Seastead 1:10.5 Scale Model Analysis

1. Froude Scaling Basics

In Froude scaling, the scale factor for length is λ = 10.5. Because physical laws scale non-linearly, we use the following derived scale factors:

Length Scale = λ = 10.5
Time Scale = λ^1/2 = 3.24
Velocity Scale = λ^1/2 = 3.24
Acceleration Scale = λ⁰ = 1 (Acceleration is 1:1!)
Mass/Weight Scale = λ³ = 1157.625

Note on your chosen scale: 10.5 is an exceptionally convenient number for imperial measurements! Because 10.5 feet is exactly 126 inches, dividing full-scale feet by 10.5 is exactly the same as multiplying full-scale feet by 12. This makes mental math for your model incredibly easy (e.g., 70 ft = 80 inches).

2. Model Dimensions (1:10.5 Scale)

Component	Full Scale	Model Scale (Inches)
Main Triangle Frame
Left/Right Sides	70 ft	80.00 in
Back Side	35 ft	40.00 in
Height (Floor to Ceiling)	7 ft	8.00 in
Legs / Floats / Foils
Length	19 ft	21.71 in
Chord (NACA 0030)	10 ft	11.43 in
Width / Max Thickness	3 ft	3.43 in
Submerged Depth (50%)	9.5 ft	10.86 in (from waterline down)
Ladder Position	Top 50% of front	10.86 in tall on front face
RIM Drive Thrusters
Diameter	1.5 ft	1.71 in
Mounting Height (from bottom)	3 ft	3.43 in
Dinghy & Deck
RIB Dinghy Length	14 ft	16.00 in
Back Deck Width (extending out)	5 ft	5.71 in
Stabilizers ("Little Airplanes")
Main Wing Span	12 ft	13.71 in
Main Wing Chord	1.5 ft	1.71 in
Body Length	6 ft	6.86 in
Elevator Span	2 ft	2.29 in
Elevator Chord	6 in (0.5 ft)	0.57 in
Wing Notch for Pivot	~25% of chord	~0.43 in deep

3. Target Model Weight

To calculate the target weight, we must first estimate the full-scale displacement. Your 3 legs provide the buoyancy. Assuming NACA 0030 area approximates 21.75% of the bounding rectangle (Chord x Width), and 50% of each 19ft leg is submerged:

Volume of one leg submerged ≈ 62 cu ft.
Total submerged volume ≈ 186 cu ft.
Weight of displaced seawater (64 lbs/cu ft) ≈ 11,900 lbs full scale.

Model Weight = Full Scale Weight / λ³
Model Weight = 11,900 lbs / 1157.625 = ~10.3 lbs

Practical Tip: Your model will likely be built from lightweight materials (foam, thin plywood, 3D printed plastic). You will likely need to add ballast (fishing weights, lead shot, or steel nuts) inside the legs to bring the total weight up to exactly 10.3 lbs so it sits correctly at the 50% waterline mark.

4. Wave Heights & Deep Water Criteria

Target Wave Heights

Full Scale Wave	Model Scale Wave
3 foot waves	3.43 inches
5 foot waves	5.71 inches
8 foot waves	9.14 inches

Deep Water Depth Requirements

Waves are considered "deep water" when the water depth is greater than half the wavelength (not the wave height). In deep water, waves travel faster and are less steep; in shallow water, they slow down, bunch up, and become steeper.

A typical ocean wave has a wavelength of about 10 to 20 times its height. For an 8-foot full-scale wave, the wavelength might be around 100 feet. Therefore, full-scale deep water would be > 50 feet deep.

Model Deep Water Depth = Full Scale Depth / 10.5
To simulate deep water for an 8ft wave, you need water deeper than: 50 ft / 10.5 = ~4.8 feet (58 inches).

If you test in 2 feet of water (24 inches), you are simulating a shallow coastal environment of about 21 feet deep. The waves will behave more steeply than they would in the open ocean. Try to find the deepest part of Sandy Hill Bay away from the shore shoals.

5. Time Scaling & Camera Setup

Because time scales by λ^1/2 (3.24), the model moves faster than real life. To make the model video look like the full-scale seastead, you must slow the video down by a factor of 3.24.

