```html 1/6-Scale Triangle Seastead – Wave Height & Motion/Acceleration Scaling

Triangle Seastead 1/6 Scale Test – What Can Be Estimated from the Video (and What Can’t)

Important limitation: I can’t directly view or measure the YouTube video from inside this chat. That means I cannot honestly “read off” wave heights, periods, or displacements from frames.

What I can do right now:
  1. Give you a reliable method to estimate wave height from the video using known dimensions (the 8-inch columns) as a scale reference.
  2. Apply correct Froude scaling (including a key point: accelerations scale ~1:1 under Froude similarity).
  3. Give first-cut, physics-based expectations for how the full-scale platform would compare to a 50 ft catamaran and a 60 ft monohull.
  4. Estimate how doubling weight (with the same waterplane area) tends to change natural periods and (often) accelerations.
If you want me to produce numeric wave-height and acceleration estimates from the actual footage, paste:

Given Geometry (Model → Full Scale)

ParameterModelFull scale (×6)
Triangle side length10 ft60 ft
Column/leg diameter8 in = 0.667 ft48 in = 4.0 ft
Column/leg length4 ft24 ft
Length scale (λ)16
Time scale (Froude)1√6 = 2.449

Froude Scaling Essentials (What “Slowed Down by √6” Means)

For gravity-wave dominated problems (boats, floats, offshore platforms), the usual similarity is Froude scaling:

Key consequence: if your slowed video is time-scaled correctly to full scale, the visual tempo of motions is representative. But even more importantly: the g-levels (vertical accelerations) you see in the model are roughly the same as the full-scale g-levels, assuming Reynolds/viscous effects and construction flexibility aren’t dominating.

How to Estimate Wave Height in the Video (and Convert to Full Scale)

1) Use the 8-inch diameter column as a ruler

In any frame where a wave crest and trough are visible near a column:

  1. Measure the column diameter in pixels: D_px
  2. Measure the local wave crest-to-trough height in pixels: H_px
  3. Convert to model inches: 
    H_model_in = H_px / D_px * 8
  4. Convert to full scale: 
    H_full_in = 6 * H_model_in
H_full_ft = H_full_in / 12

2) Quick conversion table (once you have model wave height)

Model wave heightFull-scale wave height (×6)
2 in12 in = 1.0 ft
3 in18 in = 1.5 ft
4 in24 in = 2.0 ft
6 in36 in = 3.0 ft
8 in48 in = 4.0 ft

If you tell me (or screenshot) what the model wave heights look like (even roughly, like “~4 inches crest-to-trough”), I can immediately give the “6×” full-scale number.

First-Cut Hydrostatics From Your “1/3 in the Water” Note

You said the columns were only about 1/3 submerged; you wanted ~2/3 submerged (via ballast). For a vertical cylinder, the waterplane area does not change much with submergence (until you approach ends or change shape), but the displacement/weight does.

Waterplane area (drives heave stiffness)

D = 0.667 ft
r = 0.333 ft
Awp_per_column = π r^2 ≈ 0.349 ft^2
Awp_total (3 columns) ≈ 1.05 ft^2

Heave hydrostatic stiffness (linearized):

K_heave ≈ ρ g Awp   (in force/length)
In "lb/ft" terms: K_heave ≈ 62.4 * Awp_total ≈ 62.4 * 1.05 ≈ 65.5 lb/ft

Estimated displacement/weight at ~1/3 submergence (rough)

If draft ~ (1/3)*4 ft ≈ 1.33 ft:

Submerged volume per column ≈ Awp_per_column * draft ≈ 0.349 * 1.33 ≈ 0.465 ft^3
Total displaced volume (3 columns) ≈ 1.395 ft^3
Buoyancy/weight ≈ 1.395 * 62.4 ≈ 87 lb

This is a rough “buoyancy only” number; your wood structure adds weight but must be supported by buoyancy too. It gives the right order of magnitude for the test condition you described.

Natural Period and “How Lively It Feels” (Heave)

For a simplified heave oscillator:

m z¨ + K z ≈ F_wave(t)
ω_n = sqrt(K/m)
T_n = 2π/ω_n

Using the rough numbers above:

If you doubled the weight (same waterplane area)

If weight ≈ 174 lb (mass doubles), then:

Numerically:

Implication for accelerations: if your wave encounter period is near the original natural period, adding ballast can move you away from resonance and often reduces accelerations noticeably. If you’re far from resonance (quasi-static following), added weight changes things less.

Acceleration Estimation (From Video) – What to Compute

Once you estimate a representative heave amplitude A (ft) and period T (s), a sinusoidal approximation gives:

z(t) = A sin(2π t/T)
a_max = (2π/T)^2 * A
g-level = a_max / 32.2

Important: Under Froude scaling, those g-levels are approximately the same at full scale.

Example (placeholder numbers only)

If the model heaves with amplitude A = 2.5 in = 0.208 ft and period T = 1.0 s:

a_max ≈ (2π/1.0)^2 * 0.208 ≈ 8.2 ft/s^2
≈ 0.25 g

That ~0.25 g would be a “feels lively but not insane” level on many boats. If instead T grows (with ballast) to 1.4 s at the same A: 

a_max scales ~ 1/T^2 → (1/1.4^2) ≈ 0.51
So ~0.25 g → ~0.13 g

How the Full-Scale Platform Might Compare to a 50 ft Cat and a 60 ft Monohull

Based on the geometry you described (3 columns at the corners of a wide triangle), the full-scale behavior is closer to a small semi-submersible / trimaran-platform hybrid than to a monohull.

Qualitative comparison (typical tendencies)

Aspect Triangle 3-column platform (your concept) 50 ft catamaran 60 ft monohull
Roll angle Often small due to wide stance; depends strongly on CG height and column immersion Usually small angles but can be “stiff/snappy” (high GM) Larger roll angles, slower “softer” roll
Heave / vertical motion With small waterplane area and deep draft, can be very good (low wave force). With shallow immersion it tends to follow surface more Can have high vertical accelerations and bridge-deck slamming depending on clearance Often more pitch/heave than a wide platform; can be more “forgiving” in accelerations in some sea states
Pitch Often reduced by large corner spacing, but corners can see significant vertical accel if the platform is rigid Can pitch and hobbyhorse; slamming can dominate Can hobbyhorse; long-period pitch is common
Slamming risk If deck is high and only columns touch water: low slamming. If structure/boards hit water: can slam hard Bridge-deck slamming can be severe Bow slamming possible; typically different mode than cats

A subtle but important point: “Small angles” doesn’t always mean “small accelerations”

Your full-scale triangle is about 60 ft on a side. For an equilateral triangle, the distance from center to a corner is: 

R ≈ side / √3 ≈ 60 / 1.732 ≈ 34.6 ft

Vertical acceleration at a corner includes rotational components: 

a_corner ≈ a_heave_at_CG  ±  R * θ¨   (pitch/roll angular acceleration contribution)

So even if pitch/roll angles are small, if the platform is stiff and responds quickly (large θ¨), the corners can feel sharp vertical accelerations. This is one reason very wide, stiff platforms can feel “jerkier” at the perimeter than a narrower monohull, even with less roll angle.

Effect of Adding Ballast to Reach ~2/3 Submergence

You said: “twice the weight and the same waterline area”. In that case:

In plain terms: if the unballasted model looked “bouncy” (short-period), ballast tends to make it “slower” and often lower in peak g’s, especially if the wave periods don’t also increase.

What I Need From You to Produce Real Numbers (Wave Height, Period, Accel) From This Specific Video

Any one of these is enough:

With that, I can output:

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