Seastead Design Analysis & 1/6 Scale Model Specifications
Location: Sandy Hill Bay, Anguilla | Scale Ratio (λ): 1:6 (Model : Full Scale)
1. Full-Scale Hydrostatics: Mass of Water Displaced
Single Leg (Float) Properties
- Diameter (D): 3.9 ft → Radius (r): 1.95 ft
- Total Length (L): 24 ft
- Draft (Immersed Length, Limm): 16 ft (2/3 of length)
- Angle: 45° from horizontal (down and out)
Volume Displaced per Leg
V_leg = π × r² × L_imm
V_leg = π × (1.95 ft)² × 16 ft
V_leg ≈ π × 3.8025 × 16 ≈ 191.14 ft³
Total Displaced Volume (3 Legs)
V_total = 3 × 191.14 ft³ ≈ 573.42 ft³
Mass of Displaced Water (Salt Water, ρ ≈ 64.0 lb/ft³ / 1.99 slugs/ft³)
| Property | Value |
|---|
| Weight Displaced (Buoyant Force) | 573.42 ft³ × 64.0 lb/ft³ = 36,699 lbs (~16.38 Long Tons) |
| Mass Displaced (m = W/g) | 573.42 ft³ × 1.99 slugs/ft³ = 1,141 slugs (~16,650 kg) |
Design Check: For static equilibrium, the Total Weight of the Seastead (Structure + Payload + Ballast) must equal 36,699 lbs. The Center of Gravity (CG) must be below the Center of Buoyancy (CB) for stability. With legs angled 45° down/out, the waterplane area is small (just 3 circles at waterline), so initial stability (GM) will rely heavily on the vertical separation of CG and CB (pendulum stability).
2. 1/6 Scale Model Dimensions (Froude Scaling)
Scale Factor λ = 1/6. Froude Scaling requires: Length ∝ λ, Mass ∝ λ³, Time ∝ √λ, Force ∝ λ³.
All Model Dimensions below are in INCHES.
Model Leg/Float Geometry
| Parameter | Full Scale (ft) | Calculation | Model Scale (inches) |
|---|
| Diameter | 3.9 ft | 3.9 × 12 / 6 | 7.8 in |
| Radius | 1.95 ft | 1.95 × 12 / 6 | 3.9 in |
| Total Length | 24 ft | 24 × 12 / 6 | 48.0 in |
| Draft (Immersed Length) | 16 ft | 16 × 12 / 6 | 32.0 in |
| Freeboard (Above Water) | 8 ft | 8 × 12 / 6 | 16.0 in |
Model Frame Geometry (Equilateral Triangle)
| Parameter | Full Scale | Calculation | Model Scale |
|---|
| Side Length | 60 ft | 60 × 12 / 6 | 120.0 in (10 ft) |
| Height (Altitude) | 51.96 ft | 60 × √3/2 × 12 / 6 | 103.9 in |
| Centroid to Corner | 34.64 ft | 60/√3 × 12 / 6 | 69.3 in |
Model Leg Positioning (45° Angle)
Legs angle 45° down and out from corners.
| Parameter | Full Scale | Model Scale |
|---|
| Horizontal Offset (Foot from Corner) | 16 ft × cos(45°) = 11.31 ft | 22.63 in |
| Vertical Drop (Waterline to Foot) | 16 ft × sin(45°) = 11.31 ft | 22.63 in |
| Foot Triangle Side Length | 60 + 2×11.31 = 82.63 ft | 165.3 in |
3. Model Target Weight (Mass)
Froude Scaling: Massmodel = Massfull × λ³ = Massfull / 216
| Full Scale Displaced Weight | Scale Factor (1/216) | Model Target Weight |
|---|
| 36,699 lbs | ÷ 216 | 169.9 lbs (≈ 170 lbs) |
Critical Ballasting Note: The model must weigh exactly
170 lbs total (structure + electronics + ballast) and float at the 32-inch draft mark (waterline 16 inches from top of leg).
CG Location: You must ballast the model so the Center of Gravity (CG) is at the correct scaled height.
- Full Scale CG Target: Typically 10–15 ft above waterline for stability (depends on superstructure).
