```html Seastead Design — Full-Scale & 1/6 Scale Model

🌊 Seastead Design: Full-Scale Analysis & 1/6 Scale Model

1. Full-Scale Displaced Water Mass

Given Parameters

Leg/float cylinder diameter: 3.9 ft (radius = 1.95 ft)
Total cylinder length: 24 ft
Immersed length (2/3): 16 ft
Number of legs: 3
Seawater density: 64.0 lb/ft³ (typical seawater)

Calculation

Step	Calculation	Result
Cross-sectional area of one cylinder	π × (1.95)² = π × 3.8025	11.946 ft²
Submerged volume per leg	11.946 × 16	191.13 ft³
Total submerged volume (3 legs)	191.13 × 3	573.4 ft³
Mass of water displaced (weight)	573.4 × 64.0	36,698 lbs ≈ 36,700 lbs
In short tons	36,700 / 2000	≈ 18.35 tons
In metric tonnes	36,700 / 2204.6	≈ 16.65 tonnes

    Total displaced water mass: ≈ 36,700 lbs (18.35 short tons / 16.65 metric tonnes)

    This is the maximum total load (platform structure + payload) the three floats can support at the 2/3 immersion waterline.

2. Froude Scaling Rules — Quick Reference

Froude scaling preserves the ratio of inertial to gravitational forces, which is what governs wave behavior and floating-body dynamics. For a geometric scale factor λ = 6 (full-scale is 6× the model):

Quantity	Scale Factor	Value for λ = 6
Length, distance, wave height	λ	÷ 6
Area	λ²	÷ 36
Volume	λ³	÷ 216
Mass / Weight / Force	λ³	÷ 216
Time, wave period	√λ	÷ 2.449
Velocity	√λ	÷ 2.449
Acceleration	1 (unity)	Same as full scale

Key insight: Accelerations scale 1:1 under Froude scaling. This means the accelerations you measure on your model directly represent full-scale accelerations. This makes your accelerometer data directly usable!

3. 1/6 Scale Model Dimensions

Leg/Float Dimensions

Parameter	Full Scale	÷ 6	Model (inches)
Cylinder diameter	3.9 ft	0.65 ft	7.8 in
Cylinder radius	1.95 ft	0.325 ft	3.9 in
Total cylinder length	24 ft	4.0 ft	48 in
Immersed length (2/3)	16 ft	2.667 ft	32 in

Construction tip: A 7.8-inch diameter is close to an 8-inch nominal PVC pipe (which has an actual OD of about 8.625 inches). You may want to use 8-inch PVC pipe and adjust your scale factor very slightly, or search for tubing with a closer match. Alternatively, 200mm (7.87 inch) metric pipe is very close.

Triangle Frame

Parameter	Full Scale	÷ 6	Model (inches)
Triangle side length	60 ft	10.0 ft	120 in (10 ft)

4. Cable Lengths for the 1/6 Scale Model

Full-Scale Geometry Analysis

Each leg is angled at 45° going out and down from a corner of the triangle. We need to figure out where the bottom of each leg ends up in 3D space, then compute the cable distances.

Leg Tip Position (Full Scale)

Each 24-ft cylinder is mounted at 45° from horizontal, projecting outward and downward from a corner. The leg extends outward from the triangle (perpendicular to the triangle's centroid direction, radially outward from the corner). Along the leg axis:

Horizontal projection of the 24-ft leg: 24 × cos(45°) = 24 × 0.7071 = 16.97 ft
Vertical drop of the 24-ft leg: 24 × sin(45°) = 16.97 ft

The direction each leg projects outward is radially away from the centroid of the triangle through its corner.

Triangle Geometry

For an equilateral triangle with side length s = 60 ft:

Distance from centroid to each corner: s / √3 = 60 / 1.7321 = 34.64 ft

Placing the triangle centroid at origin with corners labeled A, B, C:

A = (34.64, 0, 0)
B = (−17.32, 30.0, 0)
C = (−17.32, −30.0, 0)

Each leg projects radially outward (unit vector from centroid through the corner) and down at 45°. The bottom of leg at corner A:

Outward direction (unit): (1, 0, 0)
Bottom of leg A: (34.64 + 16.97, 0, −16.97) = (51.61, 0, −16.97)

Bottom of leg B, outward direction (−0.5, 0.866, 0):

(−17.32 + 16.97×(−0.5), 30.0 + 16.97×0.866, −16.97) = (−25.81, 44.70, −16.97)

Bottom of leg C, outward direction (−0.5, −0.866, 0):

(−17.32 − 8.49, −30.0 − 14.70, −16.97) = (−25.81, −44.70, −16.97)

Cable Type 1: Bottom of Leg to Adjacent Corners (2 cables per leg, 6 total)

Example: Cable from bottom of leg A to corner B:

Distance = √[(51.61−(−17.32))² + (0−30.0)² + (−16.97−0)²]

= √[(68.93)² + (−30.0)² + (−16.97)²]

= √[4751.3 + 900.0 + 287.98]

= √5939.3 = 77.07 ft

Cable from bottom of leg A to corner C (by symmetry):

= √[(68.93)² + (30.0)² + (−16.97)²] = 77.07 ft (same by symmetry)

By the three-fold symmetry of the structure, all 6 of these cables have the same length.

