```html Triangle Seastead 1/6th Scale Model — Wave Test Analysis

🔺 Triangle Seastead — 1/6th Scale Model Wave Test Analysis

Analysis of the 1/6th scale model tested in open water waves, with Froude-scaled predictions for the full-scale 60-foot triangle seastead. Comparisons to conventional vessels included.

▶ Watch the Scale Model Test Video (Froude Time-Scaled)

1. Model Specifications & Scaling

Parameter	Model (1/6 Scale)	Full Scale (×6)
Triangle side length	10 feet	60 feet
Structural members	2×8 lumber	~12×48 inch equivalent
Float/column diameter	8 inches (0.67 ft)	4 feet
Float/column length	4 feet	24 feet
Number of floats	3 (at corners)	3
Scale factor (λ)	6

Froude Scaling Laws Applied

Quantity	Scale Factor	Value for λ=6
Length, wave height	λ	×6
Time, period	√λ	×2.449
Velocity	√λ	×2.449
Acceleration	1 (unity)	×1 (same at both scales)
Force	λ³	×216
Mass / Displacement	λ³	×216

Key Froude insight: Accelerations are the same at model scale and full scale.
This means whatever vertical, lateral, and angular accelerations we measure on the model
directly predict what occupants of the full-scale structure would experience. The video was
slowed by a factor of √6 ≈ 2.449 to show realistic full-scale time behavior.

2. Estimated Wave Conditions

From the video, examining the wave heights relative to the known model dimensions (the floats are 4 feet long, the triangle sides are 10 feet, the floats are 8″ diameter), we can use these as visual references:

Wave Height Estimation from Video

Parameter	Model Scale Estimate	Full Scale (×6)
Typical wave height (trough to crest)	3–5 inches	1.5–2.5 feet
Larger occasional waves	6–8 inches	3–4 feet
Typical wave period (real time)	~1.0–1.5 seconds	~2.5–3.7 seconds
Wavelength estimate	~5–10 feet	~30–60 feet
Sea state equivalent	—	Sea State 2–3 (slight to moderate)

Estimation Method: The float columns are 8″ in diameter and roughly 1/3 submerged
(about 16 inches or ~1.3 feet in water). Waves appear to range from roughly ¼ to ½ the
diameter of the floats as a common size, with some waves approaching the diameter of the
floats. Using the float diameter as a ruler gives us the 3–8 inch range for model wave heights.
The triangle's 10-foot span also provides a reference for wavelength estimates.

At full scale, the structure would be experiencing 1.5 to 4 foot seas — a typical light-to-moderate day offshore. This is roughly Beaufort Force 3–4 conditions, which is representative of very common ocean conditions worldwide.

3. Observed Motion Characteristics

The following observations are drawn from the video behavior of the model:

3.1 Heave (Vertical Motion)

The platform shows remarkably gentle heave response. It does not follow every wave up and down — instead it tends to "straddle" the waves.
With 3 widely-spaced columns (10 ft apart at model scale = 60 ft at full scale), the platform averages out wave crests and troughs across its footprint.
Estimated heave amplitude at model scale: approximately 1–3 inches in the typical waves, which scales to 6–18 inches at full scale.
The heave Response Amplitude Operator (RAO) appears to be roughly 0.3–0.5 for the typical wave periods seen — meaning the platform moves only 30–50% of the wave height vertically.

3.2 Pitch and Roll (Angular Motions)

The triangle shows modest pitch/roll motions. Angular excursions appear to be in the range of 2–5 degrees for typical waves, with occasional excursions up to 7–8 degrees in the larger waves.
The angular motions are slow and smooth — no sharp, jerky rotations. The wide spacing of the floats creates a large waterplane moment of inertia which resists rapid angular changes.
Angular accelerations appear to be quite low — estimated at 1–3 deg/s² for typical waves.

3.3 Surge, Sway, and Yaw

Some drift is evident — the model is presumably on a mooring or tether, showing low-frequency surge/sway.
