Scale Model Analysis — Trimaran Semi-Submersible Seastead

The following is an estimate of the motion behavior of the full-scale seastead based on the 1/10-scale model test video, plus a comparison to a typical 50 ft catamaran and 60 ft monohull in similar seas.

1. Froude Scaling Refresher

With a length scale ratio of λ = 10, the Froude-scaling relationships are:

Quantity	Scale Factor	Full-scale multiplier
Length / wave height	λ	× 10
Time / period	√λ	× 3.162
Velocity	√λ	× 3.162
Acceleration	1	× 1 (same g-level)
Frequency	1/√λ	÷ 3.162

Important: The video was not slowed down. That means the model motions appear about 3.16× faster than the full-scale equivalent would appear. The accelerations in g's, however, are identical between model and full scale (that is the beauty of Froude scaling).

2. Estimated Wave Heights in the Video

Using the model legs as a scale reference — each foam leg is 22.8 in (~1.9 ft) tall, with ~11.4 in submerged — the waves in the video appear to be passing roughly 2–4 in trough-to-crest for most of the run, with a few larger sets around 5–6 in. Periods look short, on the order of 0.7–1.0 s.

Model wave	Height (in)	Height (ft)	Period (s)	Full-scale height (ft)	Full-scale period (s)
Typical	3	0.25	0.8	2.5	2.5
Larger sets	5	0.42	1.0	4.2	3.2
Biggest seen	6	0.50	1.1	5.0	3.5

Full-scale equivalent sea state: roughly 2.5–5 ft seas with 2.5–3.5 s periods. In the open ocean that corresponds to a short, steep wind-chop condition — somewhat worse (steeper) than what the full seastead would typically encounter at the same wave height, since real ocean waves of 3–5 ft usually have 5–8 s periods.

3. Observed Motions in the Model

From visual inspection of the video:

Heave: The triangle frame rises and falls far less than the wave height. The model appears to heave roughly ½–1 in in 3–5 in waves — a response amplitude operator (RAO) of roughly 0.15–0.25. This is the classic small-waterplane-area behavior.
Pitch: Very small. Visual estimate ≈ 1–3° peak in the larger waves. Because the frame is 8 ft long in the model (80 ft full scale), even 2° of pitch is a 2.8 ft bow-rise — noticeable but gentle.
Roll: Also small, ≈ 1–3°. The wide 40 ft (full-scale) back and the three widely spaced legs give good roll stiffness.
Frequency: The platform doesn't "track" the waves — it seems to sit through most chop and respond mainly to longer sets, consistent with a natural heave period well above the wave period.

4. Estimated Accelerations

Accelerations are the same in g's at model and full scale. For a sinusoidal heave of amplitude a and period T:

a_max = a · (2π/T)²

Case	Heave amp (model)	Period (model)	Peak heave accel	In g's
Typical chop	0.5 in = 0.013 m	0.8 s	≈ 0.8 m/s²	≈ 0.08 g
Larger set	1.0 in = 0.025 m	1.0 s	≈ 1.0 m/s²	≈ 0.10 g

Angular accelerations from ~2° pitch at ~1 s period work out to roughly 1.4 rad/s². At 40 ft forward of the center of pitch (full scale), that contributes about 0.6 m/s² ≈ 0.06 g of vertical motion at the bow.

Full-scale peak vertical accelerations in 3–5 ft short seas: roughly 0.08–0.15 g at the center, perhaps 0.15–0.25 g at the forward corners.

5. Comparison to a 50 ft Catamaran and 60 ft Monohull

In the same 3–5 ft short-period seas:

Vessel	Typical heave RAO	Typical peak vertical accel	Peak pitch	Ride character
80-ft seastead (this design)	≈ 0.15–0.25	0.1–0.2 g	1–3°	Platform-like; motions decoupled from waves; slow, long-period rocking
50-ft catamaran	≈ 0.6–0.9	0.3–0.5 g (plus slam spikes of 0.7–1.0 g)	3–6°	Follows waves closely; sharp, jerky pitching; bridgedeck slam possible
60-ft monohull	≈ 0.7–1.0	0.2–0.4 g	5–10°	Rides waves up and down; larger roll than cat; softer than cat in a chop but more heel

In short: The seastead is projected to have roughly ⅓ to ½ the peak acceleration of a catamaran the same overall length, and it should largely ignore short wind-chop that makes a monohull roll and a cat hobby-horse. Its natural heave period (with three NACA 0030 legs, 10 ft chord × 3 ft, half-submerged) will be long — probably 8–12 s — putting it above almost all wind-sea energy and only responding meaningfully to long swell.

6. What the Video Confirms Qualitatively

The small-waterplane-area concept is working: the hull "ignores" small waves rather than climbing over them.
Three-point support gives good roll and pitch stability without needing a very wide beam.
Motion is dominated by slow rigid-body oscillation, not wave-following. This is the signature of semi-submersible behavior.
Without stabilizers, there is still some residual pitch/heave oscillation that is lightly damped. This is exactly what the planned airplane-style stabilizer fins at the back of each leg should suppress — they add damping without adding waterplane area.

7. Expected Improvement With Stabilizers Added

Horizontal fins of the size described (10 ft span × 1 ft chord, one per leg, three total → ~30 ft² of lifting surface) moving vertically at even 0.2 m/s provide enough damping force to significantly reduce the residual heave and pitch oscillations seen in the video. Expect:

Heave RAO reduced from ~0.2 to ~0.1 or less in short seas.
Pitch cut roughly in half.
Active elevator trim can further reduce long-period pitch that otherwise dominates semi-submersible ride.

8. Summary

Model waves: ~3–6 in, 0.8–1.1 s period.
Full-scale equivalent: ~2.5–5 ft, 2.5–3.5 s period (a short, steep chop).
Full-scale peak vertical accelerations: roughly 0.1–0.2 g — well below a catamaran or monohull of similar length in the same seas.
Peak pitch/roll: a few degrees, versus ~5–10° for conventional hulls.
With stabilizers added, the ride should become noticeably calmer still, approaching true oil-platform quietness in normal conditions while retaining the ability to transit under power.

Estimates assume visual readings from the video are accurate to roughly ±30%. Quantitative refinement would come from on-board IMU logging of the model and, ideally, a known wave gauge in the test basin.