```html 1/6-Scale Triangular Seastead Model – Wave/ Motion Scaling & Comparison

Triangular Seastead (1/6 scale) – Wave Height Scaling, Motions, and Acceleration Comparison

Important limitation: I can’t directly view or measure the YouTube video from the link you provided from within this chat. That means I cannot honestly “estimate the wave heights in the video” or extract motion/acceleration time histories without you providing (a) screenshots/frames with a known scale in the same plane as the waves, or (b) the measured wave-maker settings / measured wave heights, or (c) tracked motion data (even rough) from the video.

Good news: I can still (1) give you the correct scaling relationships (including the key point that accelerations are the same under Froude scaling), (2) compute full-scale dimensions from your model, (3) give a method to measure wave heights from the footage, and (4) provide a physics-based comparison of expected motions vs a ~50 ft catamaran and ~60 ft monohull, with typical acceleration ranges.

1) Geometry you gave & full-scale equivalent

Item	Model	Scale factor	Full scale (≈)
Planform triangle side length	10 ft	× 6	60 ft
Float/leg/column diameter	8 in = 0.667 ft	× 6	48 in = 4.0 ft
Float/leg/column length	4 ft	× 6	24 ft

2) Correct Froude scaling (what your “slowed by Froude factor” implies)

For free-surface gravity waves and floating-body response in the “Froude similarity” regime:

Length scale: λ = L_full / L_model = 6
Time scale: T_full / T_model = √λ ≈ 2.449
Velocity scale: V_full / V_model = √λ ≈ 2.449
Acceleration scale: a_full / a_model = (L_full/T_full²) / (L_model/T_model²) = 1 → under ideal Froude scaling, accelerations in ft/s² (or g’s) match.

If your slowed-down video uses the time scale factor √6, then (in principle) the visual timing corresponds to full scale. But the wave height in the footage still needs a physical measurement (or at least a frame-based scale reference) to convert to full-scale feet.

3) How to estimate wave height from the video (what I need from you, or you can do it)

3.1 What to measure

Pick a segment where:

The camera is steady, and the wave face is visible, and
There is a known dimension in the same image plane (e.g., the 10 ft side, or the 8 in column diameter).

Then measure (even roughly) in pixels:

Wave height H = crest-to-trough distance in pixels (same vertical line)
Reference length R = known object size in pixels (e.g., column diameter = 8 in, or a side length segment)

3.2 Convert pixel measurement to model feet

If you use the column diameter as reference:

Scale (ft per pixel) = D_model(ft) / D_pixels
H_model(ft) = H_pixels * (ft per pixel)

Where D_model = 8 in = 0.667 ft.

3.3 Convert model wave height to full scale

H_full = λ * H_model = 6 * H_model

3.4 What to send me so I can compute it for you

2–3 screenshots where the wave and the column diameter are both clearly visible, and/or
Your measured wave heights in the model test (even “about 1 inch”, “about 2 inches”, etc.), and
Wave period (seconds in model time) if you know it.

4) “Six times that” – quick lookup table (fill in your measured model wave heights)

Model wave height (crest-to-trough)	Full-scale wave height (×6)
0.5 in	3 in (0.25 ft)
1.0 in	6 in (0.5 ft)
2.0 in	12 in (1.0 ft)
3.0 in	18 in (1.5 ft)
4.0 in	24 in (2.0 ft)
6.0 in	36 in (3.0 ft)
8.0 in	48 in (4.0 ft)

5) What your structure “is” dynamically (based on the dimensions): closer to a small semi-sub than a boat

A 60-ft-side triangular platform supported by three ~4-ft-diameter columns with ~24-ft length (draft/column length) behaves more like a very simplified semi-submersible / three-column platform than a displacement monohull or planing craft. Key consequences:

Small waterplane area (relative to a monohull) can reduce wave-excitation forces in heave/pitch (good for comfort).
Restoring stiffness still comes from the waterplane area of the columns; with 4-ft columns it may be “stiffer” (shorter natural periods) than typical large semi-subs.
Large transverse spacing between columns (triangle corners) can strongly reduce roll/pitch angles vs a monohull of similar length, because the buoyancy shifts at the corners provide a big righting lever arm.
Potential downside: If the deck is near the water, you can get deck-edge slamming or “wet deck” events similar to catamaran bridge-deck slamming, depending on freeboard and wave steepness.

6) First-order heave natural period estimate (illustrative, depends heavily on displacement & waterline)

This is a back-of-envelope check to explain “why it might feel stiffer/softer than a boat.” Actual values require your displacement, CG, draft, and added-mass.

Heave natural period (very simplified) can be approximated by:

T_heave ≈ 2π * √( m / (ρ g A_wp) )

For three columns, waterplane area:

A_wp ≈ 3 * (π d² / 4)

With full-scale d = 4 ft:

Area per column ≈ π·(4²)/4 = π·4 ≈ 12.57 ft²
Total A_wp ≈ 37.7 ft²

If the platform displacement is on the order of (example) 450 ft³ of seawater (≈ 28,800 lb), then the simplified heave period comes out around ~4 seconds. If displacement is much larger (ballast, heavier deck), that period increases.