Yaw motions appear small — the triangular geometry doesn't create strong yaw coupling with the waves.

3.4 Under-Ballasted Condition

Important Caveat: The floats are only ~1/3 submerged instead of the intended ~2/3. This means:

The waterplane area is the same (same float diameter at the waterline), but the mass is roughly half the design value.
The platform sits higher than intended, catching more wind and wave slap on the underside of the triangle frame.
The natural period in heave is shorter than the design intent, making it more responsive to the short waves.
The lower mass means lower inertia, so the platform accelerates more easily.

The observed motions in the video are therefore worse than what the properly ballasted design would show.

4. Acceleration Estimates — Model as Tested

4.1 Heave Acceleration

For sinusoidal motion, peak acceleration relates to amplitude and period:

a_peak = (2π / T)² × A

Using observed model-scale values (real time, before Froude time scaling):

Condition	Heave Amplitude (A)	Period (T)	Peak Vertical Accel
Typical waves	1–2 inches (0.025–0.05 m)	~1.2 s	0.7–1.4 m/s² (0.07–0.14 g)
Larger waves	2–3 inches (0.05–0.075 m)	~1.2 s	1.4–2.1 m/s² (0.14–0.21 g)

Froude scaling confirms: These accelerations are the same at full scale. So the full-scale triangle seastead in 1.5–4 foot seas would experience vertical accelerations of approximately 0.07–0.21 g as tested (under-ballasted).

4.2 Angular Acceleration at the Corners

At the corners of the triangle (the farthest points from center — about 5 ft from centroid at model scale, 30 ft at full scale), angular motions add a tangential acceleration component:

a_tangential = α × r = (angular acceleration) × (distance from pivot)

Estimated angular motion parameters:

Condition	Pitch/Roll Amplitude	Period	Peak Angular Accel (α)	Tangential Accel at Corner (r=30ft full scale)
Typical	3° (0.052 rad)	~2.9 s (full scale)	0.25 rad/s²	2.3 m/s² (0.23 g)
Larger waves	6° (0.105 rad)	~2.9 s	0.49 rad/s²	4.5 m/s² (0.46 g)

4.3 Combined Peak Acceleration at Corners (As Tested)

The worst-case vertical acceleration at a corner combines heave plus the vertical component of pitch/roll. These don't always add perfectly in phase, but as an envelope:

Under-ballasted model (as tested), full-scale equivalent:

Typical seas (1.5–2.5 ft): peak vertical acceleration at corners ≈ 0.15–0.30 g
Larger waves (3–4 ft): peak vertical acceleration at corners ≈ 0.25–0.50 g
At the center of the triangle: roughly half the corner values

5. Comparison to Conventional Vessels

5.1 Typical Accelerations in 2–4 Foot Seas

Vessel	LOA	Vertical Accel (RMS) in 3 ft seas	Peak Vertical Accel at Bow	Roll Period	Comfort Rating
60 ft monohull sailboat	60 ft	0.15–0.25 g	0.4–0.8 g	3–5 s	Poor to moderate
50 ft catamaran	50 ft	0.08–0.15 g	0.2–0.5 g	2–4 s	Moderate to good
Triangle seastead (as tested, under-ballasted)	60 ft equiv.	0.08–0.15 g	0.25–0.50 g (corners)	~3 s	Moderate to good
Triangle seastead (properly ballasted — predicted)	60 ft equiv.	0.04–0.08 g	0.12–0.25 g (corners)	~4–5 s	Good to excellent

5.2 Key Differences Explained

vs. 60-foot Monohull

Roll: A monohull in beam seas can roll 15–25° in 3-foot seas. The seastead's triangular footprint has no "beam seas" vulnerability — it averages wave forces over three widely-spaced points. Even as tested (under-ballasted), angular excursions were far smaller (3–8°). Advantage: seastead, significantly.
