates before conducting detailed field measurements or laboratory testing.

Assumptions & Limitations

  • Hudson Formula: W = (γ_r · H³) / [K_D · (S_r - 1)³ · cot(θ)].
  • Nominal rock diameter Dn50 = (W / ρ_r)^(1/3).
  • Standard double-layer armor thickness r ≈ 2.0 · Dn50 with packing density based on ~37% layer porosity.

Frequently Asked Questions

Why does rock specific gravity have such a massive impact on required armor weight?+
The submerged relative buoyancy term (Sr - 1) is cubed in the denominator. Increasing specific gravity from 2.50 to 2.70 reduces required stone weight by nearly 35%, dramatically improving slope stability.
When should concrete armor units (e.g., Tetrapods, Accropodes) be used instead of rock?+
When design wave heights exceed 4 to 5 meters, natural rock quarrystone weights exceed 15-20 tonnes, which are rare and difficult to quarry and place, making interlocking concrete units much more cost-effective.

Calculation Accuracy & Reference Note

This calculator implements verified mathematical formulas for Hudson Formula Breakwater Armor Rock Weight Calculator. Always verify critical results against official domain standards and manufacturer documentation.

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