Seastead Scale-Model Test Brief

Scale ratio λ = 10.5 | Test site: Sandy Hill Bay, Anguilla

1. Froude Scaling Basis

Length: divide by 10.5 (multiply feet by 8⁄7 to get model inches)
Time / Period: divide by √10.5 ≈ 3.24
Velocity: divide by √10.5 ≈ 3.24
Acceleration: 1 : 1 — numerically identical!
Mass / Weight: divide by λ³ = 1157.6

Key consequence: An acceleration of 0.2 g measured on the model represents exactly 0.2 g on the full-scale seastead. Thresholds for plates sliding, water sloshing, or passengers feeling uncomfortable are therefore the same numerical values in both scales.

2. Scale-Model Dimensions (inches)

Item	Full Scale	Model (inches)	Model (fraction)
Main Living Triangle (Truss)
Front sides	70 ft	80.00 in	80″
Back width	35 ft	40.00 in	40″
Truss height (floor to ceiling)	7 ft	8.00 in	8″
Legs / Floats (×3)
Overall length	19 ft	21.71 in	21 ⁵⁄₇″
Chord (leading edge to trailing edge)	10 ft	11.43 in	11 ³⁄₇″
Max thickness (port-starboard)	3 ft	3.43 in	3 ³⁄₇″
Submerged length (50% draft)	9.5 ft	10.86 in	10 ⁶⁄₇″
Built-in ladder (on above-water half)	~9.5 ft	10.86 in	10 ⁶⁄₇″
Thrusters (×6)
RIM drive diameter	1.5 ft	1.71 in	1 ⁵⁄₇″
Height above bottom	3 ft	3.43 in	3 ³⁄₇″
Rear Decks & Dinghy
Side deck extension (width)	5 ft	5.71 in	5 ⁵⁄₇″
Dinghy (14 ft RIB) length	14 ft	16.00 in	16″
Stabilizer “Airplanes” (×3)
Main wing span	12 ft	13.71 in	13 ⁵⁄₇″
Main wing chord	1.5 ft	1.71 in	1 ⁵⁄₇″
Fuselage length	6 ft	6.86 in	6 ⁶⁄₇″
Elevator span	2 ft	2.29 in	2 ²⁄₇″
Elevator chord	6 in (0.5 ft)	0.57 in	⁴⁄₇″
Wing pivot notch (≈25% chord)	—	≈0.43 in	~7⁄16″

Build tip: The trailing edge of the NACA leg at model scale is very thin. If you attach the stabilizer directly to that knife-edge, reinforce the joint with a tiny brass bracket or extend a thin flat tab from the leg so the stabilizer has a solid mounting surface.

3. Target Model Weight

Assuming the full-scale craft is sized to float at the 50% leg draft in sea water, the displaced volume is set by the submerged portion of the three NACA foils:

NACA 0030 foil area ≈ 0.685 × chord × max thickness = 0.685 × 10 ft × 3 ft ≈ 20.55 ft²
Submerged volume (3 legs) = 3 × 20.55 ft² × 9.5 ft ≈ 585.7 ft³
Buoyancy in salt water (≈64 lb/ft³) → full-scale displacement ≈ 37,500 lb

Under Froude scaling, weight is divided by λ³ = 1157.6:

Target model weight ≈ 37,500 ÷ 1157.6 ≈ 32.4 lb (≈14.7 kg)

Build the model lighter, then add sealed ballast (lead shot, steel washers, or water bottles) until it floats with exactly 10.86 in of each leg submerged. Correct draft is the single most important tuning step for dynamic similitude.

4. Simulated Wave Heights

Wave heights scale linearly. In the bay, use your graduated pole to find wave heights matching these targets:

Full-Scale Wave Height	Model Wave Height	Target in Bay
3 ft	3.43 in	3 ³⁄₇″
5 ft	5.71 in	5 ⁵⁄₇″
8 ft	9.14 in	9 ¹⁄₇″

Model wave periods will be roughly 3.24× shorter than the full-scale equivalents, so the model will bob and pitch more quickly.

5. Time & Video Scaling

Because model motions are faster by √10.5 ≈ 3.24, slow the footage by the same factor so that it looks like full-scale motion.

Slow-motion factor: 3.24×
Practical recipe: Record at 120 fps and conform the clip to a ~37 fps timeline, or apply a 31% speed factor in your video editor (e.g., 100% ÷ 3.24 ≈ 31%).
Fixed camera: The higher frame rate also gives you many more data points for frame-by-frame tracking of colored targets on the model.

6. Doll / Figure Scale

A 6‑ft (72‑in) person scales to 72 ÷ 10.5 ≈ 6.86 in. Use 7‑inch action figures for the video; they are close enough to true 1:10.5 scale and will immediately sell the size of the seastead to viewers.

7. Water Depth — Deep-Water Requirement

A wave behaves as a deep-water wave when depth h > L/2 (half the wavelength). Using the dispersion relation L = gT²/(2π) (g ≈ 32.2 ft/s²):

Model Wave Period	Model Wavelength	Min Depth for Deep Water	Full-Scale Equivalent Period
2 s	≈ 6.5 ft	≈ 3.3 ft	~6.5 s
3 s	≈ 14.6 ft	≈ 7.3 ft	~9.7 s
4 s	≈ 26.0 ft	≈ 13.0 ft	~13.0 s

If Sandy Hill Bay is shallower than ~15 ft where you test, you are testing finite-depth (shoaling) effects. That is still useful, but the waves will be steeper and the vessel response will differ slightly from true open-ocean deep water. Try to find the deepest spot available and match your test wave heights to the actual local wave periods you encounter.

