Coastal & Port Engineering, Breakwater Armor & Storm Surge Hydraulics
Hudson Breakwater Armor Stone Mass & Kd Stability Formula
Calculate Submerged Relative Rock Density S_r, Median Armor Unit Mass M_50 (metric tons) under Cubic Wave-Height Scaling H^3, Nominal Cube Dimension D_n50 (m), and Double-Layer Thickness (m).
Armor block weight scales with Wave Height CUBED (H^3)—a 25% storm-wave jump demands DOUBLE-weight boulders!
Harbor rubble-mound breakwaters and coastal revetments resist hurricane wave uplift and drag using heavy quarrystone boulders or interlocking concrete units (Tetrapods, Accropodes, Xblocs) sized by the U.S. Army Corps of Engineers Shore Protection Manual Hudson Formula: M_50 = (rho_r * (H^3)) / (K_D * ((S_r - 1)^3) * cot_theta), where rho_r (kg/m³) is armor density, S_r = rho_r / rho_w is specific gravity relative to seawater (rho_w = 1,025 kg/m³ -> submerged buoyant factor (S_r - 1)^3!), H (m) is design significant wave height, cot_theta is seaward slope run-over-rise (e.g. 2.0 for 1V:2H), and K_D is empirical interlocking stability coefficient (K_D ~ 4.0 for rough angular quarrystone vs 8.0–16.0 for interlocking concrete units)!
Verify on a 4.50 m Storm-Wave Port Breakwater—Granite_Armor_Density rho_r = 2,650.0 kg/m³ (B2), Seawater_Density rho_w = 1,025.0 kg/m³ (B3 -> Relative Density S_r = 2.585 in E2), Design_Wave_Height H = 4.50 m (B4), Stability_Coeff K_D = 4.0 (two-layer rough quarrystone, B5), and Slope_Cotangent cot_theta = 2.0 (1V:2H slope, B6): Required Median Armor Boulder Mass M_50 hits 7.58 metric tons (7,580 kg, E3), Nominal Equivalent Cube Size D_n50 = (M_50 / rho_r)^(1/3) equals 1.42 m (E4), and 2-Layer Armor Blanket Thickness (2.0 * D_n50) equals 2.84 m (E5)!
| Hudson Breakwater KPI (Granite 2,650 kg/m³, H = 4.5 m, Kd = 4.0, 1V:2H) | Formula | Verified Output |
|---|---|---|
| Relative Submerged Density Sr | Armor_Density_rhor / Water_Density_rhow | 2.585 |
| Median Armor Unit Mass M50 (t) | (rhor * H^3 / (Kd * (Sr - 1)^3 * cot)) / 1000 | 7.58 t (3.79 t @ Tetrapod Kd = 8.0) |
| Nominal Cube Size Dn50 (m) | (M50_kg / rhor)^(1/3) | 1.42 m (1.13 m @ Kd = 8.0) |
| 2-Layer Armor Thickness (m) | 2 * ROUND(Dn50, 2) | 2.84 m (2.26 m @ Kd = 8.0) |
Hudson Breakwater Median Armor Mass M50 Formula
Validate Water_Density > 950, Armor_Density > 1.8 * Water_Density (submerged S_r > 1.8!), Wave_Height H > 0, K_D in [1.0, 25.0], and Slope_Cotangent cot_theta in [1.25, 6.0]!
=LET(rr_k, B2, rw_k, B3, wh_m, B4, kd_s, B5, ct_s, B6, IF(OR(rw_k <= 950, rr_k <= 1.8 * rw_k, wh_m <= 0, kd_s < 1, kd_s > 25, ct_s < 1.25, ct_s > 6), "Invalid Breakwater Input", LET(sr_f, rr_k / rw_k, m5_k, (rr_k * (wh_m ^ 3)) / (kd_s * ((sr_f - 1) ^ 3) * ct_s), ROUND(m5_k / 1000, 2))))Interlocking Concrete Tetrapod Weight Halving Check (Set Stability K_D = 8.0)
When local quarries cannot blast 7.6-ton granite blocks, switch to interlocking concrete Tetrapods (K_D B5 doubles from 4.0 to 8.0): Required Unit Mass E3 halves cleanly from 7.58 t down to 3.79 metric tons (D_n50 = 1.13 m in E4)!
=IF(ISTEXT(E3), E3, ROUND(2 * E4, 2))Try the example
Use the original values or change them to test your understanding.