Seastead Scale Model Analysis: 1:10.5 Froude Scaling

Critical Limitation: As an AI text model, I cannot watch or analyze the YouTube video linked. The analysis below is a theoretical framework based entirely on the design specifications you provided, Froude scaling laws (Scale Factor $\lambda = 10.5$), and typical hydrodynamic responses for vessels of this type (SWATH/Small Waterplane Area Twin Hull variants). To get exact numbers, you must measure the motion amplitudes (roll, pitch, heave, accelerations) from the video pixels and apply the scaling factors below.
View Referenced Video on YouTube

1. Froude Scaling Laws (Scale Factor $\lambda = 10.5$)

Since the model is 1:10.5 scale, time, velocity, and acceleration do not scale linearly. Froude scaling ($Fr = V/\sqrt{gL} = \text{const}$) dictates:

Length Scale ($\lambda_L$): 10.5
Time Scale ($\lambda_T = \sqrt{\lambda_L}$): $\sqrt{10.5} \approx \mathbf{3.24}$
Velocity Scale ($\lambda_V = \sqrt{\lambda_L}$): $\approx \mathbf{3.24}$
Acceleration Scale ($\lambda_A = 1$): $\mathbf{1.0}$ (Model accelerations in g's = Full Scale accelerations in g's)
Force/Mass Scale ($\lambda_F = \lambda_L^3$): $10.5^3 \approx \mathbf{1,158}$
Wave Height Scale: Linear ($\lambda_L = 10.5$)

2. Estimating Full Scale Wave Environment from Video

Since I cannot see the video, you must perform this measurement:

  1. Calibrate Pixels: Measure the model triangle side (80 inches = 6.67 ft) in pixels.
  2. Measure Wave Height ($H_m$): Measure crest-to-trough height in pixels relative to the model. Convert to model feet.
  3. Calculate Full Scale Wave Height ($H_{fs}$): $H_{fs} = H_m \times 10.5$.
  4. Measure Wave Period ($T_m$): Time between crests passing a fixed point (seconds).
  5. Calculate Full Scale Period ($T_{fs}$): $T_{fs} = T_m \times 3.24$.

Example Calculation (Hypothetical):

If you measure model waves at H_m = 1.5 inches (0.125 ft) and T_m = 0.8 sec:

If model waves are 4 inches (0.33 ft) @ 1.2 sec: Full Scale = 3.5 ft @ 3.9 sec (Moderate chop).

If model waves are 8 inches (0.67 ft) @ 1.5 sec: Full Scale = 7.0 ft @ 4.9 sec (Rough).

3. Theoretical Motion Response Analysis (Seastead vs. Conventional)

Based on your geometry (Equilateral Triangle SWATH-like, $\nabla = 27,500 \text{ lbs} \approx 12.5 \text{ tonnes}$, Waterplane Area $A_{wp} \approx 3 \times (21.5 \text{ft} \times 0.5 \text{ft avg}) \approx 32 \text{ ft}^2$), here is the expected comparison.

3.1 Heave (Vertical Motion)

VesselWaterplane Area ($A_{wp}$)Heave Natural Period ($T_n$)Response to Waves (RAO)Comment
Your Seastead Very Small (~32 ft²) Long (~8-12 sec) Low at wave periods (3-6s), High at Swell (10s+) Stiffness $K = \rho g A_{wp} \approx 2,000 \text{ lb/ft}$. Mass $\approx 850 \text{ slugs}$. $\omega_n = \sqrt{K/M} \approx 1.5 \text{ rad/s} (T_n \approx 4.2s)$. Correction: Added mass of foil legs (~2-3x mass) pushes $T_n$ to 8-12 sec. Resonance likely in long swell.
50 ft Catamaran Large (~200-300 ft²) Short (~3-5 sec) Moderate (Resonant in chop) High stiffness, low added mass. "Corky" motion in short waves.
60 ft Monohull Medium (~80-120 ft²) Medium (~5-7 sec) Moderate-High Coupled with pitch. Heavy displacement dampens high freq.

Verdict: In short seas ($T < 6s$), the Seastead will have significantly lower heave acceleration than both. In long swell ($T > 10s$), the Seastead may resonate (high heave), whereas conventional boats are past resonance and follow the contour.