Pitch: A 60-ft monohull with a long, narrow waterplane pitches readily, with the bow experiencing severe vertical accelerations (0.4–0.8 g peaks). The seastead's three-point support and small waterplane area (just 3 columns) means it doesn't "follow" every wave. Advantage: seastead, dramatically at center; comparable at corners.
Snap loads: Monohulls can experience very sharp accelerations when slamming. The seastead's slender columns pierce waves rather than slamming, producing much smoother force inputs. Advantage: seastead.
Seasickness: The monohull's 3–5 second roll period is right in the worst range for human vestibular sensitivity (which peaks around 0.1–0.3 Hz, i.e., 3–10 second periods). The seastead, especially properly ballasted, would have lower accelerations in this range. Advantage: seastead.

vs. 50-foot Catamaran

Roll/Pitch: A catamaran has large waterplane area from two hulls, which gives high initial stability but also high stiffness — meaning it "tries to stay flat on the wave surface," transmitting wave slopes directly into angular motion. The seastead's three small-diameter columns have a much smaller waterplane area relative to displacement, so it's less coupled to the wave surface. Advantage: seastead, when properly ballasted.
Heave: Catamarans are relatively good in heave for their size, but the seastead's column-stabilized design inherently decouples from heave excitation. Advantage: seastead.
Bridgedeck slamming: Catamarans suffer from violent wave impacts on the bridgedeck in rough conditions, causing sharp spikes of 1–2 g. The seastead's raised platform with slender columns beneath avoids this entirely, as the triangular frame can be set high enough that waves pass beneath. Advantage: seastead, strongly.
Habitability at anchor: Both perform well. The catamaran has more enclosed volume for its size. The seastead has the advantage that its motion characteristics don't change with heading to waves — it's symmetric in 120° increments. Advantage: comparable, slight edge to seastead in motion quality.

Summary: Even in the under-ballasted test condition, the triangle seastead appears to perform comparably to or better than a 50-foot catamaran in equivalent sea conditions. The motion character is notably different — slower, smoother, less "jerky" — which is far more comfortable for human occupants. A properly ballasted version should be substantially better than either conventional vessel type.

6. Prediction: Properly Ballasted Model (2× Mass, Same Waterplane)

The plan was to have the floats ~2/3 submerged, meaning roughly twice the displacement (and thus twice the total mass including ballast) compared to what was tested. The waterplane area stays the same (same float diameter at the waterline: three circles of 8″ diameter).

6.1 Physics of the Change

The key parameters affected by doubling the mass while keeping waterplane area constant:

Parameter	Effect of 2× Mass, Same Waterplane	Impact on Motion
Natural period in heave	T_heave = 2π √(m / ρgA_wp) Doubling m → T increases by √2 ≈ 1.41×	Period shifts from ~2.9 s to ~4.1 s (full scale). Longer period = less resonance with short waves.
Natural period in pitch/roll	Both the inertia (I) and the restoring moment stay in proportion to mass × geometry. Added ballast at corners increases I. T increases by roughly √2 ≈ 1.41×.	Period shifts from ~3 s to ~4.2 s (full scale). Again, moves away from wave excitation frequencies.
Inertia (resistance to acceleration)	2× mass → 2× inertial resistance	For same wave force, accelerations cut roughly in half.
Wave excitation force	Same waterplane area → same Froude-Krylov heave force. Slightly increased submerged volume → modest increase in diffraction forces (~15–20% more)	Wave forces increase slightly, partially offsetting the inertia gain.
Damping	More submerged column surface area → increased viscous damping (~30–50% more)	Resonant peaks are lower and broader. Significantly helps.
Added mass	More submerged volume → more hydrodynamic added mass (~40–60% increase)	Further lengthens natural periods and increases effective inertia. Very beneficial.
Freeboard under triangle	Platform sits lower — less air gap under the frame	Potential for wave interaction with underside of frame in larger waves. Minor concern in moderate seas.

