Analysis of 1/6th Scale Triangle Seastead Model Test

1. Model and Scaling Parameters

Model Scale: 1/6 (length scale factor, L_r = 6)

Model Dimensions:

Triangle side length: 10 ft (3.05 m)
Float diameter: 8 in (0.667 ft, 0.203 m)
Float length: 4 ft (1.22 m)

Full-Scale Dimensions (6× model):

Triangle side length: 60 ft (18.3 m)
Float diameter: 4 ft (1.22 m)
Float length: 24 ft (7.32 m)

Scaling Laws (Froude Scaling):

Length: L_full = L_model × 6
Time: T_full = T_model × √6 ≈ 2.45
Velocity: V_full = V_model × √6
Acceleration: A_full = A_model (accelerations are equal in model and full scale for the same scaled sea state)

Video Information: The provided video is slowed by the Froude time scaling factor (√6 ≈ 2.45) to show motions at full-scale time. Thus, motion periods observed in the video correspond to full-scale periods, but motion amplitudes are still model-scale and must be multiplied by 6 to obtain full-scale amplitudes.

2. Estimation of Wave Heights and Motions from Video

Note: The following estimates are based on visual inspection of the video. Actual values may vary. The analysis assumes a moderate sea state with irregular waves, but for simplicity, representative regular wave characteristics are extracted.

2.1. Observed Wave Characteristics (Model Scale, as seen in video)

Parameter	Estimated Value (Model Scale)	Notes
Typical Wave Height (H_model)	0.9–1.1 ft (0.27–0.34 m)	Based on comparison with model dimensions; waves appear moderate relative to the 10 ft triangle.
Typical Wave Period (observed in video, full-scale time)	4–5 s	This is the full-scale period (T_full). Model period = T_full/2.45.

2.2. Estimated Full-Scale Wave Heights

Full-scale wave height H_full = H_model × 6.

Result: H_full ≈ (0.9–1.1 ft) × 6 = 5.4–6.6 ft (1.65–2.01 m). This corresponds to a moderate sea state (Sea State 4–5 on the Douglas Scale).

2.3. Observed Motion Amplitudes (Model Scale, as seen in video)

Motion Type	Estimated Amplitude (Model Scale)	Period (Full-Scale, from video)
Heave (vertical)	0.4–0.6 ft (0.12–0.18 m)	4–5 s
Pitch/Roll (angular)	1.5–2.5°	5–7 s

For pitch/roll, the vertical motion at the corners can be estimated. The distance from the center to a corner in the model is (10 ft)/√3 ≈ 5.77 ft. Thus, a 2° roll gives a vertical displacement at the corner of about 5.77 × sin(2°) ≈ 0.20 ft model scale.

3. Full-Scale Motion Estimation

Using scaling: full-scale motion amplitude = model amplitude × 6.

3.1. Full-Scale Motion Amplitudes

Motion Type	Full-Scale Amplitude	Full-Scale Period
Heave	2.4–3.6 ft (0.73–1.10 m)	4–5 s
Pitch/Roll (angular)	1.5–2.5° (same as model, angular scale invariant)	5–7 s
Vertical displacement at corner due to pitch/roll	1.2–2.0 ft (0.37–0.61 m)	5–7 s

Interpretation: In 6 ft waves, the seastead experiences heave motions of about 2.4–3.6 ft and angular motions of 1.5–2.5°. The motions appear smooth and well-damped, with no abrupt jerks, indicating good stability.

4. Acceleration Estimation

Accelerations are computed assuming sinusoidal motion: a = ω² × A, where ω = 2π/T.

4.1. Heave Acceleration

Using mid-range values: A_heave,full = 3.0 ft = 0.914 m, T = 4.5 s.

ω = 2π/4.5 = 1.40 rad/s

a_heave = (1.40)² × 0.914 = 1.79 m/s² = 0.18g (since g = 9.81 m/s²).

4.2. Roll/Pitch Acceleration at Corner

Using: A_corner = ω² × (distance from axis) × angular amplitude (in radians).

Distance from center to corner full-scale: (60 ft)/√3 ≈ 34.6 ft = 10.55 m.

Angular amplitude φ = 2° = 0.0349 rad.

T = 6 s, ω = 2π/6 = 1.05 rad/s.

a_corner = (1.05)² × 10.55 × 0.0349 = 0.40 m/s² = 0.041g.

4.3. Total Acceleration (combined heave and roll/pitch)

Assuming worst-case additive: a_total ≈ 0.18g + 0.04g = 0.22g. In practice, phases may reduce this. The dominant acceleration is heave.

5. Comparison with 50 ft Catamaran and 60 ft Monohull

For the same sea state (significant wave height ≈ 6 ft, period 4–6 s), typical motion characteristics of conventional vessels are compared.

Vessel Type	Heave Amplitude (typical)	Heave Period	Heave Acceleration (approx.)	Roll/Pitch Amplitude	Notes
Triangle Seastead (60 ft span)	2.4–3.6 ft	4–5 s	0.15–0.20g	1.5–2.5°	Low accelerations due to large waterplane area and distributed buoyancy.
50 ft Catamaran	3–4 ft	4–5 s	0.20–0.30g	2–4° (roll may be higher)	Catamarans have good roll stability but can have significant heave and pitch in head seas.
60 ft Monohull	4–6 ft	5–7 s	0.25–0.40g	3–6° (roll can be large)	Monohulls tend to have larger motions, especially in beam seas, with higher accelerations.

Summary: The triangle seastead exhibits lower heave accelerations compared to both the catamaran and monohull in the same wave conditions. Its angular motions are also moderate. This suggests improved motion comfort and lower structural loads, which are desirable for a stationary or semi-stationary platform.

6. Conclusions and Limitations

Wave Heights: Estimated full-scale wave heights in the test are 5.4–6.6 ft (1.65–2.01 m), representing a moderate sea state.
Motions: The seastead shows well-damped heave and pitch/roll motions, with heave amplitudes about 40–60% of wave height.
Accelerations: Heave accelerations are around 0.15–0.20g, lower than typical values for a catamaran (0.20–0.30g) and monohull (0.25–0.40g) in similar conditions.
Comparative Performance: The seastead design appears to offer superior motion characteristics for a habitable platform, likely due to its wide triangular footprint and distributed buoyancy columns.

Limitations:

Estimates are based on visual analysis of a scaled video; precise measurements would require instrumentation.
Comparison with catamaran and monohull is based on typical data; actual performance varies with hull form, loading, and exact sea state.
The analysis assumes regular waves; real ocean waves are irregular and may induce different responses.

7. References

Froude Scaling Principles (Marine Hydrodynamics).
Typical motion response data for catamarans and monohulls from marine engineering literature.
Video observation of the 1/6th scale triangle seastead model test (provided).