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Seastead Scale Model Analysis

1/6 Froude Scaling for Sandy Hill Bay Testing, Anguilla

Froude Scaling Fundamentals

Froude scaling maintains the ratio of inertial to gravitational forces, which is essential for hydrodynamic testing. For a scale ratio of λ = 6, the scaling rules are:

Length: Lmodel = Lfull / λ

Time: Tmodel = Tfull / √λ = Tfull / 2.45

Mass/Weight: Wmodel = Wfull / λ³ = Wfull / 216

Force/Tension: Fmodel = Ffull / λ³ = Ffull / 216

Acceleration: amodel = afull (1:1 ratio)

Velocity: Vmodel = Vfull / √λ = Vfull / 2.45

Model Dimensions (1/6 Scale)

Living Area Platform

Dimension Full Scale Model Scale (inches)
Length 40 feet (480 inches) 80 inches (6 ft 8 in)
Width 16 feet (192 inches) 32 inches (2 ft 8 in)

Corner Columns

Each column extends from corners at 45-degree angle, with half submerged.

Dimension Full Scale Model Scale (inches)
Column Width/Diameter 4 feet (48 inches) 8 inches
Column Length (total) 24 feet (288 inches) 48 inches (4 feet)
Submerged Length 12 feet 24 inches

Target Weight

Parameter Value
Full Scale Weight 36,000 lbs
Scale Factor (λ³) 6³ = 216
Model Target Weight 166.7 lbs (~75.7 kg)
Practical Note: You'll need to add ballast weight to achieve this target. Weigh the empty structure first, then add sand bags, lead weights, or water containers until you reach approximately 167 lbs. The buoyancy from the submerged column halves must equal this weight for neutral buoyancy at the waterline.

Wave Height Simulation

Waves scale linearly with the length ratio (λ = 6):

Full Scale Wave Model Scale Wave (inches) Notes for Sandy Hill Bay
3 feet (36 in) 6 inches Small chop conditions
5 feet (60 in) 10 inches Moderate sea state
8 feet (96 in) 16 inches Storm conditions

Position your model at different spots in the bay where wave heights naturally match these targets. Early morning often has calmer conditions; afternoon winds typically generate larger waves.

Cable Tension Measurement

Surgical Tubing Method

Surgical tubing can work as a qualitative tension indicator, but has limitations:

Tension Range for Surgical Tubing:

Tubing Size Typical Working Range Break Strength
1/4" ID, 1/16" wall 2-8 lbs ~15-20 lbs
3/8" ID, 1/16" wall 3-15 lbs ~25-35 lbs
1/2" ID, 1/8" wall 10-30 lbs ~50-60 lbs

Full Scale Correspondence (using λ³ = 216):

Model Tension (tubing reading) Full Scale Equivalent
5 lbs 1,080 lbs
15 lbs 3,240 lbs
25 lbs 5,400 lbs
40 lbs 8,640 lbs
Limitations of Surgical Tubing:
  • Non-linear response: Rubber has an exponential force-stretch curve, making calibration difficult
  • Hysteresis: Stretching and relaxing paths differ
  • Temperature sensitive: Properties change in warm Caribbean water
  • Hard to read dynamically: Waves cause rapid tension oscillations

Better Alternative: Digital Hanging Scales

Your search for "rope tension data logger" was too specific. Try these Amazon search terms instead:

Recommended Search Terms:
  • "Digital crane scale" (most common, waterproof options available)
  • "Hanging scale 1000lb"
  • "Dynamometer digital"
  • "Load cell display handheld"

Specific Products to Look For:

Product Type Price Range Data Capability
Digital Crane Scale (200-500 lb capacity) $25-60 LCD display only (read visually)
Crane Scale with Peak Hold $40-80 Shows maximum tension recorded
Bluetooth Load Cell + Phone App $80-150 Logs data to phone (best option)

Recommended Capacity: A 200-300 lb capacity scale is ideal. Model tensions of 10-50 lbs will be in the readable middle range of the scale.

