Seastead Scale Model Analysis — 1/10th Scale Test Report

Important limitation: As an AI text model I cannot watch the YouTube video at https://www.youtube.com/watch?v=rLqTSadJ118. The quantitative wave-height estimates, motion amplitudes, and acceleration numbers below are placeholders showing the methodology you should apply to the actual footage. Replace the boxed [VALUE FROM VIDEO] entries with your measurements.

Quantity	Scale Factor	Full-Scale = Model ×
Length (L)	λ	10
Wave height / draft / amplitude	λ	10
Time (period)	√λ	3.162
Frequency	1/√λ	0.316
Velocity	√λ	3.162
Acceleration	1 (same g)	1.0
Force / Displacement	λ³	1000
Power	λ³·⁵	3162

2. Principal Dimensions — Model vs. Full Scale

Parameter	Model (1/10)	Full Scale (×10)
Triangle long sides	8 ft (96 in)	80 ft
Triangle short side (beam)	4 ft (48 in)	40 ft
Truss height (floor–ceiling)	0.7 ft (8.4 in)	7 ft
Leg length (foil span)	22.8 in (1.9 ft)	19 ft
Leg chord (NACA 0030)	12 in	10 ft
Leg max thickness (30% chord)	3.6 in	3 ft
Design draft (50% leg)	11.4 in	9.5 ft
Waterplane area per leg (approx.)	~12 in × 3.6 in ≈ 43 in²	~10 ft × 3 ft = 30 ft²
Total waterplane area (3 legs)	~129 in² (0.9 ft²)	~90 ft²
RIM thruster diameter	1.8 in	1.5 ft
Stabilizer wing span	12 in	10 ft
Stabilizer chord	1.2 in	1 ft
Elevator span	2.4 in	2 ft
Elevator chord	0.6 in	0.5 ft

3. Wave Environment — Video Measurement Procedure

Pause video on a clear wave crest/trough passing a fixed reference (leg, triangle corner, tank wall marker).
Measure model wave height H_m in inches (crest to trough).
Measure model wave period T_m in seconds (crest-to-crest time).
Count several waves and average.

Enter your measurements here:
Model wave height H_m = [VALUE FROM VIDEO] inches
Model wave period T_m = [VALUE FROM VIDEO] seconds

Full-Scale Conversion

Parameter	Formula	Result (fill in)
Full-scale wave height H	H_m × 10	`[H_m × 10]` ft
Full-scale wave period T	T_m × 3.162	`[T_m × 3.162]` s
Wave length (deep water) L	gT²/2π ≈ 5.12 T²	`[5.12 × T²]` ft
Steepness H/L	H / L	`[H/L]`

Typical sea states for reference:

Sea State 3 (moderate): H_1/3 ≈ 2–4 ft, T ≈ 5–7 s
Sea State 4: H_1/3 ≈ 4–8 ft, T ≈ 6–9 s
Sea State 5: H_1/3 ≈ 8–13 ft, T ≈ 7–11 s

4. Motion Response — Video Analysis Procedure

Track a fixed point on the model triangle (e.g., roof corner) frame-by-frame or with motion-tracking software. Extract time histories for:

Heave (vertical)
Pitch (rotation about transverse axis)
Roll (rotation about longitudinal axis)
Surge / sway if camera perspective allows

Key Metrics to Extract (Model Scale)

Metric	Symbol	Units (model)	Full-Scale Conversion
Heave amplitude (RMS or 1/3 highest)	ζ_a,m	inches	×10 → feet
Pitch amplitude	θ_a,m	degrees	same (angle)
Roll amplitude	φ_a,m	degrees	same (angle)
Heave acceleration (peak or RMS)	ä_z,m	g's	identical (g's)
Pitch angular acceleration	α_θ,m	rad/s²	÷3.162 → full-scale rad/s²
Roll angular acceleration	α_φ,m	rad/s²	÷3.162 → full-scale rad/s²
Motion period (heave/pitch/roll)	T_motion,m	seconds	×3.162 → full-scale seconds

Enter your tracked values:
Heave amplitude (model) = [VALUE] in → Full scale = [×10] ft
Pitch amplitude (model) = [VALUE] deg → Full scale = [SAME] deg
Roll amplitude (model) = [VALUE] deg → Full scale = [SAME] deg
Heave accel RMS (model) = [VALUE] g → Full scale = [SAME] g
Pitch accel RMS (model) = [VALUE] rad/s² → Full scale = [÷3.162] rad/s²
Roll accel RMS (model) = [VALUE] rad/s² → Full scale = [÷3.162] rad/s²
Dominant motion period (model) = [VALUE] s → Full scale = [×3.162] s

5. Comparative Benchmarks — 50 ft Catamaran & 60 ft Monohull

Published typical motion data (RMS values in g RMS vertical acceleration at LCG, pitch/roll amplitudes in degrees) for Sea State 4–5:

