Seastead Bridge Deck Clearance Analysis
Triangular Platform with Hydrodynamic Wing Legs

1. Established Bridge Deck Clearance Rules (Catamarans/Trimarans)

1.1 Classification Society Rules

1.2 Key Variables

• C = bridge deck clearance (underside of deck to calm waterline), meters
• L_WL = waterline length of hull/float, meters
• H_s = significant wave height (design sea state), meters
• ∇ = displacement volume, m³

2. Probabilistic Pounding Frequency — State of the Art

2.1 Semi-Empirical / Spectral Methods

• Relative Motion Spectral Analysis: Compute RAOs for heave/pitch/roll → relative motion spectrum at deck edge → Rayleigh distribution of peaks → upcrossing rate of clearance threshold. Standard in seakeeping codes (WAMIT, AQWA, SESAM, OrcaFlex).
• Ochi & Motter (1973) / Ochi (1964): Probability of slamming for monohulls based on relative velocity and emergence. Adapted for multihulls by Molland et al. (1994), Rosén & Svensson (2008).
• Kapsenberg (2011) / van der Plas (2018): Model test regression for catamaran cross-deck clearance vs. slamming probability in irregular seas.

2.2 Simplified Engineering Approximation (for screening only)

If relative motion at deck corner η_rel(t) is narrow-banded Gaussian with std dev σ_η:

P(pounding in one wave) ≈ exp( -C² / (2 σ_η²) )   [Rayleigh exceedance]
Expected pounding rate (per hour) ≈ N_z × P(pounding per wave)

Where N_z = mean zero-upcrossing rate (~600–1000/hr for T_z ≈ 6–10 s).

But σ_η depends on: wave spectrum, heading, speed, hull geometry, hydrostatic stiffness, damping, added mass — not a simple function of clearance alone.

2.3 What Exists for Your Hull Type

Your design is a triangular semi-submersible / SWATH-variant with wing columns. Closest literature:

• SWATH seakeeping: Lee & Curphey (1977), McCreight (1987), Liang et al. (2017)
• Column-stabilized units (MODU): API RP 2A, DNV-OS-J101 — air gap rules: Air Gap ≥ H_max/2 + 1.5 m or spectral analysis
• Trifoil / hydrofoil-assisted cats: Doctors et al., INCE (2010s)

3. Your Design — Parameter Extraction

4. First-Principles Estimation of Required Clearance

4.1 Static + Quasi-Static Components

4.2 Dynamic Pounding Margin (Probabilistic)

For <1 event/day in ~1000 waves/day (T_z ≈ 8 s):

Target exceedance probability per wave: P < 10⁻³
Required margin above RMS relative motion: C_dyn ≥ 3.1 × σ_η   (Rayleigh)

Estimated σ_η at corner (heave + pitch/roll):

• Conservative (low damping, resonant): σ_η ≈ 0.8–1.2 m
• Moderate (some viscous damping from wing legs): σ_η ≈ 0.5–0.8 m

→ Dynamic margin needed: 1.5–3.7 m

4.3 Air Gap Rules for Column-Stabilized Units (API/DNV)

Air Gap ≥ H_max/2 + 1.5 m  (API RP 2A-WSD)
Air Gap ≥ 1.2 × H_s + 1.0 m  (DNV-OS-J101 simplified)

For H_s = 2.13 m, H_max ≈ 4.0 m:

• API: 2.0 + 1.5 = 3.5 m
• DNV: 2.6 + 1.0 = 3.6 m

5. Synthesis — Recommended Clearance

6. Critical Design Considerations for Your Concept

6.1 Wing Leg Hydrodynamics

• t/c = 0.4 is not a "wing" — it's a thick strut. At low Fn, it behaves as a bluff body with significant vortex shedding (St ≈ 0.15–0.2). Expect VIV (vortex-induced vibration) at low speeds. This adds damping (good for motions) but causes fatigue (bad for structure).
• Orientation matters: If chord is radial (pointing to center), wave forces are on thick face → high drag/inertia. If chord is tangential (along triangle side), lower wave load but different VIV characteristics.
• Added mass: Thick sections have high added mass coefficient (C_m ≈ 1.5–2.0). This lowers natural periods → may move heave resonance into wave energy band (T ≈ 6–8 s).