Capture Frame Rate	Playback Frame Rate	Result
120 fps (GoPro)	30 fps	4x slow motion (Close enough to 3.24x for excellent visualization)
60 fps	18.5 fps	Exact Froude scaling (though 18.5fps playback is slightly stuttery)

Shooting at 120fps and playing back at 30fps yields a 4x slow-down. This is slightly slower than the 3.24x Froude requirement, meaning the full-scale vessel will appear to move just a tiny bit faster than your slowed-down video, but it is an industry-standard compromise that looks very natural to the eye.

6. Android Apps for Motion Tracking

Modern Android phones have highly capable IMUs (Accelerometers and Gyroscopes). To record pitch, roll, heave, velocity, and jerk:

phyphox (Highly Recommended): Created by RWTH Aachen University, this app is specifically designed for physics experiments. It gives you raw access to the accelerometer (with and without gravity), gyroscope, and linear acceleration. You can export data as CSV for Excel analysis, and it has a remote access feature so you can monitor the phone via Wi-Fi while it's on the model.
Sensor Kinetics: A good alternative for real-time viewing of accelerometer and gyroscope data, but phyphox is much better for data export.
Navionics / OpenSeaMap: (For your full-scale later) Not for testing, but essential for boating.

Mounting the Phone: Place the phone exactly at the Center of Gravity (CG) of the model. If it's placed at the extreme edges, the rotational accelerations (pitch/roll) will create false linear acceleration readings (centripetal force).

7. Accelerations & Comfort Metrics

The Beauty of Froude Scaling

Because the acceleration scale factor is 1:1, any acceleration you measure on the model in m/s² or Gs is EXACTLY the acceleration the full-scale seastead will experience. You do not multiply or divide the acceleration numbers.

Plates Sliding on a Table

The static coefficient of friction (μ) for a ceramic plate on a wooden table is roughly 0.3 to 0.4. To overcome friction and slide, the lateral acceleration must exceed μ × gravity.

0.3 × 9.8 m/s² = 2.94 m/s² (or ~0.3 G)

If your model phone records a lateral surge acceleration of >0.3 G, plates are sliding in the real seastead.

Other Comfort Metrics (ISO 2631 / MSI)

Motion Sickness Incidence (MSI): Caused primarily by vertical heave acceleration in the 0.1 Hz to 0.5 Hz range. Model heave accelerations > 0.15 G sustained for a few minutes will cause nausea over time at full scale.
Mobility / Walking: People stumble when lateral accelerations exceed ~0.15 G.
Jerk: (Rate of change of acceleration). High jerk is what causes drinks to spill suddenly, even if peak acceleration is low. A sharp "snap" in the data indicates an uncomfortable ride.

8. Visual Scale References

Doll Height

Average human height is roughly 5'9" (5.75 ft). Using your scale factor:

5.75 ft × 12 / 10.5 = 6.57 inches tall

Look for standard 1:12 scale dollhouse dolls (which are typically 5.5 to 6.5 inches tall). They will be perfect for this.

Water Glass / Rock Test

This is an excellent, simple qualitative test. A standard drinking glass holds about 12-14 oz. Full scale, that's about 4 inches tall. Your model glass should be about 0.38 inches tall (roughly a thimble or a bottle cap). Fill it with water and place a few tiny pebbles (like aquarium gravel) in it. The sloshing and spilling will be incredibly telling on camera.

9. Other Recommended Measurement Methods

ArUco Markers (Computer Vision): Since you are already using a tripod and high-speed camera, print small ArUco markers (square fiducial markers) and stick them to the side of the model. You can run the video through free software like Tracker (Open Source Physics) or OpenCV. The software will automatically track the X, Y, and rotation of the marker to sub-pixel accuracy, giving you perfect heave, surge, and pitch data without relying on an IMU that might shift.
Mooring Line Tension: Attach a small digital luggage scale (or a tiny spring scale) inline with your stretchy holding line. This will record the peak mooring loads. In Froude scaling, Force scales by λ³. So a 1 lb force on the model equals ~1,158 lbs of mooring tension at full scale.
Wave Staff / Wooden Pole: Your wooden pole with marks is great. For better video contrast, paint it with black and white alternating bands (like a barber pole) every inch. This makes reading the exact wave height from video much easier.