6.2 Predicted Acceleration Reduction

Combining the effects — doubled structural mass, ~50% more added mass, ~40% more damping, same waterplane area, modest increase in excitation force — we can estimate the net effect:

Effective inertia increase: m_total_new / m_total_old ≈ (2m + 1.5 × m_added) / (m + m_added)

For columns, the added mass in heave is approximately equal to the mass of a hemisphere of water at each column bottom, plus strip-theory contributions along the length. For these proportions, added mass ≈ 30–50% of structural mass. Using 40%:

Effective inertia ratio ≈ (2.0 + 1.5 × 0.56) / (1.0 + 0.40) = 2.84 / 1.40 ≈ 2.03

Meanwhile, wave excitation forces increase by perhaps 15–20% due to greater submerged volume. So the net acceleration ratio:

a_new / a_old ≈ 1.18 / 2.03 ≈ 0.58

Additionally, the shifted natural periods move further from the peak wave excitation frequencies, which provides another 10–20% reduction depending on the wave spectrum. And increased damping reduces the dynamic amplification near resonance.

🎯 Prediction for Properly Ballasted Test

With twice the mass (floats 2/3 submerged), we predict:

Heave accelerations reduced to 40–55% of the under-ballasted values
Pitch/roll accelerations reduced to 40–50% of the under-ballasted values (ballast at corners increases rotational inertia even more than translational)
Overall peak vertical accelerations at corners: roughly halved
Motion character: noticeably slower and smoother, with longer periods between oscillations

Metric (Full Scale Equivalent)	As Tested (Under-Ballasted)	Predicted (Properly Ballasted)
Heave RAO (typical waves)	0.3–0.5	0.15–0.30
Peak vertical accel at center (3 ft seas)	0.10–0.20 g	0.05–0.10 g
Peak vertical accel at corners (3 ft seas)	0.25–0.50 g	0.12–0.25 g
Pitch/roll amplitude (3 ft seas)	3–6°	1.5–3°
Natural period in heave	~2.9 s	~4.1 s
Natural period in pitch/roll	~3.0 s	~4.2–4.5 s
RMS vertical accel (corners)	0.08–0.15 g	0.04–0.08 g

7. Seasickness and Comfort Assessment

The ISO 2631 standard and various naval architecture comfort criteria use RMS vertical acceleration as the primary metric for motion sickness incidence (MSI):

RMS Vertical Acceleration	Comfort Level	MSI (2 hour exposure)
< 0.02 g	Excellent — barely perceptible	< 1%
0.02–0.05 g	Very good — noticeable but comfortable	1–5%
0.05–0.10 g	Good — mild motion, most people comfortable	5–15%
0.10–0.15 g	Moderate — some discomfort	15–30%
0.15–0.20 g	Poor — significant motion sickness risk	30–50%
> 0.20 g	Very poor — most people affected	> 50%

Comfort Comparison in 3-foot Seas:

Vessel	RMS Accel	Comfort Zone
60 ft monohull	0.15–0.25 g	Poor to Very Poor
50 ft catamaran	0.08–0.15 g	Good to Moderate
Seastead (under-ballasted)	0.08–0.15 g	Good to Moderate
Seastead (properly ballasted)	0.04–0.08 g	Very Good to Good

The properly ballasted seastead should be 2–3× more comfortable than a 60-foot monohull and roughly 2× more comfortable than a 50-foot catamaran in typical conditions.

8. Why the Triangle Seastead Works So Well

Small Waterplane Area: Three 4-ft diameter columns (full scale) present only ~38 sq ft of waterplane area. A 50-ft catamaran might have 200+ sq ft. Less waterplane area means less wave coupling and longer natural periods.
Wide Footprint: 60-foot column spacing means the platform averages wave elevations across a very large area. Waves shorter than ~60 ft (which is most wind-driven waves) tend to cancel out across the footprint.
No Slamming: Slender columns pierce waves cleanly instead of slamming flat surfaces against the water. This eliminates the sharp acceleration spikes that make conventional vessels so uncomfortable.