6.2 Stability & Weight Distribution

• Weight in legs lowers KG → good for static stability (GM). But: legs are at waterline, so weight there does not lower KG as much as weight deep in a SWATH lower hull (which would be 10–15 m below waterline).
• Rotational inertia (I_xx, I_yy): Mass at corners (R ≈ 14 m from center) gives huge I. I ≈ 3 × m_leg × R². If m_leg = 50 t each → I ≈ 30,000 t·m². This reduces pitch/roll accelerations but increases motion periods (T_φ ∝ √(I/ρg∇GM_T)). Longer periods = larger motion amplitudes in energetic wave bands.
• Low waterplane area → low GM_T unless VCB is very low. With legs only 3 m draft, KB ≈ 1.5 m. If KG ≈ 4–5 m (platform + deckhouse), GM_T = KB + BM_T – KG. BM_T = I_wp / ∇. I_wp for 3 legs at 14 m radius ≈ 3 × (8.8 × 14²) ≈ 5,200 m⁴. For ∇ = 2000 m³ → BM_T ≈ 2.6 m. GM_T ≈ 1.5 + 2.6 – 4.5 = –0.4 m (unstable!)
• → You need either: (a) much deeper ballast in legs (extend legs down 10+ m below waterline), (b) much larger waterplane (flare at waterline), or (c) active ballast / variable draft.

6.3 Pounding Load Magnitude

If pounding occurs, peak pressure on flat deck underside:

p_max ≈ ½ ρ v_rel² × C_s    (von Karman / Wagner theory)
C_s (slamming coeff) ≈ 2.0–5.0 for flat plate
v_rel ≈ 2–4 m/s in 2 m waves → p_max ≈ 40–160 kPa (6–23 psi)

For a 256 m² deck, total slam force = 10–40 MN. This drives structural scantlings. A 4 m clearance avoids this load case almost entirely.

6.4 Container Shipping Constraint

40 ft container internal: 12.03 m × 2.35 m × 2.39 m (L×W×H). Your leg (10 ft chord = 3.05 m) does not fit diagonally in a standard container (diagonal = √(2.35²+2.39²) ≈ 3.35 m — barely fits chord, but 19 ft length = 5.79 m > 12.03 m). You need flat-rack or open-top containers, or modular leg assembly.

7. Recommended Next Steps

1. Hydrostatic stability model (Excel / Python / GHS / Maxsurf) — verify GM_T > 1.0 m minimum, preferably > 2.0 m. Iterate leg draft, ballast, waterplane flare.
2. Seakeeping analysis (WAMIT, ANSYS AQWA, or OrcaFlex) — compute RAOs for 6 DOF, relative motion at corners, slamming probability via spectral method. Test headings 0°–180°, H_s = 1–4 m.
3. CFD / model test for leg VIV, slamming pressures, and added mass/damping at low Fn.
4. Structural FEA of deck-to-leg connection for slam loads (even if rare) — this is typically the governing load case for deck scantlings.
5. Classification engagement early — ABS/DNV "Alternative Design" or "Novel Craft" pathway. They will require spectral seakeeping + slamming analysis per their rules.

8. Quick-Reference Calculation Sheet

# Python snippet for air gap check (run in your design notebook)
import math

H_s = 2.13          # m, design significant wave height
H_max = 1.86 * H_s  # m, max expected wave height (Rayleigh)
T_p = 7.5           # s, peak period

# API RP 2A simplified air gap
air_gap_API = H_max/2 + 1.5
# DNV simplified
air_gap_DNV = 1.2 * H_s + 1.0

# Spectral estimate (very rough)
# sigma_eta = sqrt(m0) of relative motion at corner
# Need RAOs → placeholder:
sigma_eta_est = 0.7  # m, estimated from similar SWATH
target_prob_per_wave = 1e-3
N_waves_per_day = 86400 / T_p
required_sigma_margin = math.sqrt(-2 * math.log(target_prob_per_wave))  # ~3.7
C_dynamic = required_sigma_margin * sigma_eta_est
C_total = H_max/2 + C_dynamic + 0.3  # +0.3 tide/tolerance

print(f"H_max = {H_max:.2f} m")
print(f"API air gap = {air_gap_API:.2f} m")
print(f"DNV air gap = {air_gap_DNV:.2f} m")
print(f"Est. dynamic margin (1/day) = {C_dynamic:.2f} m")
print(f"Recommended clearance ≈ {C_total:.2f} m")

Generated for conceptual design review. Not for construction. Engage a naval architect and classification society before finalizing clearance.