- Model CG Target: (Full Scale CG Height) / 6.
If the model is too light, it won't submerge to 32". If too heavy, it sinks. If CG is too high, it capsizes. Use lead shot or steel plate low in the legs/frame for ballast.
4. Cable Lengths
Geometry Assumptions
- Frame Corners: At waterline level (Top of legs).
- Leg Attachment: Bottom of leg (Foot), 22.63 in below and 22.63 in outboard of corner (Model Scale).
- Cable 1 & 2 (Per Leg): Foot → Adjacent Frame Corners (2 per leg, 6 total).
- Cable 3 (Loop): Foot → Foot → Foot → Foot (Triangle connecting 3 feet).
Model Scale Cable Lengths (Straight Line Distance)
| Cable Description | Geometry | Model Length (in) | Full Scale (ft) |
|---|
| Leg Foot → Adjacent Corner (x2 per leg) | √(22.63² + 22.63² + 120²) = √(1024 + 14400) | 124.2 in | 62.1 ft |
| Loop Cable: Foot → Foot (Side of Foot Triangle) | 165.3 in (Calculated in Sec 2) | 165.3 in | 82.6 ft |
| Total Loop Length (3 sides) | 3 × 165.3 | 495.9 in (41.3 ft) | 248 ft |
Construction Recommendations
- Material: Dyneema/Spectra (low stretch) or Nylon (high stretch) depending on test goal. For "gentle force" mooring, Nylon or Polyester double-braid is good.
- Terminations: Use thimbles and swages or knots (Bowline, Figure-8) with chafe gear.
- Slack: Add **2–5% slack** (approx +2.5 to +6 inches on model cables) to prevent cables from going "bar tight" instantly, which induces shock loads not representative of full-scale catenary behavior. If testing taut-leg behavior, pre-tension to 5-10% of breaking strength.
- Redundancy Check: The loop cable (Foot→Foot) provides geometric redundancy. If one Corner→Foot cable breaks, the leg is held by the other Corner cable + the Loop cable.
5. Wave Testing Parameters (Sandy Hill Bay)
Target Model Wave Heights (Froude Scaling: Height ∝ λ)
| Full Scale Wave Height (Hs) | Scaling (÷ 6) | Model Wave Height (inches) |
|---|
| 3 ft | 36 in / 6 | 6.0 in |
| 5 ft | 60 in / 6 | 10.0 in |
| 8 ft | 96 in / 6 | 16.0 in |
Model Wave Periods (Froude Scaling: Time ∝ √λ = 1/√6 ≈ 0.408)
Assuming typical open ocean periods (T) for these heights (e.g., T ≈ 4–6s for 3-5ft wind swell; 8-10s for 8ft ground swell):
| Full Scale Period (s) | Model Period (s) | Model Frequency (Hz) |
|---|
| 4.0 s (Wind chop) | 1.63 s | 0.61 Hz |
| 6.0 s (Swell) | 2.45 s | 0.41 Hz |
| 8.0 s (Long Swell) | 3.27 s | 0.31 Hz |
Required Water Depth (Deep Water Condition)
Deep water waves require Depth > L/2 (Wavelength / 2). Wavelength L = gT²/2π.
Worst case (Longest Period = 3.27s model / 8s full):
L_model = (32.17 ft/s² × 3.27²) / (2π) ≈ 17.2 ft ≈ 206 inches
Required Depth > L/2 ≈ 103 inches (8.6 ft)
| Wave Condition | Model Period | Model Wavelength | Min Depth (L/2) |
|---|
| 3 ft / 4s | 1.63 s | 4.3 ft (51 in) | 25.5 in |
| 5 ft / 6s | 2.45 s | 9.7 ft (116 in) | 58 in |
| 8 ft / 8s | 3.27 s | 17.2 ft (206 in) | 103 in (8.6 ft) |
Sandy Hill Bay Reality Check: Sandy Hill Bay is generally shallow (often < 6-8 ft / 72-96 in at low tide, deeper at high tide near channel).
- For 3ft & 5ft seas (Model 6"-10"), you likely have sufficient depth (> 5 ft) at mid-to-high tide.