Typical semi-submersibles are designed for much longer heave periods (often 15–25 s) by reducing waterplane area and increasing effective mass/added-mass. Your 4-ft columns may produce a comparatively “stiff” response unless the overall displacement is large and/or the columns are shaped to reduce waterplane effects.

7) Accelerations: how to infer them from the video (and why model ≈ full-scale)

7.1 Key scaling point

Under Froude similarity, accelerations match between model and full scale (in g’s). So if the model shows (for example) “noticeably snappy” vertical motion, the full-scale will feel similarly “snappy” in terms of acceleration, even though the absolute distances are larger and the time is longer.

7.2 From observed heave amplitude and period

If a point on the platform heaves approximately sinusoidally:

z(t) = A sin(ω t),  where ω = 2π/T
a_max = A ω² = A (2π/T)²

Example (just to show the math): if the model heave amplitude is A = 1 inch = 0.083 ft at period T = 1.6 s:

ω = 2π/1.6 = 3.93 rad/s
a_max = 0.083 * (3.93²) = 1.28 ft/s² ≈ 0.040 g
Full-scale: A_full = 6 inches, T_full = √6·1.6 ≈ 3.9 s → a_max remains ≈ 0.040 g

7.3 From video tracking (best method)

If you can provide a clip or frames, you can extract motion vs time by tracking:

A corner of the deck (or a marker) relative to the horizon (for pitch/roll), and
Vertical position relative to a fixed scale reference (for heave).

Then numerically differentiate (with smoothing) to get velocity and acceleration. If you send me the tracked (time, position) data (even exported from a simple tracker), I can compute peak/RMS accelerations.

8) Comparison to a ~50 ft catamaran and ~60 ft monohull (qualitative + typical acceleration magnitudes)

8.1 What usually drives “comfort”

Monohull (60 ft displacement): typically larger roll angles, longer roll periods; can be “softer” in some vertical motions midship but can slam at the bow; roll can be fatiguing.
Catamaran (50 ft): typically lower roll angles, but can have sharper vertical accelerations and bridge-deck slamming depending on clearance and sea state; can feel “stiffer”/snappier.
Three-column platform: often low pitch/roll angles (good) if the deck is high enough and columns are well spaced; vertical accelerations depend strongly on heave natural period vs wave period.

8.2 Expected motion tendencies for your triangle (if deck clearance is adequate)

Roll & pitch angles: likely smaller than a monohull and often comparable-to-or-better than a cat, because buoyancy is at three widely spaced points.
Heave: could be moderate. If the heave natural period is short (few seconds), it may follow shorter waves more than a “true” semi-sub, increasing vertical acceleration.
Surge/sway/yaw: depends mostly on mooring and damping; a free-floating platform can yaw/translate more than a monohull underway.

8.3 Typical vertical acceleration ranges on 50–60 ft boats (order-of-magnitude)

These are broad “sea state dependent” comfort/operation ranges reported across seakeeping literature and design guidance (exact values vary with speed, heading, and sea spectrum).

Craft / Condition	Typical vertical accel (RMS / peak) felt onboard	Notes
60 ft displacement monohull (moderate seas, slow)	~0.03–0.10 g RMS; peaks ~0.15–0.25 g	Often roll-dominant discomfort; bow can see higher peaks.
50 ft cruising cat (moderate seas)	~0.05–0.12 g RMS; peaks ~0.20–0.40 g	Bridge-deck slamming can create sharp transient peaks.
3-column platform (your concept, if no slamming)	Could be ~0.03–0.10 g RMS; peaks depend on resonance & slamming	If heave period is short and matches waves, accelerations can rise; if long/decoupled, can be very comfortable.

The single biggest factor that can make your platform feel “worse than expected” is slamming (deck-edge impact, column emergence/re-entry, or wave slap under structure). Slamming produces high, short-duration accelerations that a simple sinusoid model won’t predict.

9) What I can infer from your described test (even without seeing the footage)

Because your model is relatively large (10 ft side) and the columns are slender, the test likely captures qualitative behavior well for relative pitch/roll/heave tendencies, provided the wave steepness and Reynolds effects aren’t dominating.
If the platform in the test mainly shows small pitch/roll and smooth heave, that is a good sign that full scale will avoid the “violent roll” a monohull can have at anchor.
If the test shows quick, snappy vertical motion, full scale will likely have similar g-levels (since acceleration scales ~1 under Froude scaling).

10) What to send me to produce the specific numbers you asked for (wave heights + accelerations)

Wave height from the test (even rough): e.g., “~2 inches crest-to-trough at the model.”
Wave period at the model: seconds between crests (video timestamp is fine).
A screenshot where I can see:
- the wave crest and trough, and
- the 8-inch diameter column clearly (so I can scale pixels → inches)
Draft / freeboard in the test (how submerged were the columns; deck height above mean waterline).

With those, I can:

Estimate model wave height H and full-scale H_full = 6H
Estimate heave amplitude and compute peak and RMS accelerations (in g)
Compare those accelerations directly to typical ranges for a 50 ft cat and 60 ft mono

If you upload 2–3 clear frames (or tell me “the model waves were about X inches”), I’ll fill in the wave-height estimates and produce a revised HTML block with the actual numbers.

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