Cable Type 2: Loop Cable Between Leg Bottoms

Distance from bottom of leg A to bottom of leg B:

= √[(51.61−(−25.81))² + (0−44.70)² + (0)²]

= √[(77.42)² + (−44.70)²]

= √[5993.9 + 1998.1]

= √7992.0 = 89.40 ft

By symmetry all three bottom-to-bottom distances are equal. The total loop cable length is:

3 × 89.40 = 268.2 ft

Model-Scale Cable Lengths (÷ 6, converted to inches)

Cable	Full Scale (ft)	Model Scale (ft)	Model Scale (inches)
Leg bottom to adjacent corner (×6 cables)	77.07 ft each	12.84 ft	154.1 in (≈ 12 ft 10 in) each
Bottom-to-bottom loop segment (×3 segments)	89.40 ft each	14.90 ft	178.8 in (≈ 14 ft 11 in) each
Total loop cable	268.2 ft	44.70 ft	536.4 in (≈ 44 ft 8 in)

Practical note: Add a few percent extra length for knots, shackles, or attachment hardware. Use a non-stretch line (such as braided Dyneema/Spectra fishing line or thin stainless steel cable) to properly model the stiff cable behavior at scale.

5. Target Model Weight

Under Froude scaling, mass scales as λ³ = 6³ = 216.

Parameter	Full Scale	÷ 216	Model Scale
Total displaced water weight (= max supported weight)	36,700 lbs		169.9 lbs ≈ 170 lbs

    The total target weight of the 1/6 scale model (structure + ballast + instrumentation) should be approximately 170 lbs to achieve the same 2/3 immersion draft as the full-scale design.

Verification by direct calculation: Each model cylinder has radius 3.9 in = 0.325 ft, immersed length 32 in = 2.667 ft. Submerged volume per leg = π × (0.325)² × 2.667 = 0.885 ft³. Three legs = 2.654 ft³. Weight of seawater displaced = 2.654 × 64.0 = 169.9 lbs. ✓ This confirms the Froude-scaled value.

6. Wave Height Scaling for Sandy Hill Bay Testing

Wave heights scale linearly (÷ 6):

Full-Scale Wave Height	÷ 6	Model-Scale Wave Height (inches)
3 ft (36 in)	0.50 ft	6.0 inches
5 ft (60 in)	0.833 ft	10.0 inches
8 ft (96 in)	1.333 ft	16.0 inches

Wave period scaling: Time scales as √λ = √6 ≈ 2.449. So if you're targeting full-scale wave periods of, say, 6–10 seconds, you want model wave periods of about 2.4–4.1 seconds. This is a useful check — if the waves in the bay have much longer or shorter periods, your results may not properly represent the target sea state.

Typical Full-Scale Wave Periods and Corresponding Model Periods

Full-Scale Period (s)	Model Period (s)
5	2.0
7	2.9
10	4.1
12	4.9

7. Required Water Depth

For waves to behave as deep-water waves (approximating open ocean conditions), the water depth must be at least half the wavelength:

Depth ≥ λ_wave / 2

Deep-water wavelength relates to wave period by: L = (g × T²) / (2π) = 5.12 × T² (in feet, with T in seconds).

Model-Scale Wavelengths and Minimum Depths

Full-Scale Period (s)	Model Period (s)	Model Wavelength (ft)	Min Depth = L/2 (ft)
5	2.04	21.3	10.7 ft
7	2.86	41.8	20.9 ft
10	4.08	85.3	42.7 ft
12	4.90	122.8	61.4 ft

    Practical recommendation for Sandy Hill Bay:
    For shorter-period wind waves (5–7 second full-scale, which are common in the Caribbean), you need at least 10–21 feet of water depth.
For longer-period swell (10+ seconds full-scale), you'd need 40+ feet, which may require positioning the model further offshore.
A minimum of 15–20 feet of water depth is a good practical target for most tests. This keeps you in the deep-water regime for the shorter-period waves that will dominate in a bay setting.
