```html 1/6-Scale Froude Model – Seastead Test Planning

1/6-Scale (Froude) Model Dimensions, Wave Targets, and Instrumentation Ideas

Assumptions used:

Geometric length scale: λ = L_model/L_full = 1/6
Same gravity field, and wave/motion behavior is primarily gravity/inertia dominated (Froude similarity).
Full-scale weight estimate: 36,000 lb
Columns: 4 ft wide, 24 ft long, set at 45°, with half the length underwater.

Froude scaling does not match Reynolds number; drag/viscous effects may not scale perfectly (often acceptable for buoyancy/mooring-motion checks, less so for fine drag predictions).

1) Froude Scaling Rules (quick reference)

Quantity	Scaling with λ (1/6)	Notes
Length	L &propto λ	All linear dimensions scale by 1/6
Area	A &propto λ²
Volume / Displacement	V &propto λ³	Important for buoyancy and mass
Mass / Weight (same density)	W &propto λ³	Target model weight = full weight / 216
Time / Period	T &propto √λ	Model motions happen faster; video often slowed by 1/√λ
Velocity	U &propto √λ
Acceleration (linear)	a &propto 1	Key: accelerations tend to be comparable model vs full scale under Froude similarity
Force (hydrostatic / gravity dominated)	F &propto λ³	Useful for cable tension scaling in gravity-dominated regimes

2) 1/6 Scale Model Dimensions (inches)

2.1 Living area (platform above water)

Item	Full scale	1/6 scale
Living area length	40 ft	80 in
Living area width	16 ft	32 in

2.2 Corner columns (floats/arms) at 45°

Item	Full scale	1/6 scale	Notes
Column/arm length along its centerline	24 ft	48 in	At 45° down from the platform corner
Column/arm width (you said “4 ft wide”)	4 ft	8 in	If the member is square-ish; scale any other cross-section dims by 1/6 as well
Above-water length (half the arm)	12 ft	24 in	Because “half underwater”
Underwater length (half the arm)	12 ft	24 in
Horizontal projection of full arm	24 ft × cos45° = 16.97 ft	33.94 in	How far outboard the bottom is from the corner, if measured horizontally
Vertical drop of full arm	24 ft × sin45° = 16.97 ft	33.94 in	Corner to arm bottom, vertically
Depth of the arm bottom below the waterline (if waterline is mid-arm)	(12 ft)×sin45° = 8.49 ft	16.97 in	Because only the lower 12 ft is submerged

3) Target Total Weight of the 1/6 Model (Froude)

Weight scales as λ³. With λ=1/6:

Scale factor: (1/6)³ = 1/216
Target model weight = 36,000 lb / 216 = 166.7 lb

Practical note: For meaningful motion results, try to match not only total weight but also: (a) center of gravity height, (b) roll/pitch moments of inertia, and (c) hydrostatic properties (waterplane area, metacentric height). That often requires ballast placed intentionally, not just “total weight”.

4) Wave heights to represent 3 ft / 5 ft / 8 ft full scale

Wave height scales linearly with length: H_model = H_full/6.

Full-scale wave height	Model wave height
3 ft (36 in)	6 in
5 ft (60 in)	10 in
8 ft (96 in)	16 in

Time scaling: T_model = T_full√(1/6) = 0.408 T_full. So to “look like” full scale, slow model video by about 1/0.408 = 2.45×.

5) Surgical tubing as a “tension indicator” (and full-scale equivalence)

5.1 What tension range is surgical tubing good for?

Latex surgical tubing is usable as a force indicator, but the force depends strongly on: tubing size (ID/OD), stretch ratio, temperature, aging/UV, and whether it’s preconditioned. Typical practical working behavior:

Working stretch for repeatable measurements: often ~100% to 200% elongation (2× to 3× original length).
Typical tensions (very rough, depends on size):
- Smaller tubing (e.g., ~3/8" OD class): on the order of 5–25 lbf over moderate stretches.
- Larger tubing (e.g., ~1/2" OD class): on the order of 10–50+ lbf over moderate stretches.

Recommendation: If you use surgical tubing for tension estimation, calibrate each piece: hang known weights (or use a spring scale) and record extension vs force. Also “pre-stretch” a few cycles before calibrating.

5.2 What does that correspond to in the full-scale model?

Under Froude scaling for gravity-dominated loads, force scales as λ³. So:

T_full ≈ T_model / (1/216) = 216 × T_model

Model tubing tension	Full-scale equivalent (≈216×)
5 lbf	~1,080 lbf
10 lbf	~2,160 lbf
25 lbf	~5,400 lbf
50 lbf	~10,800 lbf

Is that a reasonable range? For mooring/cable loads it can be plausible, but actual tensions depend on wave drift forces, stiffness of the mooring/cables, pretension, and geometry. The range above is a reasonable “order-of-magnitude” window to instrument, but you should expect spikes and dynamics.

6) Low-cost waterproof digital tension measurement “in series with a rope” (Amazon)

I can’t directly browse Amazon listings in real time from here, so I can’t guarantee specific current products, prices, or availability. But I can tell you what types of devices to look for, what search terms work better, and what tends to be realistically “low cost”.

