```html Seastead 1:10.5 Scale Model Test Plan — Sandy Hill Bay, Anguilla

Seastead 1:10.5 Scale Model — Test Plan

Sandy Hill Bay, Anguilla — Froude-scaled open-water testing

1. Froude Scaling Rules Used

With geometric scale λ = 10.5 (full : model):

Quantity	Scale factor (model / full)	Value for λ = 10.5
Length	1/λ	1/10.5 ≈ 0.0952
Area	1/λ²	1/110.25
Volume / Mass / Weight	1/λ³	1/1157.625
Time / Period	1/√λ	1/3.240
Velocity	1/√λ	1/3.240
Acceleration	1 (unchanged)	1 : 1
Jerk (da/dt)	√λ	3.240 × (model jerk is higher)
Force	1/λ³	1/1157.6

2. Scale-Model Dimensions (inches)

Full-scale dimensions first converted to inches, then divided by 10.5.

Triangle Living-Area Frame

Item	Full scale	Model (inches)
Left / right side length	70 ft = 840 in	80.0 in
Back (stern) side width	35 ft = 420 in	40.0 in
Truss height (floor to ceiling)	7 ft = 84 in	8.0 in

Buoyancy Legs / Foils (×3)

Item	Full scale	Model (inches)
Leg length (vertical)	19 ft = 228 in	21.71 in
Chord (NACA 0030)	10 ft = 120 in	11.43 in
Thickness (30% of chord)	3 ft = 36 in	3.43 in
Submerged portion (50%)	9.5 ft = 114 in	10.86 in
Ladder (upper half front)	9.5 ft high	10.86 in

RIM-Drive Thrusters (×6)

Item	Full scale	Model (inches)
Diameter	1.5 ft = 18 in	1.71 in
Height above bottom of leg	3 ft = 36 in	3.43 in

Airplane-Style Stabilizers (×3)

Item	Full scale	Model (inches)
Main wing span	12 ft = 144 in	13.71 in
Main wing chord	1.5 ft = 18 in	1.71 in
Fuselage length	6 ft = 72 in	6.86 in
Elevator span	2 ft = 24 in	2.29 in
Elevator chord	6 in	0.57 in

Dinghy & Rear Deck

Item	Full scale	Model (inches)
RIB length	14 ft = 168 in	16.0 in
Rear side decks (width)	5 ft = 60 in	5.71 in

3. Target Model Weight

The full-scale seastead's displacement can be estimated from the submerged volume of the three NACA-0030 legs:

A_foil ≈ 0.30 × 10 ft × 10 ft × (NACA area coeff ≈ 0.684) ≈ 20.5 ft²
V_submerged per leg = 20.5 ft² × 9.5 ft ≈ 195 ft³
Total submerged volume ≈ 3 × 195 = 585 ft³
Seawater displacement ≈ 585 ft³ × 64 lb/ft³ ≈ 37,400 lb (full scale)

Applying the mass scale factor 1/1157.6:

Model target weight ≈ 37,400 / 1157.6 ≈ 32.3 lb

Aim for ~30–33 lb all-up model weight (including ballast, camera, electronics). You can tune exact ballast once you measure actual waterline.

4. Wave Heights to Target

Model wave height = full-scale height / 10.5.

Full-scale wave	Model wave height
3 ft (36 in)	3.43 in
5 ft (60 in)	5.71 in
8 ft (96 in)	9.14 in

Wave period also scales by 1/√10.5 ≈ 1/3.24. A full-scale 6-second swell becomes ~1.85 s on the model; a 10-s swell becomes ~3.1 s.

5. Android Apps for Motion Logging

Modern phones (and GoPros) contain 3-axis accelerometers, gyroscopes, and magnetometers that are plenty sensitive for this work. Recommended apps:

Phyphox (free, from RWTH Aachen) — highly recommended. Logs accel, gyro, orientation, magnetometer with timestamps; exports CSV/Excel; remote control via browser over Wi-Fi so you can start/stop from shore.
Sensor Logger (Kelvin Choi) — clean UI, records every sensor to CSV/JSON, good battery life, can stream live.
Physics Toolbox Sensor Suite — good for quick tests; has a "G-force meter" and inclinometer.
AndroSensor — older but reliable multi-sensor logger.
Matlab Mobile or SensorLog — if you want higher sample-rate streaming to a laptop.

Top pick: Phyphox. It computes pitch/roll/yaw (Euler angles) directly, and its "Acceleration with g" + "Orientation" modules together give you heave-proxy, pitch, and roll in one session. Remote start/stop is a big deal when the phone is sealed inside the model.

Mount the phone rigidly at or near the model's CG, in a waterproof case (a Pelican 1010 or similar Ziploc-in-dry-bag works fine). Note the mounting orientation so axes map correctly.

6. Accelerations & "Plates Sliding" Threshold

Because acceleration scales 1:1 under Froude, the acceleration you measure on the model is the acceleration you'd feel at full scale. That is a huge convenience.

A plate or glass begins to slide on a table when the horizontal acceleration exceeds μ·g, where μ is the static friction coefficient:

Surface pair	μ (static)	Accel to slide
Ceramic on wet wood	~0.20	0.20 g (≈ 6.4 ft/s²)
Ceramic on dry wood / varnish	~0.30	0.30 g
Rubber placemat / silicone	~0.60–0.80	0.6–0.8 g
Glass on glass	~0.40	0.40 g

So if your model's measured horizontal acceleration peaks stay below ~0.15 g, dishes are safe on almost any table. Above ~0.25 g, expect sliding on bare varnished wood.

Other useful acceleration / motion metrics

RMS vertical acceleration — correlates with seasickness. ISO 2631 "motion sickness dose value" (MSDV) uses 0.1–0.5 Hz weighted RMS. Values < 0.05 g RMS are typically comfortable; > 0.15 g RMS for extended time causes nausea in most people.
