```html Seastead Scale Model — Froude Scaling Analysis (1:10.5)

🌊 Seastead 1:10.5 Scale Model — Froude Scaling Analysis

Wave-tank testing preparation for Sandy Hill Bay, Anguilla

λ = 10.5 √λ = 3.240 λ³ = 1,157.6

1 Froude Scaling Overview

Froude scaling is the standard method for models where gravity and free-surface waves dominate — exactly the physics governing how a floating structure interacts with ocean waves. The central requirement is that the Froude number is equal in model and full scale:

Fr = V ⁄ √(g · L)  →  Frmodel = Frfull–scale

This means the ratio of inertial to gravitational forces is preserved. The trade-off is that the Reynolds number (viscous drag) will be lower on the model. For wave-response testing, gravity effects dominate, so this trade-off is acceptable.

Master Scaling Table ( λ = Lfull ⁄ Lmodel = 10.5 )

Quantity Model ← Full Scale Full Scale ← Model Factor
Length Lm = Ls ÷ λ Ls = Lm × λ × 10.5
Time / Period Tm = Ts ÷ √λ Ts = Tm × √λ × 3.240
Velocity Vm = Vs ÷ √λ Vs = Vm × √λ × 3.240
Acceleration am = as as = am (same!) × 1.0
Jerk (da/dt) jm = js × √λ js = jm ÷ √λ ÷ 3.240
Angle (pitch, roll) θm = θs θs = θm (same!) × 1.0
Angular velocity ωm = ωs × √λ ωs = ωm ÷ √λ ÷ 3.240
Angular acceleration αm = αs × λ αs = αm ÷ λ ÷ 10.5
Force Fm = Fs ÷ λ³ Fs = Fm × λ³ × 1,157.6
Mass / Weight mm = ms ÷ λ³ ms = mm × λ³ × 1,157.6
Pressure Pm = Ps ÷ λ Ps = Pm × λ × 10.5
🔑 Key Insight: Accelerations and angles are identical in model and full scale. A phone accelerometer mounted on the model reads the exact same g-forces the full-scale seastead would experience — no conversion needed!

2 Scale Model Dimensions (inches)

All dimensions computed as: Model = Full Scale ÷ 10.5

Main Triangle Frame (Living Area)

Dimension Full Scale Model (inches) Model (cm)
Left side 70 ft 80.00″ 203.2
Right side 70 ft 80.00″ 203.2
Back (base) 35 ft 40.00″ 101.6
Base-to-apex height of triangle 67.78 ft 77.46″ 196.7
Truss height (floor → ceiling) 7 ft 8.00″ 20.3
Enclosed floor area 1,186 sq ft 1,550 sq in 10,003 sq cm
Perimeter 175 ft 200.00″ 508.0

Triangle Vertex Coordinates (model, inches, from centre of base)

Vertex X (left–right) Y (front–back) Interior Angle
Back-Left −20.00″ 0.00″ 75.5°
Back-Right +20.00″ 0.00″ 75.5°
Front Apex 0.00″ +77.46″ 29.0°

Buoyancy Legs / Foils (× 3)

Dimension Full Scale Model (inches) Model (cm)
Vertical length 19 ft 21.71″ 55.1
Chord (fore–aft) 10 ft 11.43″ 29.0
Max thickness (NACA 0030 = 30 % of chord) 3 ft 3.43″ 8.7
Cross-section area ≈ 0.686 × chord × thickness 20.6 sq ft 26.8 sq in 173 sq cm
Draft below waterline (50 %) 9.5 ft 10.86″ 27.6
Freeboard above waterline (50 %) 9.5 ft 10.86″ 27.6
Waterline-to-floor (freeboard + leg top) 9.5 ft 10.86″ 27.6
Waterline-to-ceiling 16.5 ft 18.86″ 47.9

RIM-Drive Thrusters (× 6)

DimensionFull ScaleModel (inches)
Diameter1.5 ft (18″)1.71″
Position up from bottom of leg3 ft3.43″

Stabilisers — "Little Airplanes" (× 3)

DimensionFull ScaleModel (inches)
Main wing span12 ft13.71″
Main wing chord1.5 ft1.71″
Fuselage length6 ft6.86″
Elevator span2 ft2.29″
Elevator chord6 in0.57″
Pivot at 25 % chord from leading edge4.5 in0.43″

Dinghy & Decks

DimensionFull ScaleModel (inches)
RIB dinghy length14 ft16.00″
Side-deck width (extends past back)5 ft5.71″

3 Target Weight

Full-Scale Buoyancy Calculation

All buoyancy comes from the submerged halves of the three NACA 0030 legs.