6.1 What to search for (works better than “rope tension data logger”)

wireless crane scale bluetooth (hanging scale; not usually waterproof, but some are rugged)
digital hanging scale IPX7 or waterproof hanging scale
inline load cell or tension load cell (often needs external display/logger)
S-beam load cell stainless + HX711 + ESP32 data logger (DIY, often the cheapest way to get logging)
dynamometer tension meter (marine/rigging style; usually accurate but often not cheap)

6.2 Reality check: “waterproof + in-line + logs data” is uncommon at low cost

Cheap hanging/fishing scales can measure peak-ish tension but are usually not designed for continuous logging or immersion.
True waterproof dynamometers (IP-rated, stainless, designed for marine load monitoring) usually get expensive.
Best-cost approach for logging is often:
- A small stainless S-beam load cell sized for your expected model tensions (e.g., 0–100 lbf or 0–200 lbf),
- A waterproof box containing an ESP32 (or similar) + HX711 ADC + microSD logger,
- Short shackles/links to insert it in series with the rope/cable.

If you tell me your expected maximum model cable tension (guess is fine) and whether you need water immersion or just spray proof, I can propose specific load-cell capacities, sampling rates, and a simple BOM that tends to be inexpensive.

7) Android apps to record acceleration / orientation (pitch/roll/heave)

7.1 Sensor logging apps (Android)

phyphox: Excellent for logging accelerometer/gyro, exporting CSV, remote control via browser. Good first choice.
Physics Toolbox Sensor Suite: Good general-purpose sensor logging and export.
AndroSensor / Sensor Kinetics: Useful for quick checks and logging; features vary by phone.

Notes:

Pitch/roll: usually derived from gyroscope + accelerometer sensor fusion (often provided as a “rotation vector” sensor).
Heave (vertical displacement): integrating acceleration to displacement drifts quickly. Video tracking or a dedicated motion reference is often better.

7.2 “Record FPV video + overlay acceleration on the same video”

Can phyphox do this directly? Typically, phyphox focuses on sensor logging and does not act as a full video recorder with telemetry overlay. In practice you usually do one of these:

Record video and sensor data separately (recommended), then combine later.
Use an action camera that records telemetry and then overlay with a telemetry tool.

Practical workflow that works well:

Mount phone (or GoPro) for FPV video.
Log IMU data with phyphox (CSV). Start with a clear sync event: a clap, a sharp tap on the model, or flashing a light in view.
Overlay later using:
- Dashware (Windows; older but common for telemetry overlays),
- After Effects / Premiere (more work, very flexible),
- ffmpeg (possible, but you’ll likely script a custom overlay).

If you use a GoPro model that records telemetry (varies by generation/model and settings), you can often overlay in post more easily than with a phone.

8) Accelerations: what corresponds to plates sliding on a table?

8.1 Sliding threshold (full scale and model scale)

Plates start to slide when horizontal acceleration exceeds static friction: a_h > μ_s g.

If μ_s ~ 0.3 (slippery plate/table): threshold ~ 0.3 g (~2.9 m/s²)
If μ_s ~ 0.5 (stickier contact): threshold ~ 0.5 g (~4.9 m/s²)

Important: Under Froude similarity, linear accelerations are approximately scale-invariant. So if your 1/6 model sees ~0.3 g lateral peaks at the “table” location, the full scale is expected to be in that same ballpark (assuming similar dynamics and that the motion is wave/gravity dominated).

8.2 Other useful acceleration metrics

Peak horizontal acceleration (g): directly ties to sliding and “stuff falling over”.
RMS acceleration over a window (e.g., 30–120 s): correlates with comfort/“shake”.
ISO 2631-style weighted RMS (more work): common human comfort metric for whole-body vibration/motion.
Jerk (rate of change of acceleration): can correlate with “snappiness”. Note: jerk scales roughly as 1/√L, so the model jerk tends to be ~2.45× higher than full scale for similar Froude motion.

8.3 Cup-of-water indicator

A glass/cup with water (and rocks) is a good qualitative indicator. If you want it to be more quantitative:

Use a cup with known diameter and mark a scale on it.
Film from a consistent angle and measure maximum free-surface tilt/slosh height.
Consider a lidded clear container for safety and repeatability.

9) Other measurement ideas worth considering

ArUco markers (printed fiducials) on the model: use shore camera video + OpenCV to estimate pitch/roll/heave more objectively.
Simple inclinometer: a pendulum + protractor, or a cheap digital angle sensor in a dry box (backup to IMU).
Draft/waterline marks: paint/mark a scale on columns to see static and dynamic immersion changes.
Cable pretension measurement: measure initial pretension on each cable before waves, not just dynamic changes.
Wave characterization: your marked pole is good; also record wave period (stopwatch + video) since period strongly affects response.
Repeatability: run multiple takes at similar conditions; log wind and tide state if possible.

10) Quick checklist for your planned setup

Model dimensions built to 1/6; ballast to hit ~166.7 lb and correct CG.
Wave target heights: 6 in / 10 in / 16 in for 3 ft / 5 ft / 8 ft.
Video analysis: slow playback by 2.45× to approximate full-scale time.
Tension: surgical tubing can work if calibrated; otherwise consider an in-line load cell + logger.

If you share (a) your best guess of maximum model cable tension, (b) whether sensors will get splashed vs submerged, and (c) whether you prefer phone-based logging or standalone, I can narrow this down to a specific instrumentation plan (including load-cell sizing, sampling rates, and a simple post-processing workflow for overlaying telemetry on video).

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