```html Seastead 1/6 Scale Model Testing Plan - Froude Scaling Analysis

Seastead Scale Model Testing Plan

Location: Sandy Hill Bay, Anguilla | Scale: 1:6 (λ = 1/6) | Prototype Displacement: 36,000 lbs

Froude Scaling Law Summary (λ = 1/6):
• Length: ÷ 6 | Time: ÷ √6 ≈ ÷ 2.45 | Velocity: ÷ √6 ≈ ÷ 2.45
• Mass: ÷ 6³ = ÷ 216 | Force: ÷ 216 | Acceleration: 1:1 (unchanged)

1. Model Dimensions & Weight

Component Full Scale Model Scale (1/6) Notes
Living Area 40' × 16' (480" × 192") 80" × 32" (6.67' × 2.67') Rectangular platform
Column Width 4' (48") 8" Square or cylindrical cross-section
Column Length 24' (288") 48" (4 feet) At 45° angle
Submerged Length 12' (half of column) 24" Draft measurement
Target Weight 36,000 lbs 166.7 lbs (~167 lbs) Include ballast adjustment margin: 150-180 lbs
Construction Tip: Build the model to weigh slightly less (≈140 lbs) and add removable ballast (lead shot or steel plates) to tune to exactly 167 lbs after construction. This allows you to adjust for different loading conditions.

2. Cable Tension Measurement

Surgical Tubing Method

Standard latex surgical tubing (3/8" OD, 1/4" ID) has a useful working tension range of approximately 2–20 lbs depending on wall thickness and percent elongation (100–300% stretch).

Full-Scale Equivalent: Multiply by 216 (6³)

Assessment: This is a reasonable but low range. For a 36,000 lb vessel in 8-foot seas, peak mooring loads could exceed 10,000 lbs (storm conditions). However, for moderate sea states (3–5 ft), the 1,000–4,000 lb range represents typical working loads on individual mooring legs. The tubing will provide good sensitivity in the operational range but may max out during extreme events.

Alternative: Digital Load Measurement

Instead of "rope tension data logger," search Amazon for these terms:

Budget Recommendation: A $40-60 crane scale (like the Klau or MULAN 300kg models) can be wrapped in a waterproof bag or pelican case with the display/viewing window exposed. Most do not log data internally, so you'll need to video-record the display or hack in a data logger.

DIY Data Logger Option: Use a 50kg–200kg S-type load cell ($15) + HX711 amplifier ($5) + ESP32 microcontroller ($8) in a waterproof enclosure. Power with 18650 batteries. Log to SD card or transmit via Bluetooth to shore. Total cost: ~$40 per cable.

3. Wave Height Scaling

To simulate full-scale wave conditions in Sandy Hill Bay:

Full-Scale Wave Height Model Scale Height Location Strategy
3 feet (calm-moderate) 6 inches Protected inner bay, minimal fetch
5 feet (moderate-rough) 10 inches Middle bay, moderate boat wake
8 feet (rough-storm) 16 inches Outer bay or channel entrance, wind against tide
Time Scaling for Video: Record shore camera at 60 fps and play back at 24.5 fps (slowed by 2.45×) to see full-scale motion timing. Alternatively, record at 50 fps and play at 20.4 fps. This matches the Froude time scaling (√6 ≈ 2.45).

4. Instrumentation & Android Apps

IMU/Acceleration Logging

Recommended Apps:

Video + Data Overlay (FPV)

Can Phyphox do video overlay? No. Phyphox records sensor data only. For synchronized video with acceleration data overlay, you have three options:

  1. GoPro + Telemetry: Use a GoPro Hero 9/10/11 mounted on the model. Enable "GPS" and "Accelerometer" in settings. The MP4 file embeds telemetry data (G-force, orientation) which can be extracted with tools like GoPro Telemetry Extractor and overlaid using Dashware or GoPro Quik.
  2. Dual Recording + Post-Sync:
  3. Single Phone + Screen Recorder: Run Phyphox in split-screen with camera, but this is clumsy and reduces sampling rate.
Best Practice: Use the GoPro for FPV (it has wide-angle and stabilization) and tuck a cheap Android phone running Phyphox inside the hull for high-rate IMU data. The GoPro's internal accelerometer is sufficient for "feel" videos, while the phone's data provides scientific precision.

5. Acceleration Analysis & Comfort Metrics

Sliding Objects Threshold

Objects begin to slide when horizontal acceleration exceeds the static friction coefficient (μ):

Critical Threshold: 0.3g to 0.5g (9.6–16 ft/s² or 3–5 m/s²) horizontal acceleration.

Important: Since acceleration scales 1:1 with Froude, if your model experiences 0.4g lateral acceleration, the full-scale vessel will also experience 0.4g — plates will slide in both cases.

Additional Metrics

Metric Model Threshold Full-Scale Interpretation
Walking Difficulty >0.15g sustained lateral Crew must hold handrails; difficult to carry items
Seasickness (Heave) 0.1g vertical at 0.5–2 Hz (model freq) 0.1g at 0.2–0.8 Hz full scale (resonant for humans)
Jerk (da/dt) Sudden changes >2g/s Perceived as "snapping" motion; uncomfortable
Roll Angle 6° model 6° full scale (linear angle scale)

Your "Glass with Rocks" Method: Excellent qualitative indicator. For quantitative analysis:

6. Additional Measurement Techniques

Beyond your current plan, consider these low-cost additions:

  1. Motion Tracking with Colored Markers: Place bright orange balls at the 4 corners of the deck. Use the shore camera with Tracker Video Analysis (free software) to automatically track heave and pitch vs. time with sub-pixel precision.
  2. Wave Staff: Instead of just a marked pole, use two parallel PVC pipes with copper tape strips (resistance wave gauge) connected to an Arduino. This gives you exact wave elevation time-series to correlate with vessel motion (RAO calculation).
  3. Decay Tests: Before wave testing, pull the model sideways with a line and release (or give it a push-down for heave). Measure the decay rate of oscillations to determine the damping ratio. This validates your structural damping assumptions.
  4. Step Response (Snap Test): Use the surgical tubing to apply a known step load (sudden release) and measure the transient response. This reveals the natural period of the mooring system.
  5. Underwater Video: If water clarity permits, a GoPro on a weighted line looking up at the hull can visualize column entry angles and vortex shedding.
  6. Strain Gauges: Bond foil strain gauges to the column surfaces (waterproofed with epoxy) to measure bending moments. This validates if the 45° angle is optimal for load distribution.

7. Testing Protocol Summary

Phase Action Data to Capture
1. Calibration Static heel test (shift known weight side-to-side) Verify 167 lbs displacement, measure GM (metacentric height)
2. Decay Push-down/heave release Natural period, damping ratio
3. Regular Waves 6", 10", 16" waves RAO (Response Amplitude Operator), cable tensions
4. Irregular Waves Random boat wake or wind chop Statistical motion (RMS acceleration), peak events
5. Failure Mode Intentionally slack one cable Redundancy behavior, remaining cable loads
Safety Note for Sandy Hill Bay: With 167 lbs of model plus ballast, ensure your shore crew can retrieve the model if it flips or sinks. Attach a recovery line with adequate breaking strength (500+ lbs) and a floatation buoy. The 45-degree columns should provide positive stability, but test the righting moment in calm water first.

8. Data Processing Checklist

Good luck with the experiment in Anguilla! The 1/6 scale provides a good balance between manageable size (80" platform) and sufficient mass (167 lbs) to resist wind and minor currents while responding accurately to wave forcing.

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