DIY Option: A small "luggage scale" ($10-15) can work for qualitative readings. Mount it in a waterproof bag or position it above water. They typically have a "hold" button to freeze the reading.

Android Apps for Data Recording

Recommended: Physics Toolbox Sensor Suite

Developer: Vieyra Software

Cost: Free (with Pro version available)

This is my top recommendation because it can record video with data overlays:

  • Records accelerometer data (X, Y, Z acceleration)
  • Records gyroscope (pitch, roll, yaw rates)
  • Video Recording with Overlay: Can burn accelerometer values directly onto video in real-time
  • Exports data as CSV for analysis
  • Shows "G-Force" magnitude directly
How to Set Up Physics Toolbox:
  1. Open app, select "G-Force" or "Accelerometer" from menu
  2. Tap the video camera icon (this enables video + data recording)
  3. In settings, select which data to overlay (acceleration magnitude is most useful)
  4. Mount phone securely on the model with camera pointing forward
  5. Start recording before placing in water

Alternative: phyphox

Developer: RWTH Aachen University

Cost: Free (Open Source)

Phyphox is excellent for analysis but does NOT natively overlay data on video. It can:

  • Record all motion sensors simultaneously
  • Export high-quality CSV data
  • Run remote experiments via browser

You would need to record video separately and synchronize in post-production.

Post-Production Video + Data Overlay

If you record data and video separately, use these tools to combine them:

  • Dashware (Free/Paid): Professional software for overlaying data gauges on video
  • DaVinci Resolve (Free): Video editor where you can add text layers linked to CSV timecode
  • Python + OpenCV: For custom overlay if you're comfortable coding

Easiest path: Use Physics Toolbox with its built-in overlay feature.

Acceleration Interpretation

The Key Insight: Acceleration Scales 1:1

Under Froude scaling, accelerations are identical between model and full scale. This is extremely convenient:

Acceleration in model = Acceleration in full scale
(No conversion needed!)

Practical Thresholds for Comfort and Safety

Acceleration Threshold Effect Model Reading
0.05 - 0.1 g Noticeable motion, slight discomfort over long periods Same
0.1 - 0.2 g Walking becomes difficult, seasickness likely Same
0.2 - 0.3 g Must hold on to move, objects slide off tables Same
0.3 - 0.5 g Plates/glasses slide, difficult to stand Same
> 0.5 g People may fall, dangerous conditions Same

Plate Sliding Test

A typical plate on a table has a coefficient of static friction around μ ≈ 0.3 - 0.5. Sliding begins when horizontal acceleration exceeds:

aslide = μ × g = 0.3 × 9.8 ≈ 3 m/s² ≈ 0.3 g

If your model accelerometer reads above 0.3 g horizontally, objects will start sliding in the full-scale version.

The "Glass of Water" Test

Your idea of a glass with water and rocks is excellent for visual assessment:

  • The water surface angle shows the vector sum of gravity + horizontal acceleration
  • Water angle θ = arctan(ahorizontal / g)
  • At 0.3 g horizontal, water tilts about 17 degrees
  • At 0.5 g, water tilts 27 degrees
Pro tip: Use a clear plastic container with a grid pattern taped to the back. This makes it easy to measure the water angle on video. Add food coloring to make the water level more visible on camera.

Video Recording Strategy

Shore Camera (Fixed Reference)

Purpose: Measure absolute heave, pitch, and roll against known scale

  • High frame rate: 120 fps or higher
  • Zoom in to fill frame with model
  • Include the measurement pole in frame
  • Later slow down by factor of 2.45× for Froude-correct visualization

Playback speed calculation:

If recording at 120 fps:
Play back at 120/2.45 ≈ 49 fps
(or slow 30 fps footage to ~12 fps)

On-Board Camera (FPV Experience)

Purpose: Give viewers the "feel" of being on the seastead

  • GoPro or phone in waterproof case
  • Mount low, near eye level when seated
  • Include the water glass in frame
  • Point toward horizon to show pitch/roll dramatically

When this footage is slowed by 2.45×, viewers will experience the motion as if they were on the full-scale structure.

