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Calcimator

Breakwater Design Calculator

Size rubble-mound breakwater armor units using the Hudson formula. Computes armor weight, layer thickness, unit count, and stability number.

Inputs

%

Results

Armor unit weight (N)

29,369.9

Armor unit mass (tonnes)

2.99

Nominal diameter Dn (m)1.04
Armor layer thickness (m)2.13
Units per m² of slope1.18
Stability number Ns1.82
Recommended crest freeboard (m)4.5
How to Use This Calculator
  1. Enter design significant wave height Hs (m) at the breakwater toe.
  2. Enter armor slope angle (degrees), Hudson stability coefficient K_D, armor unit density (kg/m3), and water density (kg/m3).
  3. Read required armor unit weight (kg and tonnes) from the Hudson formula.
  4. Use armor unit weight to select appropriate rock class or concrete armor unit type.
  5. Review required crest width and layer thickness for the design wave height.

How the result changes with Water density (kg/m³)

Water density (kg/m³)Armor unit weight (N)Armor unit mass (tonnes)
92017,600.11.79
97022,525.72.3
1,03030,078.63.07
1,08038,094.53.88

What each input means

Design wave height Hs (m)
Significant design wave height at the breakwater toe.
Armor slope angle (°)
Angle of the armor slope from horizontal. 33.7° ≈ 1V:1.5H.
Stability coefficient K_D
Hudson stability coefficient. Rough angular rock ~4, Dolos ~16, Tetrapods ~8.
Armor unit density (kg/m³)
Mass density of the armor material. Granite ~2650, concrete ~2400.
Water density (kg/m³)
Seawater density, typically 1025 kg/m³.
Number of armor layers
Number of armor unit layers (typically 2).
Packing porosity (%)
Porosity of the armor layer (rock ~37%, Dolos ~56%).
Layer coefficient k_Δ
Layer thickness coefficient. Smooth rock ~1.02, rough rock ~1.00.

What each result means

Armor unit weight (N)
Minimum required weight of each armor unit from the Hudson formula.
Armor unit mass (tonnes)
Equivalent mass per armor unit.
Nominal diameter Dn (m)
Equivalent cube side length of one armor unit.
Armor layer thickness (m)
Total thickness of the armor layer (n layers).
Units per m² of slope
Estimated number of armor units per square meter of slope surface.
Stability number Ns
Hs / (Dn * (Sr-1)). Lower is more stable.
Recommended crest freeboard (m)
Rule-of-thumb crest height above SWL (1.5 * Hs).

How this is calculated

Worked example, using the default values

  1. Identify Input Parameters
    4 parameters
    Design wave height Hs (m) = 3, Armor slope angle (°) = 33.7, Stability coefficient K_D = 4, Armor unit density (kg/m³) = 2650 = 8 input(s) provided
  2. Calculate Armor unit weight
    Armor unit weight = (rhoArmor * g * Hs * Hs * Hs) / (KD * pow(Sr - 1, 3) * cotAlpha)
    29369.9 = 29369.9
  3. Calculate Armor unit mass
    Armor unit mass = massKg / 1000
    2.994 = 2.994
  4. Calculate Nominal diameter Dn
    Nominal diameter Dn = pow(massKg / rhoArmor, 1 / 3)
    1.042 = 1.042
  5. Calculate Armor layer thickness
    Armor layer thickness = numLayers * kDelta * Dn
    2.125 = 2.125

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