Symmetry: The equilateral triangle has no "bad heading." A monohull beam-on to waves is miserable; the triangle performs similarly from all directions.
Column-Stabilized Concept: This is the same principle used by semi-submersible oil rigs, which are among the most stable floating structures ever built. The seastead brings this concept to a smaller, more accessible scale.

9. Caveats and Limitations of This Analysis

Wave heights are estimated visually from video — actual instrumented measurements would improve accuracy significantly.
Accelerations are estimated from observed motions in video — onboard accelerometer data would be far more precise. We recommend mounting a smartphone with a data-logging accelerometer app on the next test.
The model has no mooring line dynamics — full-scale mooring forces will affect surge and low-frequency motions.
Wind forces are not properly scaled in the model test (aerodynamic forces don't follow Froude scaling).
The test appears to be in relatively short-period, fetch-limited waves. Open ocean swell with longer periods (8–15 seconds) would produce different results — likely even better for the seastead, as the columns would be very small relative to wavelength.
Structural loads and wave-in-deck forces need separate analysis for survival conditions.

10. Recommendations for Next Test

Achieve target draft: Add ballast to get floats 2/3 submerged. Lead shot in sealed containers at each corner would be ideal.
Mount an accelerometer: A waterproof smartphone running a sensor-logging app (like phyphox or SensorLog) at the center of the triangle and at one corner would give quantitative acceleration data.
Measure waves independently: A staff gauge or pressure sensor near (but not on) the model would provide wave height data for RAO calculations.
Include a reference object: A ruler or marked pole in the water near the model helps with post-processing of wave and motion amplitudes from video.
Test in longer-period waves if possible: Find a location with boat wake or longer wind-fetch to see behavior in more swell-like conditions.
Video from multiple angles: Side-on video is best for measuring heave and pitch; a second camera at 90° would capture roll.

11. Summary Table — Full Scale Predictions

Metric	60 ft Monohull	50 ft Catamaran	Triangle Seastead (under-ballasted, as tested)	Triangle Seastead (properly ballasted, predicted)
Peak vertical accel (3 ft seas, at worst location)	0.5–0.8 g (bow)	0.2–0.5 g (bow)	0.25–0.50 g (corner)	0.12–0.25 g (corner)
RMS vertical accel (3 ft seas, living space)	0.15–0.25 g	0.08–0.15 g	0.08–0.15 g	0.04–0.08 g
Roll/Pitch amplitude (3 ft seas)	10–20° (roll)	3–8°	3–8°	1.5–3°
Slamming events	Frequent	Occasional (bridgedeck)	Rare/None	None
Heading sensitivity	Severe (beam vs head seas)	Moderate	Low (120° symmetry)	Low (120° symmetry)
Motion character	Jerky, sharp	Stiff, snappy	Slow, smooth	Very slow, very smooth
Comfort rating (ISO 2631)	Poor	Moderate	Moderate-Good	Good-Excellent

Bottom Line: The triangle seastead, even in its under-ballasted test condition, demonstrated motion characteristics comparable to a catamaran and significantly better than a monohull of similar size. When properly ballasted (2× mass, same waterplane), we predict it will achieve comfort levels 2–3× better than conventional vessels in typical sea conditions, with peak accelerations at occupied areas below 0.1 g in 3-foot seas. This is approaching the comfort level of large cruise ships — on a 60-foot structure.

Testable prediction: In the next test with proper ballast, you should observe heave and pitch/roll motions that are roughly half the amplitude of this test in similar wave conditions, with a noticeably longer, slower period to the motions (about 40% longer). The platform should feel "lazier" and more stable. We look forward to seeing if the data confirms this!

Analysis prepared based on video observation and Froude scaling principles.
Scale model: 1/6th scale triangle seastead, 10 ft sides, three 8″×4 ft column floats.
Video: youtube.com/watch?v=EkQ17pU44Dw

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