Additional Measurement Methods

1. Free Video Analysis Software: Kinovea

Free, Windows only - kinovea.org

Load your shore-camera footage into Kinovea to:

  • Track specific points on the model frame-by-frame
  • Calculate velocities and accelerations from position data
  • Measure angles directly (pitch, roll)
  • Set calibration scale using your marked pole

2. Natural Period Measurement

The natural period of oscillation scales by √λ = 2.45:

If Model Period Is... Full Scale Period Is...
2 seconds 4.9 seconds
3 seconds 7.4 seconds
4 seconds 9.8 seconds

Record how long the model takes to complete one full rocking cycle after being tipped and released. This natural period should not match common wave periods (5-12 seconds full scale) to avoid resonance.

3. Wave Period Measurement

Time 10 wave crests passing your pole, divide by 10 for average period. For Froude scaling:

Full-scale wave period = Model period × 2.45

A 3-second period wave in your bay represents a 7.4-second period wave at full scale—typical for Caribbean wind waves.

4. Draft Marks

Paint inch marks on the submerged portions of columns. Video will show:

  • How deep each corner goes during pitching
  • Average waterline (is the model correctly ballasted?)
  • Dynamic emergence (columns coming out of water = bad)

5. Mooring Line Tension Scope

For the mooring line you'll hold or anchor:

  • Use a stretchy line (bungee or shock cord) so the model isn't jerked
  • Keep slack in the system—mooring should only prevent drift, not restrain motion
  • Full-scale mooring forces will be 216× model forces

Summary Reference Card

Parameter Full Scale Model Scale (1/6)
Living Area 40' × 16' 80" × 32"
Columns 4' wide × 24' long 8" wide × 48" long
Weight 36,000 lbs 167 lbs
Wave: Small 3 feet 6 inches
Wave: Medium 5 feet 10 inches
Wave: Large 8 feet 16 inches
Cable Tension 5,000 lbs 23 lbs (readable on crane scale)
Time / Video Speed 1.0× (real time) Slow to 0.41× for visualization
Acceleration 0.3 g (plate slides) 0.3 g (same reading!)
Oscillation Period 8 seconds 3.3 seconds

Final Recommendations

Essential Equipment for Testing Day:

  1. Scale model at 167 lbs total weight
  2. Android phone running Physics Toolbox, mounted in waterproof case
  3. GoPro or second phone for shore camera (120 fps mode)
  4. Marked pole for wave height reference
  5. Crane scale or luggage scale for cable tension (if measuring)
  6. Clear plastic container with colored water for tilt visualization
  7. Anchors or helpers with stretchy lines to hold position
  8. Scale reference (marked pole or ruler) visible in all camera angles

Safety Notes for Sandy Hill Bay:

  • Test during slack tide if possible—currents will complicate wave effects
  • Have a chase boat or strong swimmer ready; the model could break free
  • Mark all measurement poles with bright tape for visibility
  • Protect phones in quality waterproof cases (test seals beforehand)
``` --- ## Key Answers Summary **Model Dimensions:** - Living area: **80" × 32"** (6.67 ft × 2.67 ft) - Columns: **8" wide × 48" long** **Target Weight:** **166.7 lbs** (scale factor 216×) **Wave Heights to Find:** - 3 ft full scale → **6 inches** - 5 ft full scale → **10 inches** - 8 ft full scale → **16 inches** **Surgical Tubing:** Works qualitatively but has non-linear response. A 15 lb reading = 3,240 lbs full-scale tension. Better to use a **digital crane scale** (search "digital crane scale" or "dynamometer" on Amazon, $25-60). **Best App:** **Physics Toolbox Sensor Suite** — it can overlay acceleration data directly onto video recording in real-time. **Acceleration Thresholds:** Scale 1:1. If model reads **0.3 g horizontal**, plates will slide in full scale.