ParameterValue
NACA 0030 cross-section area (chord 10 ft)20.6 sq ft
Submerged height per leg (50 % of 19 ft)9.5 ft
Submerged volume per leg195.2 cu ft
Total submerged volume (3 legs)585.6 cu ft
Seawater density (Sandy Hill Bay)64.0 lb / cu ft (1,025 kg/m³)
Full-scale displacement at 50 % draft ≈ 37,500 lbs (17.0 tonnes)

Model Target Weight

Model weight = 37,500 ÷ λ³ = 37,500 ÷ 1,157.6 ≈ 32.4 lbs (14.7 kg)

Practical target range: 30 – 35 lbs.
Ballast the model (lead shot, fishing sinkers, steel bolts) until each leg sits at 10.86″ draft in seawater.

Cross-check (model volumes):

⚠️ Centre of Gravity: Make sure the model’s CG is positioned to match the full-scale design — vertically (low for stability) and longitudinally (centred so the waterline is even on all three legs). Adjust fore-and-aft ballast until the model floats level at the design waterline.

4 Wave Heights for Testing

Wave heights scale as length: Hmodel = Hfull ÷ λ

Full-Scale Significant Wave Height Model Wave Height Sea State (approx.)
3 ft (0.91 m) 3.43″ (8.7 cm) Moderate seas
5 ft (1.52 m) 5.71″ (14.5 cm) Rough seas
8 ft (2.44 m) 9.14″ (23.2 cm) Very rough seas
📏 Measuring waves: Pound the graduated wooden pole into the sand near the model, clearly visible to the shore camera. Measure peak-to-trough height. Use the camera’s zoom to read the pole precisely, and time 10–20 wave crests with a stopwatch to get the average wave period.

Wave Period Scaling

Periods also scale by √λ: Tmodel = Tfull ÷ 3.24

Full-Scale Period Model Period Typical Wave Source
5 sec1.54 secShort wind chop
6 sec1.85 secTrade-wind waves
8 sec2.47 secMixed wind waves / swell
10 sec3.09 secMedium Atlantic swell
12 sec3.70 secLong Atlantic swell

Record the actual wave period at your test location — the bay will produce whatever nature provides. Use those real numbers when converting back to full-scale equivalents.

5 Time Scaling & Video Recording

Events in the model happen 3.24 × faster than at full scale. To make model video look “real time,” slow the playback by 3.24×.

Recommended Recording Frame Rates

Recording FPS After 3.24× Slow-Down Playback Quality Verdict
30 fps 9.3 fps ⚠️ Choppy Minimum usable
60 fps 18.5 fps ✓ Acceptable Good baseline
120 fps 37 fps ✓ Smooth ⭐ Recommended
240 fps 74 fps ✓ Very smooth Best for frame-by-frame analysis
✅ Recommendation: Record at 120 fps at 1080p — supported by most smartphones and all recent GoPros. After a 3.24× slow-down the video plays at a smooth 37 fps. If your phone supports 240 fps at 720p, use that for the GoPro POV camera.

Free-Decay Tests (Do These Too!)

Before wave testing, perform free-decay tests in calm water:

  1. Heave decay: Push the model down and release. Film the vertical oscillation.
  2. Roll decay: Tilt the model to one side and release.
  3. Pitch decay: Push the bow down and release.

From the video, measure the natural period and decay rate (logarithmic decrement). The natural period at model scale ÷ 3.24 gives the full-scale natural period. These are fundamental design parameters.

Slow-Motion Software

6 Acceleration & Motion Metrics

🔑 Critical fact: In Froude scaling, accelerations are identical in model and full scale. A reading of 0.3 g on the model’s accelerometer means the full-scale seastead would also experience exactly 0.3 g. Angles (pitch, roll) are also identical.