Avoid positioning where you can see waves steepening and starting to break — that indicates the depth is too shallow and the waves are transitioning to shallow-water behavior.

Shore-breaking warning: As a rough rule, waves break when the depth is approximately 1.3× the wave height. For your largest model waves (16 inches ≈ 1.33 ft), breaking starts at about 1.7 ft depth. Stay well away from any area that shallow. The deep-water criteria above (10+ ft) already ensure this, but be aware if the model drifts toward shore.

Additional Depth Consideration: Model Draft

The legs extend downward at 45° for 24 ft full-scale, meaning the bottom of each leg is about 17 ft below the waterline at full scale, or about 34 inches (2.8 ft) below the waterline at model scale. Ensure you have enough water depth that the float bottoms don't touch the seabed — at least 5+ feet of water under the model is wise even ignoring wave dynamics.

8. Free Android Apps for Recording Accelerations

The following free Android apps can record accelerometer data and export it to files (CSV, text, etc.) that you can transfer to a desktop computer:

App Name	Key Features	Export Format
phyphox (Physical Phone Experiments)	Developed by RWTH Aachen University. Excellent scientific tool. Records accelerometer (with and without gravity), gyroscope, and more. Adjustable sample rate. Can export data directly. Can also be controlled remotely via web browser over WiFi, which is very useful — you can start/stop recording and download data without touching the phone on the model.	CSV, Excel
Physics Toolbox Sensor Suite (Vieyra Software)	Records accelerometer (x, y, z and magnitude), gyroscope, and many other sensors. Simple interface. Adjustable recording rate. Widely used in educational and research settings.	CSV
Accelerometer Analyzer (Mobile Tools)	Focused specifically on acceleration data. Real-time graphs. Logs data for export. Simple and lightweight.	CSV / Text
Sensor Logger (Kelvin Choi)	Clean interface. Records all phone sensors including accelerometer and gyroscope. Good data export options. Supports high-frequency logging.	CSV, JSON
AndroSensor	Logs all available sensors. Adjustable interval. Runs in background. Simple interface.	CSV, Text

Top Recommendation: phyphox

Free and open-source, no ads, developed by a university.
Remote access feature is invaluable: Put the phone on the model in a waterproof case, then use a laptop on shore to control recording over WiFi. No need to touch the model!
Built-in "Acceleration (without g)" experiment gives you the dynamic accelerations you care about.
You can create custom experiments with specific sample rates (e.g., 50–100 Hz is good for wave motion).
Data exports cleanly as CSV for analysis in Excel, MATLAB, Python, etc.

Practical tips for phone-based measurements:

Waterproof case: Use a waterproof phone pouch or dry bag, secured firmly to the model platform so it doesn't shift.
Mount orientation: Align the phone axes with your model's axes (e.g., phone flat = measuring heave; phone long axis along a float = measuring pitch/surge). Document the orientation!
Sample rate: 50 Hz is more than sufficient for wave-frequency motions (model wave periods are 2–5 seconds, so frequencies of 0.2–0.5 Hz). Even 10 Hz works, but 50 Hz gives cleaner data.
Battery: Turn off unnecessary phone functions (WiFi if not using remote access, Bluetooth, screen brightness down) to extend recording time.
Transfer: After recording, connect the phone via USB cable or transfer the CSV file via email, Google Drive, or Bluetooth to your desktop.
Acceleration scales 1:1 under Froude scaling, so the accelerations you record on the model directly represent the full-scale accelerations occupants would experience!

9. Complete Model Dimensions Summary

Component	Full Scale (ft)	Model Scale (in)
Float/Leg diameter	3.9 ft	7.8 in
Float/Leg total length	24 ft	48 in
Float/Leg immersed length	16 ft	32 in
Triangle frame side	60 ft	120 in (10 ft)
Leg angle from horizontal	45°	45°
Leg-to-corner cable (×6)	77.1 ft	154.1 in (≈ 12′ 10″) each
Bottom loop cable segment (×3)	89.4 ft	178.8 in (≈ 14′ 11″) each
Bottom loop cable total	268.2 ft	536.4 in (≈ 44′ 8″)
Total model weight target		170 lbs

Wave Testing Targets

Full-Scale Waves	Model Wave Height (in)	Minimum Water Depth (ft)
3 ft seas	6 in	15–20 ft recommended (10 ft absolute minimum)
5 ft seas	10 in
8 ft seas	16 in

Seastead Design — 1/6 Froude Scale Model Specification
Testing Location: Sandy Hill Bay, Anguilla
Seawater density used: 64.0 lb/ft³

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