Seastead 1:10.5 Scale Model Specification & Test Plan

1. Scaling Laws (Froude Scaling)

Scale Factor λ = 10.5 (Model : Full Scale = 1 : 10.5)

2. Scale Model Principal Dimensions (Inches)

All full-scale feet converted to inches (×12) then divided by 10.5.

3. Target Model Weight & Displacement

Full Scale Rated Buoyancy (Displacement) Δ_FS = 27,500 lbs.

Δ_Model = Δ_FS / λ³ = 27,500 / (10.5)³

Δ_Model = 27,500 / 1157.625 ≈ 23.75 lbs (10.77 kg)

Weight Budget Breakdown (Target)

4. Test Wave Conditions (Sandy Hill Bay)

Target Full Scale Wave Heights (H_FS) scaled by λ = 10.5.

Wavelength & Period Scaling (Deep Water Approx.)

Full Scale: $L_{FS} \approx 5.12 T_{FS}^2$ (ft), $T_{FS} \approx \sqrt{H_{FS}/0.035}$ (approx for fully developed seas).
Model: $T_M = T_{FS} / \sqrt{10.5}$, $L_M = L_{FS} / 10.5$.

5. Water Depth Requirement (Deep Water Simulation)

Deep water condition: Depth $d > L/2$ (where L is wavelength).

Max Model Wavelength (8ft sea @ 7s period) $\approx$ 270 inches (22.5 ft).

Minimum Required Depth: > 135 inches (11.25 ft / 3.4 meters).

Sandy Hill Bay depths vary. Verify chart/sonar at test site. If depth < 11 ft, waves will feel bottom, becoming steeper and slower (shoaling), invalidating Froude scaling for deep-water seastead response. Select a location with > 12 ft depth at low tide.

6. Human Scale Dolls

Average Human Height: 5'9" = 69 inches.

Model Doll Height = 69 / 10.5 = 6.57 inches (16.7 cm).

Recommendation: Use standard 1:12 scale (6 inch) or 1:10 scale (7 inch) action figures (e.g., G.I. Joe, Barbie, Playmobil 1:12.5 ~5.5in). 1:10 scale dolls (~7in) are closest. Place them on the walkway, inside behind windows, and on the dinghy.

7. Android Apps for Motion Data Acquisition

Requirements: High sample rate (≥100 Hz), CSV export, GPS timestamp sync, raw sensor access (accel, gyro, mag), no aggressive low-pass filtering.

Phone Mounting Protocol

• Mount phone rigidly to the main deck structure (center of gravity height) using 3D printed clamp or heavy duty double-sided tape + zip ties.
• Orientation: Y-axis = Forward (Bow), X-axis = Starboard, Z-axis = Up. Verify in app.
• Enable "Linear Acceleration" (gravity subtracted) AND "Raw Accelerometer" (gravity included) if possible.
• Start logging > 30 sec before wave exposure to capture calm baseline.
• Sync: Clap phone against hull (sharp accel spike) visible in both phone data and shore video audio track for perfect time alignment.

8. Acceleration Metrics: Model to Full Scale Correlation

Fundamental Rule: Under Froude Scaling, Acceleration in g's is invariant (Scale Factor = 1.0). The numbers on the phone are the full-scale numbers.

Threshold: "Plates Sliding on Table"

Coefficient of static friction (ceramic on wood/tablecloth) $\mu_s \approx 0.3 - 0.5$.

Slide Threshold: $a_{lat} > \mu_s \cdot g \approx \mathbf{0.3g \text{ to } 0.5g}$ lateral acceleration.

• If model reads **> 0.3g sustained lateral accel** $\rightarrow$ Full scale plates slide.
• If model reads **> 0.5g peak lateral accel** $\rightarrow$ Full scale plates definitely slide / walking difficult.

Standard Seakeeping Metrics (Calculate from Phone Data)

9. Visual Validation: The "Water Glass" Method

Excellent low-tech validation. Scale the glass too.