Converting Measured Quantities to Full Scale

What You Measure on the Model Conversion to Full Scale
Acceleration (heave, surge, sway) in g or m/s² × 1  (same value)
Pitch & roll angles in degrees × 1  (same value)
Heave displacement (inches) × 10.5
Velocity (in/s or ft/s) × 3.24
Roll / pitch rate (°/s) ÷ 3.24
Roll / pitch angular acceleration (°/s²) ÷ 10.5
Jerk (m/s³) ÷ 3.24
Mooring force (lbs) × 1,158
Time duration (seconds) × 3.24

Practical Acceleration Reference

Acceleration Subjective Feel Effect on Unsecured Objects (Full Scale)
0.05 gGentleWater surface ripples slightly
0.10 gNoticeableWater in glass tilts ≈ 5.7°
0.20 gFirmLight objects on smooth surfaces begin to creep
0.30 gSignificantPlates on tables begin to slide
0.50 gHardMost unsecured items sliding; standing difficult
0.80 gSevereMust hold on; furniture shifting
1.00 gExtremeCapsizing / free-fall territory

7 Sliding-Plates Threshold

A plate (or any loose object) on a table starts sliding when the horizontal acceleration exceeds the friction coefficient × g:

aslide = μ × g
Surface μ Sliding Threshold In g’s
Ceramic on varnished wood0.2 – 0.36.4 – 9.7 ft/s²0.2 – 0.3 g
Plate on laminate / formica0.3 – 0.49.7 – 12.9 ft/s²0.3 – 0.4 g
Glass on wet counter0.1 – 0.23.2 – 6.4 ft/s²0.1 – 0.2 g
Plate on rubber mat0.5 – 0.816 – 26 ft/s²0.5 – 0.8 g
✅ Because accelerations are identical at both scales: If your model phone reads 0.3 g horizontal, that’s exactly what a plate on a table would feel on the full-scale seastead. A plate with μ = 0.3 would begin to slide. No conversion needed — just read the number directly.

Other Useful Acceleration Metrics

Metric What It Tells You Model → Full Scale
Peak acceleration Worst-case shock; correlates with injury / damage risk × 1 (same)
RMS acceleration Overall ride comfort (ISO 2631 standard) × 1 (same)
Vibration dose value (VDV) Cumulative comfort metric; accounts for duration × 1 (same, for same real-time duration)
Spectral analysis (PSD) Dominant frequencies of motion; identify resonances Frequencies × 3.24 for full scale
Heave RAO (Response Amplitude Operator) Ratio of heave amplitude to wave amplitude vs. frequency Same (dimensionless)

8 Water-in-a-Cup Test

The “glass with rocks and water” is an excellent simple diagnostic! The water surface in the cup tilts in response to the model’s accelerations:

θtilt = arctan(ahorizontal ⁄ g)
Horizontal Acceleration Water Tilt Angle Full-Scale Condition
0.05 g2.9°Calm / gentle
0.10 g5.7°Comfortable
0.20 g11.3°Noticeable tipping
0.30 g16.7°Concerning
0.50 g26.6°Rough ride
🔑 The tilt angle in the model cup is the SAME as a cup on the full-scale seastead — because accelerations are identical. The sloshing happens 3.24× faster in the model; slowing your video by 3.24× makes the sloshing look realistic.

Tips for a Good Cup Test

9 Scale Dolls / Figures

Recommended doll height: 6.5 – 7.0 inches (16.5 – 17.8 cm)
Based on a 5′10″ (70″) adult: 70″ ÷ 10.5 = 6.67″
Figure Type Typical Height Scale Match
1:10 scale action figures (many brands) 6.5 – 7″ ✅ Excellent
Marvel Legends / Star Wars Black Series 6 – 7″ ✅ Great
GI Joe (classic 12″) ~12″ ❌ Too tall (1:6)
Barbie / Ken ~11.5″ ❌ Too tall (1:6)
Matchbox / Hot Wheels figures ~1.5–2″ ❌ Too small
3D-printed custom (from free STL files) Customisable ✅ Perfect if 6.67″

Suggestion: Search for “1:10 action figure” or “7-inch action figure.” Many affordable options exist. Place 2–3 figures inside the model for visual scale in both the shore camera and GoPro POV footage. Coloured clothing helps the figures stand out on video.

