Seastead Design – 1/6‑Scale Model (Froude Scaling)

All calculations assume seawater density = 64 lb/ft³ (≈ 1.025 g/cm³). Linear scale λ = 1/6.

1. Full‑Scale Geometry (Original Design)

Parameter	Value (ft)	Value (inches)
Leg diameter	3.9 ft	46.8 in
Leg radius	1.95 ft	23.4 in
Leg length	24 ft	288 in
Submerged length (2/3 of leg)	16 ft	192 in
Triangle side length	60 ft	720 in

Buoyancy (full‑scale)

Volume displaced per leg = π · r² · L_sub = π · (1.95 ft)² · 16 ft ≈ 191 ft³.
Total displaced volume (3 legs) ≈ 573 ft³.
Weight of displaced water = 573 ft³ · 64 lb/ft³ ≈ 36 700 lb (≈ 1 140 slugs or 16 640 kg).

2. 1/6‑Scale Model Dimensions

Parameter	Full‑Scale	Scaled (λ = 1/6)	Value in Inches
Leg diameter	3.9 ft	0.65 ft	7.8 in
Leg radius	1.95 ft	0.325 ft	3.9 in
Leg length	24 ft	4 ft	48 in
Submerged length	16 ft	2.667 ft	32 in
Triangle side	60 ft	10 ft	120 in

Target Model Weight (neutrally‑buoyant)

Weight scales as λ³: 36 700 lb ÷ 6³ = ≈ 170 lb total.

Break‑down per leg (≈ 56.7 lb each). Adjust with ballast to reach the desired list‑free condition.

3. Cable Lengths (model)

Full‑scale geometry (legs at 45° outward/down, 2/3 submerged) gives:

Horizontal offset of leg bottom from its corner ≈ 16.97 ft.
Vertical depth of leg bottom ≈ 11.31 ft.

Resulting full‑scale cable lengths (rounded):

Leg‑to‑adjacent‑corner (×6): ≈ 76 ft → 76 ft ÷ 6 ≈ 12.67 ft ≈ 152 in each.
Loop connecting all three leg bottoms (×1): ≈ 89 ft → 89 ft ÷ 6 ≈ 14.83 ft ≈ 178 in.

These are straight‑line lengths. Add a few inches for termination hardware.

4. Wave‑Height Scaling (Froude)

Wave height scales linearly (λ). Required model wave heights to represent full‑scale 3 ft, 5 ft, and 8 ft:

Full‑scale wave height	Model wave height (ft)	Model wave height (in)
3 ft	0.50 ft	6 in
5 ft	0.83 ft	10 in
8 ft	1.33 ft	16 in

Wave period scales as √λ ≈ 0.408. For example, a 6‑s full‑scale wave becomes ≈ 2.45 s in the model.

5. Water Depth for “Open‑Ocean” Waves

To avoid bottom‑interaction (deep‑water condition) the water depth must exceed about half the wavelength:

Full‑scale wavelength (deep water) λ_w = g T² / (2π). For a 6‑s wave, λ_w ≈ 184 ft → half ≈ 92 ft.
Model depth ≈ 92 ft ÷ 6 ≈ 15.3 ft ≈ 184 in.

In practice you can choose a depth that is at least a few times the model wave height. A convenient field depth of 5 ft (60 in) in the model corresponds to a full‑scale depth of ~30 ft, which is sufficient for the 3–8 ft wave heights you plan to test. If deeper water is available, aim for ≥ 7 ft (≈ 84 in) to reduce any bottom‑effect.

6. Acceleration‑Recording Apps (Android, free)

App	Key Features	Output Format
AndroSensor	Records accelerometer, gyroscope, magnetometer, etc.; adjustable sampling rate.	CSV, JSON, txt (exportable)
SensorLog	Lightweight sensor logger; continuous logging to file.	CSV
Physics Toolbox Sensor Suite	Full suite (accel, gyro, baro, GPS). Can record to CSV.	CSV, Excel (via Google Drive)
Accelerometer Monitor	Simple real‑time display + logging to file.	CSV

All of the above can write data to a file that you can later copy to a desktop for analysis.

7. Quick‑Reference Summary

Model leg dimensions: Ø 7.8 in, length 48 in, submerged 32 in.
Target model weight: ≈ 170 lb (≈ 56.7 lb per leg).
Cable lengths (model): ~152 in (leg‑to‑corner), ~178 in (loop).
Wave heights to generate: 6 in, 10 in, 16 in.
Recommended water depth: ≥ 5 ft (60 in) – better if ≥ 7 ft (84 in) for minimal bottom effect.
Data‑logging: Use AndroSensor, SensorLog or Physics Toolbox.

All numbers are rounded to the nearest tenth. Adjust for actual seawater density, temperature, and any additional hardware (fittings, connectors, etc.).