8. Android Apps for Logging Motion

Mount the phone rigidly near the model’s center of gravity with its axes aligned to the vessel (forward, starboard, down). Here are recommended apps:

Recommended Apps

Physics Toolbox Sensor Suite (Vieyra Software) — the most complete tool for this job. It logs acceleration (with or without gravity), gyroscope, orientation, and barometer; exports CSV; and even offers a web-based remote view so you can monitor from shore without touching the model.
Sensor Logger — lightweight, minimal UI, high-rate CSV logging. Excellent if you just want raw data files to analyze later in Excel/Python.
AndroSensor — a classic all-in-one logger. Records accelerometer, gyroscope, magnetic field, and GPS. (GPS is usually too coarse for model-scale velocity, but the inertial sensors are fine.)
MATLAB Mobile — ideal if you already use MATLAB; streams sensor data straight to your computer for live processing.

What Each Metric Means for Scaling

Metric	How to Capture	Scaling / Interpretation
Heave / Surge / Sway Acceleration	Phone accelerometer (linear, gravity removed)	1:1 — a 0.1 g reading is 0.1 g full scale
Roll / Pitch / Yaw Angle	Orientation (sensor fusion) or derived from gyro	1:1 — 5° on model = 5° full scale
Angular Velocity (roll/pitch rate)	Gyroscope	Model reads 3.24× faster. Divide by 3.24 for full-scale equivalent.
Angular Acceleration	Derivative of gyro	Model reads 10.5× higher.
Jerk	Differentiate accel in post-processing	Model jerk is 3.24× full-scale equivalent.
Velocity / Heave Displacement	Prefer video tracking; phone double-integration drifts quickly	Divide video-derived values by 3.24.

GoPro Telemetry

Recent GoPros record built-in IMU data directly inside the MP4. You can extract raw accelerometer & gyro on a computer with GoPro Telemetry Extractor or the open-source gpmf-extract tools. The overlay in GoPro Quik is handy for a quick gut check, but the raw CSV gives you synchronized data to compare against the phone.

9. Acceleration, Sliding Plates & “Feel”

Sliding plates: A plate on a table begins to slide when horizontal acceleration exceeds μ·g. For typical dishware on a smooth table, the static coefficient μ is roughly 0.15–0.30, so expect sliding to start around 0.15–0.3 g. Because acceleration scales 1:1, if you see >0.2 g sustained horizontally on the model, the full-scale seastead will slide plates exactly the same way.
Glass with rocks & water: This is a great qualitative proxy. If you scale the cup linearly (a ~1.5″ tall cup), the internal slosh frequency scales with Froude rules too, so the visual behavior is representative. Add food coloring for contrast and use a few small pebbles to create turbulence without immediately capsizing the glass.
Other useful metrics:
- RMS acceleration — comfort/seasickness standards (ISO 2631) use the same numerical thresholds for model and ship.
- Peak horizontal accel — direct proxy for furniture and gear shifting.
- Roll angle amplitude — identical; 10° on the model is 10° in real life.
- Roll/pitch period — the model’s period is 3.24× shorter. Human comfort depends on both angle and period; mentally “slow down” the motion by ~3× when interpreting how it would feel full scale.

10. Other Measurement Methods to Consider

Video Motion Tracking: Tape bright dots or small LEDs on the model. Use Tracker (free, from physlets.org) or Kinovea to extract heave, pitch, and surge displacement from the fixed shore camera automatically.
Mooring-Line Tension: Put a small luggage-scale load cell or a fishing scale inline with the stretchy restraining line. Force scales by ÷1157.6, but the relative time history tells you when the vessel is being pushed hardest.
Ultrasonic Wave Probe: A cheap ultrasonic distance sensor (HC-SR04) on a fixed frame over the water can log the instantaneous wave height at the model’s location, removing guesswork from the pole readings.
Onboard “Sliding Testbed”: Build a tiny table with a weighted plate resting on a micro load cell (or a simple tilt switch). It gives you a direct yes/no event tied to acceleration.
Flow Visualization: Dye (food coloring) or bubbles released near the aft stabilizers show flow attachment and stall. Hard to quantify, but excellent for proving the control surfaces are working.
Underwater Camera: A small waterproof camera on the sea bed looking up shows how cleanly the legs move through the water and whether the thrusters cavitating or ingesting air.
Higher-rate dedicated IMU: If the phone’s ~50–200 Hz isn’t enough for crisp jerk calculations, a $10 Arduino/MPU-6050 logger can record at 1 kHz to an SD card.

Quick Reference Card

Parameter	Scale Factor	Model / Note
Linear dimension	÷ 10.5	1 ft → 1.143 in (8⁄7 in)
Mass / Weight	÷ 1157.6	Target ≈ 32.4 lb
Time / Period	÷ 3.24	Events are 3.24× faster
Velocity	÷ 3.24	—
Acceleration	1 : 1	Direct comparison
Jerk	× 3.24	Divide by 3.24 for full-scale equivalent
Force	÷ 1157.6	—
Power	÷ 3880	÷ λ^3.5

Bottom line: Build the model to ~32 lb, float it at the 10.86″ draft mark, put a 7″ doll inside, and test in waves of roughly 3.4″, 5.7″, and 9.1″. Record everything at high frame rate, slow the footage to ~31% speed, and read accelerations 1‑for‑1 against full-scale expectations.