10 Water Depth & Deep-Water Waves

Deep-Water Wave Condition

A wave behaves as a “deep-water” wave when the water depth d exceeds half the wavelength:

d > λwave / 2  where  λwave = (g ⁄ 2π) × T² ≈ 5.12 × T² (feet)
Wave Period (T) Deep-Water Wavelength Min. Depth for Deep Water Feasible in Sandy Hill Bay?
2 sec20.5 ft10.3 ft✅ Yes
3 sec46.1 ft23.0 ft⚠️ Possibly (deeper spots)
4 sec81.9 ft41.0 ft⚠️ Unlikely
6 sec184 ft92 ft❌ Too shallow
8 sec328 ft164 ft❌ Too shallow
10 sec512 ft256 ft❌ Too shallow
⚠️ Reality for Sandy Hill Bay (est. 10–30 ft deep):
  • Short-period wind waves (T < 3 sec) — will be in deep or near-deep water. Good for testing.
  • Longer-period swell (T > 4 sec) — will be in transitional / shallow water. Waves will slow, steepen, and may break prematurely. Note this as a limitation.
  • Choose the deepest accessible spot in the bay — aim for 20+ feet.
  • Minimum depth for the model: At least 2–3 feet below the model’s legs so they don’t touch the bottom during heave excursions.

Practical Depth Rule of Thumb

Water depth ≥ 3 × the full-scale wave height prevents wave breaking at the test location:
  • 3 ft waves → depth ≥ 9 ft
  • 5 ft waves → depth ≥ 15 ft
  • 8 ft waves → depth ≥ 24 ft

Measure the depth with a weighted line or depth sounder and record it in your test log.

What If the Bay Is Too Shallow for Long-Period Waves?

The test is still very valuable! You will learn about:

For deeper-water / longer-period validation, a wave tank at a naval-architecture lab would be the next step. The bay test gives you the critical first-pass data.

11 Camera & Recording Setup

📷 Shore Camera (Main)

  • Mount: Tripod on shore, elevated (higher = better wave overview)
  • Lens: Zoom (200–400 mm equiv.) for detail on the model
  • Frame rate: 120 fps minimum (240 fps ideal)
  • Resolution: 1080p (balance of quality & file size)
  • Purpose: Measure heave, pitch, roll from a fixed reference frame
  • Must include in frame:
    • Wave pole (for wave height & period)
    • Cup of water (for tilt angle)
    • Enough of the model for scale reference
  • Tips:
    • Lock exposure & white balance (prevents flickering)
    • Use a spirit level to ensure camera is plumb
    • Affix a ruler or known-length reference in the frame
    • Record a 10-second slate at the start (date, test #, conditions)

🎥 GoPro (On-Model POV)

  • Position: On the model — looking forward, or angled 45° down at the deck & cup
  • Frame rate: 120 fps at 1080p (or 240 fps at 720p)
  • FOV: Wide orSuperview
  • Purpose: “First-person” wave experience + accelerometer data
  • GoPro accelerometer: Export via GoPro Quik app (records g-forces)
  • Tips:
    • Waterproof housing essential!
    • Anti-fog inserts in the housing
    • Secure firmly — vibration ruins footage
    • Start recording before launching the model
    • Consider a second GoPro underwater, looking at the legs

Video Analysis Software

12 Recommended Android Apps for Sensor Logging

🥇 phyphox — Physical Phone Experiments

  • Developer: RWTH Aachen University (Germany)
  • Price: Free, open-source
  • Sensors: Accelerometer (linear + gravity), gyroscope, magnetometer, barometer, GPS, proximity, light, sound
  • Sample rate: Up to 500+ Hz (device-dependent)
  • Export: CSV, Excel, direct share
  • Killer feature: Remote control via web browser — control the phone from a laptop on shore while the phone is on the model! Start/stop recording, view live data, download files, all without touching the model.
  • Google Play →

⭐ TOP RECOMMENDATION — Purpose-built for scientific experiments. The remote-access feature is perfect for this project.