3.2 Pitch & Roll (Rotational Motion)

VesselRoll Inertia / BeamRoll DampingTypical Roll Accel (g's) in 4ft/4s waves
Your Seastead Extreme (Legs at 44ft vertices, $I_{xx} \approx M \cdot (22\text{ft})^2$) High (Foil legs + Heave Plates + Active Stabilizers) < 0.02 g (RMS)
50 ft Catamaran High (Beam ~25-30ft) Low (Hull friction only) 0.05 - 0.10 g
60 ft Monohull Low (Beam ~16-18ft, Ballast low) Medium (Keel + Bilge keels) 0.08 - 0.15 g

Key Insight: Your Roll Moment of Inertia ($I_{xx}$) is massive due to the 44ft leg spacing. Even with low roll damping, the acceleration ($\alpha = M/I$) is tiny. The active heave plates (if implemented) or passive foil damping will likely suppress roll to < 1-2 degrees in conditions that roll a cat 5-10 degrees.

3.3 Acceleration Comparison (The "Comfort Metric")

ISO 2631 / MSI (Motion Sickness Incidence) is driven by vertical acceleration at the Center of Gravity (CG). Assuming CG is near the geometric center of the triangle, ~7ft above waterline.

Estimated Vertical Acceleration RMS (at CG) in Beam Seas (H=4ft, T=4s)

MSI (2hr exposure): Seastead < 1% | Cat ~5-10% | Mono ~10-20%.

4. Specific Design Feature Impacts

4.1 NACA 0035 Foil Legs (vs. Cylinders)

4.2 Heave Plates (Bolt-on)

Essential for station-keeping motions. Without them, the low $A_{wp}$ gives a very low natural frequency but very low damping ratio ($\zeta \approx 0.01-0.02$). A 1ft wave at resonance (10s period) could induce 3-5ft heave amplitudes. Plates increase $\zeta$ to $0.1-0.15$, limiting resonance amplification to < 2x.

4.3 Tension Leg Mooring (Helical Screws)

Pre-tensioning the legs (pulling down 3ft) increases stiffness $K_{total} = K_{hydro} + K_{mooring}$.

5. Container Packing Verification (Sanity Check)

ItemDimensionContainer Fit (7.7' W x 8.9' H x 44.6' L)
3x Legs (Stacked 2+1)Chord 8.5ft (Cut to 8.0ft?), Thickness ~12" (0035 @ 15% t/c = 15.75" max). 2 stacked = ~2.6ft. 3rd beside = ~1.3ft. Total Width ~3.9ft.Fits along 7.7ft width (Right side). Height 21.5ft requires diagonal or vertical? ISSUE: Legs are 21.5ft long. Container is 44.6ft long. They fit lengthwise easily. Height is 8.9ft. Standing upright (21.5ft) IMPOSSIBLE. Must lie flat.
Triangle Walls (3 sections)7ft High x ~15ft Long (44ft/3 + overlap). Width/Thickness ~10-12".Fits standing upright (7ft < 8.9ft) along Left wall (44.6ft length). 3 x 15ft = 45ft. TIGHT: 44.6ft container vs 44ft triangle sides. Sections must be < 14.8ft each.
Mid-triangle Beams (22ft)22ft long.Fits diagonally (diag = 45.5ft) or flat on top of legs.
Dinghy (14ft RIB deflated)Compact bundle.Fits in center void.
Batteries (25% Disp = ~7,000 lbs)LiFePO4 ~120 Wh/kg. ~250 kWh total.Fits low in legs (best) or center floor. Weight OK (62,000 lb limit).

Critical Packing Note: The 21.5ft legs must lie flat in the container (8.9ft height limit). Stacking 3 legs flat (3 x 15.75" thick $\approx$ 3.9ft) fits width easily. Length 21.5ft fits easily in 44.6ft.

6. Action Items for You (Video Analysis Protocol)

To finalize this report for your website, extract these data points from the video:

  1. Wave Calibration: Measure pixel height of known model part (e.g., 80" triangle side). Measure wave height in pixels $\rightarrow$ Model Wave Height (ft).
  2. Model Wave Period: Stopwatch time for 5 waves / 5.
  3. Model Motion Amplitudes: Track a dot on the model CG (center of triangle). Measure Heave (vertical pixels), Roll (angle of horizon/triangle), Pitch (angle of triangle side).
  4. Apply Scaling:
    • Full Scale Wave Height = Model $\times$ 10.5
    • Full Scale Period = Model $\times$ 3.24
    • Full Scale Heave/Amplitude = Model $\times$ 10.5
    • Full Scale Accel (g's) = Model Accel (g's) [Same]
  5. Compare: Plot your Full Scale Accel vs. the "Comfort Metric" table in Section 3.3.

Generated for Seastead Design Analysis. Froude Scaling Factor $\lambda = 10.5$. Design Displacement 27,500 lbs. Container: 45ft HC.