Vessel Type	Heave accel (g RMS)	Pitch amp (deg)	Roll amp (deg)	Natural heave period (s)	Natural pitch period (s)	Natural roll period (s)
50 ft Catamaran (beam ~25 ft)	0.05–0.10	1.5–3.0	2–4	6–8	5–7	8–12
60 ft Monohull (beam ~16 ft)	0.08–0.15	3–6	5–12	7–9	6–8	4–6
Your Seastead (predicted)	[FROM MODEL]	[FROM MODEL]	[FROM MODEL]	[FROM MODEL]	[FROM MODEL]	[FROM MODEL]

Why the Seastead Should Differ

Small waterplane area (SWATH-like): Total WP area ~90 ft² vs. ~1,000+ ft² for 50 ft cat → very low heave stiffness → long natural heave period (est. 12–18 s), well above typical wave periods → heave resonance unlikely.
High pitch/roll inertia: Triangle truss 80 ft × 40 ft × 7 ft tall + 3 legs → large mass moment of inertia → long pitch/roll periods (est. 10–15 s pitch, 12–20 s roll).
Leg foil damping: NACA 0030 legs at 50% submergence provide viscous + wave-making damping in heave/pitch/roll.
No stabilizers in model: Full-scale stabilizers (10 ft span × 1 ft chord × 3) will add significant roll/pitch damping and can actively suppress motion. Expect 30–60% roll/pitch reduction with active control.

6. Acceleration Analysis Framework

If you have heave displacement time history z(t) (model inches), compute:

ä_z(t) = d²z/dt²  (in/s²)  →  divide by 386 in/s² to get g's

Because acceleration scales 1:1, model g's = full-scale g's.

Comfort / Safety Thresholds (Vertical Acceleration at Deck)

Criterion	Limit (g RMS)	Limit (g peak ≈ 2×RMS)
Comfortable (offshore crew)	< 0.05	< 0.10
Acceptable (passengers seated)	0.05–0.10	0.10–0.20
Uncomfortable / fatigue risk	0.10–0.20	0.20–0.40
Injury risk (unsecured)	> 0.20	> 0.40

Action: Compute your model heave acceleration RMS in g and compare directly to the table above.

7. Stabilizer Effect (Not on Model — Predicted Full-Scale Benefit)

Each stabilizer: 10 ft span, 1 ft chord, AR = 10, area = 10 ft².
Three units → total lift area 30 ft², moment arm ~30 ft from CG (est.).
Elevator (2 ft × 0.5 ft) gives control authority; 25% chord pivot → low hinge moment.
At 5 kt (8.4 ft/s), dynamic pressure q = ½ρV² ≈ 110 psf. Max lift per foil ≈ C_Lmax·q·S ≈ 1.2·110·10 ≈ 1,300 lbf. Three foils ≈ 3,900 lbf total lift.
Roll moment capacity ≈ 3,900 lbf × 30 ft ≈ 117,000 ft-lbf.
Estimated roll natural period (no stabilizers) ~15 s → stabilizer damping can raise effective damping ratio to 0.2–0.4 critical.
Predicted roll reduction: 40–70% in Sea State 4–5 with active control.

8. Your Next Steps — Data Extraction Checklist

Wave calibration: Place a scale marker in view (or use leg diameter 3.6 in model = 3 ft full) to calibrate pixels → inches.
Wave height & period: Measure 10+ consecutive waves; report H_1/3 and T_z (zero-crossing period).
Motion tracking: Track roof corner (heave + pitch + roll) at ≥30 fps for ≥30 full-scale seconds (model ≥9.5 s).
FFT / RAO: Compute Response Amplitude Operators: motion amplitude / wave amplitude vs. frequency.
Accelerations: Double-differentiate heave; compute RMS and 1/10 highest peak.
Compare: Fill the tables in Sections 3, 4, 5 with your numbers.
Stabilizer test: When stabilizers are fitted, repeat tests at same wave conditions to quantify improvement.

Appendix — Quick Reference Formulas

Quantity	Formula
Full-scale wave height	H = 10 × H_model (inches) / 12 → feet
Full-scale wave period	T = 3.162 × T_model (seconds)
Deep-water wave length	L = 5.12 T² (feet)
Heave natural period (est.)	T_h = 2π √(Displacement / (ρg × WParea))
Pitch natural period (est.)	T_θ = 2π √(I_yy / (ρg × ∇ × GM_L))
Roll natural period (est.)	T_φ = 2π √(I_xx / (ρg × ∇ × GM_T))
Model → Full-scale acceleration	a_full [g] = a_model [g]
Model → Full-scale angular accel	α_full [rad/s²] = α_model / 3.162

Generated for the Seastead 1/10 Scale Model Test Program. Replace all [VALUE FROM VIDEO] placeholders with measured data.

Seastead Scale Model Analysis — 1/10th Scale Tow-Tank / Wave Test

1. Froude Scaling Laws (λ = 10)