🥈 Physics Toolbox Sensor Suite

  • Developer: Vieyra Software
  • Price: Free (ads) / Paid (no ads, more features)
  • Sensors: All phone sensors with real-time graphing
  • Export: CSV
  • Interface: More polished / user-friendly than phyphox
  • Built-in experiments: G-force meter, inclination meter, seismograph
  • Google Play →

🥉 AndroSensor

  • Price: Free
  • Records all Android sensors; CSV export
  • Simple, reliable, lightweight
  • Google Play →

📱 iOS Alternative: Sensor Logger

  • Platform: iPhone / iPad
  • Price: Free
  • Records accelerometer, gyroscope, magnetometer, GPS
  • CSV export
  • App Store →
💡 Pro Tip: Mount a cheap “burner” phone on the model (waterproof bag or case!). Use phyphox’s remote access from your main phone or laptop on shore. Start logging before launch, stop after recovery. Download CSV data over Wi-Fi. No need to touch the model between runs!

What to Log

Sensor Channel Measures (Model) Full-Scale Conversion
Accelerometer X (surge) Fore–aft acceleration × 1 (same)
Accelerometer Y (sway) Port–starboard acceleration × 1 (same)
Accelerometer Z (heave) Vertical acceleration × 1 (same)
Gyroscope (pitch, roll, yaw rates) Angular velocity in °/s ÷ 3.24
Orientation / rotation vector Pitch & roll angles in ° × 1 (same)
Barometer Altitude change (proxy for heave) × 10.5 for displacement
Magnetometer Heading / yaw × 1 (same)

13 Additional Measurement Methods to Consider

Low-Cost / DIY

  1. Reference Grid on Model
    Draw or tape a grid on the model floor and walls. The shore camera uses this to precisely measure pitch, roll, and heave from video (especially with Tracker software).
  2. Pendulum Inclinometer
    Hang a small weighted string (plumb bob) from a visible point. The pendulum angle directly shows static tilt. Film it from shore. Simple, cheap, and effective.
  3. Coloured Tape Markers
    Place bright tape at bow, stern, port, starboard, and centre. Gives Tracker software clear tracking points for measuring 3D motion.
  4. Mooring-Line Force (Fish Scale)
    Attach a spring scale or digital fish scale in-line with the tether. Read peak mooring forces. Scale by λ³ = 1,158 for full-scale mooring loads.
  5. Tow Drag Measurement
    If you tow the model behind a dinghy at various speeds, a fish scale in the tow line measures drag. Scale force by λ³ and speed by √λ.
  6. Anemometer
    A handheld wind meter records wind speed & direction. Aerodynamic loads on the living area become important at higher wind speeds. Record wind for each test run.
  7. Current Float Test
    Throw a small float and time its travel over a measured distance to estimate current speed. Current affects mooring loads and wave superposition.

More Advanced Methods

  1. Resistance Wave Probe
    Two parallel wires dipped in water — resistance changes with submersion depth. Connect to an Arduino or phone audio input. Gives continuous wave-height time series at the model location. Very inexpensive to build.
  2. Arduino + IMU Data Logger
    An Arduino Uno/Nano with an MPU-6050 IMU (< $15 total) logs 6-axis data at 200+ Hz. Higher bandwidth than a phone; can be customised for your experiment.
  3. Load Cells on Leg Attachments
    Strain-gauge load cells at the leg-to-hull connections measure individual leg forces. Reveals load distribution and peak loads during wave impacts.
  4. Underwater Camera
    A GoPro in its waterproof housing, mounted below the waterline or on a separate pole, can show: leg behaviour in waves, stabiliser operation, flow patterns, and any cavitation on the thrusters.
  5. Pressure Sensors
    Small barometric pressure sensors (e.g., BMP280 on Arduino) taped to the hull measure wave-slam pressures at specific locations.