- For 8ft seas (Model 16", T~3.3s), you need **> 8.6 ft depth**. This may only be available at **High Tide in the main channel** or just outside the bay entrance.
- Shallow Water Effect: If depth < L/2, waves slow down, get steeper, and break (shoaling). This invalidates Froude scaling for open ocean simulation. Target High Slack Tide for deepest water.
6. Android Apps for Acceleration Data Logging
Requirements: High sample rate (>50 Hz, ideally 100+ Hz), CSV/Excel export, works offline, no intrusive ads, background logging capability.
| App Name | Max Rate | Export Format | Key Features / Notes |
|---|
| Physics Toolbox Sensor Suite (by Vieyra Software) |
100+ Hz (device dependent) |
CSV (email, Drive, local file) |
Top Recommendation. Scientific grade. Linear Accelerometer (gravity removed) + Gyro + Magnetometer + GPS. Clean UI, no ads, exports metadata (sensor specs). |
| Sensor Log (by Siegfried Hopp) |
Up to 100 Hz (set manually) |
CSV, JSON, MATLAB, GPX |
Excellent batch logging. Can log "Linear Acceleration" (software fused) or raw "Accelerometer". Very configurable timers/start delays. Free version limits file size/rows; Pro is cheap (~$3). |
| Phyphox (RWTH Aachen University) |
100+ Hz |
CSV, Excel, Raw (via web interface) |
Unique "Remote Access" via WiFi: view live graph on laptop browser & download CSV without touching phone. Great for "human holding line" scenario. Experiments: "Acceleration with g", "Centrifuge", etc. |
| Accelerometer Data Logger (by Mobile Tools) | 50-100 Hz |
CSV |
Simple, lightweight. Good if others crash. Check "Linear Acceleration" option to remove gravity vector automatically. |
Best Practice for Seastead Model Testing
- Mounting: Rigidly mount phone to the Triangle Frame (Deck), not the legs. Center of frame is best for rigid body motion (Surge, Sway, Heave, Roll, Pitch, Yaw).
- Sensor Selection: Log Linear Acceleration (m/s²) + Gyroscope (rad/s) + Magnetometer (µT). Linear Accel removes gravity, giving pure motion dynamics. Gyro allows attitude reconstruction (Pitch/Roll) via integration (sensor fusion).
- Sample Rate: Set to **100 Hz** (10ms interval). Model periods are ~1.6–3.3s. 100Hz gives 160–330 samples/wave → excellent resolution.
- Orientation: Note phone axes relative to Frame (e.g., Phone Y = Forward/Surge, Phone X = Starboard/Sway, Phone Z = Up/Heave).
- Sync: Start recording, wait 10s (calibration baseline), run test, wait 10s, stop. Record video simultaneously (GoPro/Phone 2) for visual correlation.
7. Summary Checklist for Model Build
| Item | Target Spec | Status |
|---|
| Leg Diameter | 7.8 in (PVC Pipe Sch 40: 8" Nominal = 7.981" ID / 8.625" OD. 6" Nominal = 6.065" ID / 6.625" OD. Custom/Composite likely needed for exact 7.8") | ☐ |
| Leg Length | 48 in | ☐ |
| Draft (Waterline) | 32 in from bottom (Mark clearly!) | ☐ |
| Frame Side Length | 120 in (10 ft) | ☐ |
| Leg Angle | 45° Down/Out | ☐ |
| Foot Horizontal Offset | 22.63 in from Corner | ☐ |
| Total Weight (Wet) | 170.0 lbs | ☐ |
| CG Height above Waterline | Scale from Full Design (e.g. 20-30 in) | ☐ |
| Corner→Foot Cables (6x) | ~124.5 in + slack | ☐ |
| Foot Loop Cable (1x) | ~496 in + slack (or 3x 165.5 in segments) | ☐ |
| Phone Mount | Center of Frame, Rigid | ☐ |
| Test Depth (High Tide) | > 8.6 ft (for 8ft wave sim) | ☐ |
Generated for Seastead Model Testing. Verify all calculations against final engineering drawings. Froude scaling assumes gravity dominance (Fr = V/√gL). Viscous effects (Reynolds number) are not scaled; model drag will be relatively higher than full scale.