• Glass Height: Standard 4.5 in tumbler $\rightarrow$ Model = 0.43 in (11 mm). Use a small **shot glass (1.5 oz ~1.3 in tall)** or **bottle cap** or 3D printed scaled cup (0.43 in).
• Water Fill: Scale volume by λ³. Full glass (350ml) $\rightarrow$ Model = 0.3 ml (tiny drop). Better: Fill model glass to same *visual fraction* (e.g., 80% full). Surface tension dominates at 11mm scale, so meniscus will look wrong.
• Rocks: Use coarse sand or 1-2mm beads.
• Analysis: Measure max water angle $\theta$ from video. $\tan(\theta) = a_{lat} / g$. Since $g$ is same, $\theta_{model} = \theta_{fullscale}$.

10. Camera & Video Analysis Protocol

Camera 1: Shore Tripod (Primary Science Camera)

• Frame Rate: 120 fps or 240 fps (High speed).
• Playback Speed: Slow down by **$\sqrt{10.5} \approx 3.24\times$**.
• 120 fps $\rightarrow$ Play at 37 fps (standard 30/60 timeline).
• 240 fps $\rightarrow$ Play at 74 fps.
• Reference Markers: Paint high-contrast targets (red/white checkerboard) on:
  Triangle corners (3 pts), Leg tops (3 pts), Dinghy bow/stern.
• Scale Reference: Floating pole with 1-inch bands (or 10cm bands) in foreground.
• Analysis Software: Tracker (Open Source Video Analysis), Kinovea, or custom Python (OpenCV). Track 6-DOF (x, y, z, roll, pitch, yaw) of triangle centroid.

Camera 2: On-Board GoPro (FPV / Human Factor)

• Mount at "Eye Level" on forward wall center (approx 5.7 in above model floor = 5 ft FS).
• Enable Hypersmooth OFF (Raw footage). Linear FOV (no fisheye).
• Enable GoPro Telemetry (GPMF): Records internal IMU (Accel/Gyro) at 200Hz+ synced to video frames.
• Extract telemetry via gopro2gpx, ffmpeg, or GoPro Telemetry Extractor Python scripts.
• Playback slowed 3.24x gives visceral "seasickness" test for viewers.

11. Additional Measurement Recommendations

1. Mooring Line Load Cell: Instrument the "stretchy line" (bungee/shock cord) with a small **S-type load cell (50-100 lb capacity)** + HX711 ADC + Arduino/ESP32 logging to SD card. Measures surge/sway excitation forces directly. Correlate with phone accel.
2. Wave Probe (Staff Gauge): The marked pole is good. Add a **capacitive wave wire** (two parallel SS wires, measure capacitance) or **pressure transducer** (submerged 1ft, logging at 10Hz) at model location for exact $H_s, T_p, \eta(t)$ time history. Essential for RAO (Response Amplitude Operator) calculation.
3. Draft Marks / Waterline Indicators: Paint distinct marks on legs at Design WL (12.29"), ±1", ±2". Video analysis of submergence validates heave & pitch.
4. Thruster Current/Voltage Logging: If testing propulsion/DP, log motor controller telemetry (Amps, Volts, RPM) per leg. Verify independent power redundancy.
5. Relative Motion (Two Models): If building Model #2 later, test the connecting walkway. Measure relative heave/pitch/sway between hulls. Critical for walkway structural design.
6. Heave Plate Effectiveness Test: Run tests WITH and WITHOUT bolt-on heave plates. Quantify reduction in Heave RAO at resonance (natural period $T_n \approx 2\pi\sqrt{(Mass+AddedMass)/Stiffness}$).
7. Drift / Yaw Stability: Release model (with safety line slack) in beam waves. Measure drift angle and yaw RAO. Validates "weathervaning" of foil legs.

12. Summary Checklist for Sandy Hill Bay Trip