Peak pitch & roll angles — scale 1:1 (dimensionless). Comfort threshold ~2–3°; objects start tipping around 10–15°.
Pitch/roll angular rates — scale by √λ (model is 3.24× faster). Divide measured °/s by 3.24 to get full-scale °/s.
Heave amplitude — scales by λ (multiply model heave in inches by 10.5 for full scale).
Jerk — scales by √λ; divide measured model jerk by 3.24 for full-scale jerk. Jerk > ~0.3 g/s is where motion feels "snappy" and unpleasant.
RAO (Response Amplitude Operator) — ratio of response amplitude (heave, pitch) to wave amplitude, per frequency. Very informative for comparing to other hulls.

7. "Water-in-a-Glass" Indicator

A clear glass ~2/3 full of water (plus a few pebbles for visibility) is an excellent, intuitive qualitative indicator. Since acceleration scales 1:1 and gravity is the same, the slosh angle and sloshing you see is directly representative of full scale. Pick a glass whose natural sloshing frequency is close to the scaled wave period:

First-mode slosh period in a cylindrical glass of radius r, depth h:
T ≈ 2π √( r / (g · 1.84 · tanh(1.84 h / r)) )

For a 2-inch-radius glass filled to 3 in, T ≈ 0.35 s — much faster than the ~1.85–3 s wave period, so it will mostly just tilt with the boat. That's fine; it's the tilt you want to see.

8. Wave-Height Measuring Pole

Your staked/moored wooden pole with marks is a proven technique. Suggestions:

Use high-contrast 1-inch bands (alternating black/white or fluorescent). With 1:10.5 scaling, 1 inch on the pole = ~10.5 inches (≈0.88 ft) full scale.
Add a distinctive every-6-inch marking for easy reading from video.
Place the pole in-frame of the shore camera so each wave can be read directly.
Consider two poles at known spacing to also measure wavelength and celerity.

9. Scale Dolls for Visual Reference

Average adult height ≈ 5 ft 8 in = 68 in. At 1:10.5:

Doll height ≈ 68 / 10.5 ≈ 6.5 inches

Standard "Barbie" is ~11.5 in (too tall); Polly Pocket or Playmobil (~3 in) is too short. The closest common toys are Lego minifigures (~1.6 in, far too short), Schleich figurines (4 in), or 6-inch action figures (G.I. Joe Classified, Marvel Legends, Star Wars Black Series). A 6-inch figure is essentially perfect. Painted wooden artist mannequins (12-inch are too big; 5–6-inch are sold) also work and are robust outdoors.

10. Deep-Water Depth Requirement

Waves behave as "deep-water" when depth d > L/2, where L is the wavelength. Using the deep-water relation L = g·T² / (2π):

Full-scale wave	Typical period (full)	Model period	Model wavelength L	Min depth (L/2)
3 ft	~5 s	1.54 s	~12 ft	~6 ft (1.8 m)
5 ft	~7 s	2.16 s	~24 ft	~12 ft (3.7 m)
8 ft	~9 s	2.78 s	~40 ft	~20 ft (6 m)

So for short chop (3 ft full scale), ~6 ft of water is enough; for the 8 ft ocean swell case you want at least ~20 ft of water. Sandy Hill Bay has a shoal inner area (~4–8 ft) and deeper outer water; picking your test location by depth will naturally let you choose between shoaling-wave and deep-water regimes — which is itself a useful experimental variable.

11. Cameras & Slow-Motion

Your plan is solid. For reference: to play back at "real time" for the full-scale viewer, slow model video by √λ = 3.24×. Easy frame-rate targets:

Shoot at 120 fps and play back at 30 fps → 4× slowdown (slightly slower than true; visually fine).
Shoot at 97 fps played at 30 fps → exactly 3.24× (ideal, but most cameras don't offer 97 fps; use 120 fps and speed up slightly in post, or shoot 60 fps and play at ~18.5 fps).
The GoPro's built-in IMU data (GPMF stream) can be extracted with tools like Telemetry Overlay or gopro-telemetry, giving you synchronized accel/gyro with the video.

12. Other Measurements Worth Considering

Tension-line load cell — put a small load cell (e.g., 50-lb S-beam, or a fishing scale with data logging like the Dr.meter PS01) in the tether to the mooring/human. Multiplied by λ³ = 1157, this gives full-scale mooring load. Very useful for sizing anchors.
Second IMU/phone at the bow vs. one at the stern — lets you separate rigid-body motion from structural flex.
Waterproof pressure sensor on one leg bottom → measures heave directly from hydrostatic pressure variation (bypasses double-integration noise from accelerometers).
Video-based motion tracking — Blender's motion tracker or Tracker (physlets.org) can track a high-contrast dot on the model against the fixed shore camera frame, giving extremely clean heave/surge/pitch data.
String potentiometer or fishing-reel encoder — a line from a fixed point on shore to the model measures surge displacement directly.
Drone overhead video — top-down view gives yaw and surge/sway that the shore camera misses. Hover at a known altitude for easy scaling.
Small microphone / hydrophone — slap and impact noise correlates with slamming events; useful to flag "bad" moments in post.
Dye or confetti wake study — put biodegradable dye upstream of the model, you can visualize flow around the foils in wave conditions.
Tell-tales or yarn tufts on the foil stabilizer's elevator — visual flow behavior under dynamic pitch.
Repeat tests with and without the airplane stabilizers, mooring, and dinghy, so you can quantify each subsystem's contribution.
Weather/wave log — record wind speed (a handheld Kestrel or even a phone anemometer app with a small vane), tide, and time of day. Sandy Hill Bay conditions shift quickly with the trades.

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