Recommended Test Measurement Checklist

# Measurement Method Priority
1Wave height at modelWave pole + shore camera⭐ Essential
2Wave periodWave pole + stopwatch / video⭐ Essential
3Water depth at test locationWeighted line / depth sounder⭐ Essential
4Heave / surge / sway accelerationsPhone (phyphox) + GoPro⭐ Essential
5Pitch & roll anglesShore camera video + Tracker⭐ Essential
6Cup-of-water tiltShore camera video⭐ Essential
7Wind speed & directionHandheld anemometer🔶 Important
8Mooring-line forceSpring scale / fish scale🔶 Important
9First-person POV videoGoPro on model🔶 Important
10Free-decay natural periodsPush-and-release + camera🔶 Important
11Current speed & directionFloat test / current meter🔷 Nice to have
12Water temperatureThermometer🔷 Nice to have
13Bottom profile at test siteLead line at several spots🔷 Nice to have

14 Sandy Hill Bay — Test Location Notes

Expected Conditions

Finding Different Wave Heights

Target (Full Scale) Model Height Needed Where / When to Find It
3 ft waves 3.43″ Typical trade-wind chop in exposed parts of the bay — most days
5 ft waves 5.71″ Moderate trade winds (15–20 kt) or when Atlantic swell enters the bay
8 ft waves 9.14″ Strong trades or significant swell event — may need to wait for the right conditions
⚠️ Realistic expectation: Sandy Hill Bay may not produce 9″ model-height (8 ft full-scale) waves frequently. That’s perfectly OK! The 3-foot wave condition (3.43″) is the most likely to be available and is very informative. Test in whatever waves nature provides — document the actual conditions thoroughly.

Suggested Test Procedure

  1. Scout the bay (on foot or by dinghy) to find the deepest, most wave-exposed accessible spot.
  2. Measure depth at the chosen location; map the bottom profile if possible.
  3. Deploy the wave pole near the model position, clearly visible from shore.
  4. Waterproof the phone (dry bag or case), mount on model, start phyphox via remote access.
  5. Start all cameras (shore cam, GoPro). Slate each take with a test number and conditions.
  6. Launch the model; secure with the stretchy tether line held by a person or tied to a mooring.
  7. Record baseline in calm conditions (if available).
  8. Record each wave condition for at least 2–3 minutes of model time (≈ 6–10 min full-scale equivalent).
  9. Log wave heights and periods from the pole. Log wind speed.
  10. Perform free-decay tests between wave runs (heave, roll, pitch).
  11. Retrieve model, check for water intrusion, adjust ballast if needed.
  12. Repeat at different locations in the bay for different wave exposures.

15 Known Limitations of Froude Scaling

Froude scaling is the right tool for this test, but be aware of these caveats when interpreting results:

Effect Issue at Model Scale Impact on Your Test
Reynolds number mismatch Model has much lower Re; viscous drag is relatively larger Model drag will be proportionally higher than full scale. Motion response (heave/pitch/roll) is mostly unaffected since it’s gravity-driven.
Surface tension Capillary effects are relatively stronger at small scale Negligible for model dimensions > ~2″. Your model is large enough that this won’t matter.
Structural elasticity Model material may be proportionally more or less flexible Keep the model rigid. Stiffness doesn’t auto-scale.
Aerodynamic drag Wind loads on the model are proportionally larger relative to wave loads Test in low-wind conditions if possible, or note wind speed.
Mooring dynamics Stretchy tether may not perfectly mimic scaled mooring stiffness Use the softest tether that still keeps the model in position. Measure tether force.
Wave reflection / basin effects In a bay, waves reflect off shores and interfere Note any reflected waves; position model away from hard reflecting surfaces.
Bottom line: For wave-induced motion (heave, pitch, roll) and stability assessment, Froude scaling is excellent and your results will be meaningful. For speed / drag predictions, Reynolds number effects make model drag data less directly applicable. The bay test is ideal for validating the motion and stability design.

16 Quick Reference Card

ParameterValue
Scale factor (λ)10.5
√λ (time & velocity factor)3.240
λ³ (mass & force factor)1,157.6
Model target weight32 lbs (30–35 lbs range)
Model leg draft (waterline)10.86″ from bottom of leg
Model main frame80″ × 80″ × 40″ triangle, 8″ tall
Model leg dimensions21.71″ tall × 11.43″ chord × 3.43″ thick
3 ft waves → model3.43″
5 ft waves → model5.71″
8 ft waves → model9.14″
Slow video by3.24×
Recommended recording FPS120 fps (1080p)
Doll / figure height6.5 – 7.0 inches
Minimum water depth (recommended)20+ feet (15 ft minimum)
Acceleration scaling1:1 (identical in model & full scale)
Angle scaling1:1 (identical in model & full scale)
Plate-sliding threshold~0.2–0.4 g (same at both scales)
Top-recommended appphyphox (free, remote access)
```