Here's a complete, self-contained HTML report you can drop into your website. It covers the vortex-shedding physics, per-speed noise/vibration estimates, lock-in risk vs. your cable's natural frequencies, a comparison of the four mitigation options, and a recommendation with post-mitigation predictions.
```html
Tension-Leg Cable Noise & Vibration Assessment — Seastead Mooring Cables
Bottom line: A bare ¾″ cable in cross-flow will shed vortices strongly at all four
speeds (Reynolds numbers 4,000–17,000 — the classic strong-shedding regime). Because your tension-leg
pretension puts the cable's first natural frequency almost exactly inside the vortex-shedding band,
lock-in ("strumming") is likely near 1.0–1.5 mph, and again near 2.0 mph on the second mode.
The water-radiated sound itself is modest (roughly 75–90 dB re 1 µPa @ 1 m,
narrowband — barely above quiet-ocean ambient), but the structure-borne path is the real problem:
each cable can feed ~10–20 lbf of alternating force at 5–10 Hz into the deck corners, producing a
perceptible hum, buzzing panels, and long-term fatigue duty at the terminations.
Recommendation:Option 1 — Helical strakes as the primary fix
(omnidirectional, passive, proven on risers/tendons), plus an elastomeric isolation pad at the top
termination (the "other solution" component) to block the structure-borne path. Avoid fixed snap-on fairings —
tidal current reversals will misalign them and can trigger galloping, which is worse than VIV.
With strakes fitted, residual vibration drops below perceptibility at all four speeds.
2. Basis of Estimate & Assumptions
Parameter
Value used
Note
Cable diameter, D
0.75 in (19.05 mm)
Duplex stainless wire rope
Cable dry mass
≈ 1.10 lb/ft (1.64 kg/m)
Typical 6×36 IWRC construction
Effective wetted mass, me
≈ 1.30 lb/ft (1.93 kg/m)
Incl. ~0.20 lb/ft entrained water (added mass)
Pretension per cable, T
≈ 3,900 lbf (17.3 kN)
From your numbers: 27,500 lb ÷ 7 ≈ 3,930 lbf/ft of extra submergence × 3 ft pull-down ÷ 3 legs
Representative span, L
30 ft (9.1 m)
Scaling laws given below for other depths
Strouhal number, St
0.20
Subcritical cylinder, ±10%
Water kinematic viscosity, ν
1.0×10⁻⁶ m²/s
Seawater, ~20 °C
Structural damping ratio, ζ
0.5–1.0%
Wire rope in water
Fluctuating lift coeff., C′L
0.1–0.2 (free shedding) 0.3–0.5 (lock-in)
Subcritical empirical range
All results are order-of-magnitude engineering estimates (±5 dB on sound levels, roughly ±50% on
forces/amplitudes). A tow-tank or field trial with an accelerometer on one cable top is the logical next step.
Key formulas used
Re = U·D / ν fs = St·U / D (vortex shedding frequency)
Audible low buzz (~10 Hz fundamental felt; harmonics heard), vibration
Why the hum is felt more than heard: 5 Hz is below human hearing (threshold ~20 Hz) — it arrives as
vibration through the structure, shaking panels, hatches, and fixtures which then rattle at their own
resonances. Harmonics at 2–3× fs (10–28 Hz) are genuinely audible as a low drone. Underwater, the
radiated tonals are inefficient (heavy fluid loading suppresses the "aeolian tone" mechanism), so divers or
marine life nearby would hear little beyond ambient — the habitability problem is structure-borne, not water-borne.
Natural frequency vs. depth (why every site gets hit)
With T ≈ 3,900 lbf and me ≈ 1.30 lb/ft, the wave speed on the cable is √(T/m) ≈ 311 ft/s, so
f₁ = 311/(2L):
Depth/span L
Mode 1 f₁
Mode-1 lock-in speed (U = f₁·D/St)
20 ft
7.8 Hz
≈ 1.7 mph
30 ft
5.2 Hz
≈ 1.1 mph
40 ft
3.9 Hz
≈ 0.8 mph
You cannot tune the cable out of the danger band: pushing f₁ above 9.4 Hz would need ~13,000 lbf per cable
(more than your entire 3-ft pull-down provides), and dropping it below 2.3 Hz would need ~800 lbf (too slack to
hold the platform down). Every plausible depth puts a lock-in point somewhere in your 0.5–2.0 mph
envelope — so geometric suppression is the right call, not tuning.
Lock-in map
Wherever the shedding line crosses a mode line (±30% band shaded), the cable locks in and strums.
Your operating envelope straddles both crossings.
4. Mitigation Options Compared
Criterion
1) Helical strakes
2) Fixed wing fairing (snap-on)
3) Freely rotating fairing
4) Hybrid: strakes + elastomer isolator
VIV suppression
★★★★☆ (80–95%)
★★★★★ (90–98%) when aligned
★★★★☆ (85–95%)
★★★★★
Immune to flow direction?
Yes — fully
No — fails beyond ~±15°
Yes — self-aligns
Yes
Failure mode
Benign (degrades gracefully)
Misalignment → galloping (2–3× worse than VIV)
Bearing wear / fouling jam → becomes misaligned fixed fairing
Benign
Drag penalty
Cd 1.1→~1.5 (still < 25 lbf @ 2 mph — trivial vs 3,900 lbf pretension)
Lowest (Cd ~0.4)
Low (Cd ~0.5)
Same as strakes
Caribbean fouling tolerance
Good — performance decays slowly
Moderate
Poor — jamming risk
Good
Maintenance
None
None, but inspect angle
Periodic bearing checks/cleaning
None
Fits shipping container plan
Clamp-on shells pack flat
Yes
Bulkier, many parts
Yes
Verdict
RECOMMENDED
Avoid for tension legs
Acceptable alternate
BEST OVERALL
About Option 2 specifically: the "we always move the same direction" logic only holds if the
flow direction is set by the vessel. It isn't — these are vertical tension legs, so the flow past them
is set by ambient current and tide, which reverse. A fixed fairing caught 30–60° off the flow
doesn't just lose effectiveness; at certain angles of attack its lift-curve slope goes negative and it
gallops — larger-amplitude, lower-frequency oscillations that are harder on the terminations than the
VIV you started with. Reserve fixed fairings for anything truly aligned with a fixed flow direction.
Recommended specification (Option 1 + isolator)
Strakes: 3-start helix, clamp-on HDPE or polyurethane half-shells, height ≈ 0.10–0.125·D
(≈ 3/32″), pitch ≈ 14–17·D (≈ 11–13″), full span. Bolt/clamp pairs so they ship flat in the container.
Top isolator: 60–70 Shore-A elastomer (neoprene/PU) pad or bushing in the clevis where each
cable meets the leg — blocks the structure-borne path and adds ~2–3% damping. Cheap insurance; this is the
"option 4" component that kills the cabin hum even if a strake section is ever damaged.
Terminations: fatigue-rated sockets; duplex stainless is excellent in seawater corrosion, but
keep carbon-steel tools away (iron contamination → staining) and inspect strands at the socket for fretting
annually.
Fouling plan: strake performance tolerates light growth; schedule a brush-down whenever the
legs are cleaned.
5. Predicted Performance WITH Helical Strakes + Isolator
Metric
0.5 mph
1.0 mph
1.5 mph
2.0 mph
Residual amplitude A/D
< 0.05
≤ 0.05–0.10
≤ 0.05–0.10
≤ 0.05–0.10
Oscillating end force
< 1 lbf
< 2 lbf
< 2 lbf
< 2–3 lbf
Radiated noise (narrowband SL)
≈ 50–65 dB re 1 µPa @ 1 m — at or below quiet-coastal ambient; tonal content suppressed ≥ 15–20 dB
Structure-borne hum in cabin
None perceptible at any listed speed
Occupant experience
Silent — indistinguishable from a calm day
Mean drag per cable
≈ 1.5 lbf
≈ 5.8 lbf
≈ 13 lbf
≈ 23 lbf
Fatigue outlook
Residual VIV duty is negligible; terminations should exceed 20-year service with annual inspection
6. Caveats & Suggested Next Steps
All figures assume the cables are submerged only while moored (relative flow = current +
small wave-orbital velocities). If you ever transit with cables in the water, that's a different analysis
(catenary drag, bottom contact) — don't.
The 1.5–2.0 mph cases are conservative envelopes; protected Caribbean sites rarely see sustained currents
above ~0.5–1.0 mph, which means your everyday exposure is the 0.5–1.0 mph rows — exactly where bare-cable
lock-in near mode 1 lives. Strakes are cheap peace of mind.
Estimates are ±5 dB / ±50%. Before cutting metal, log current speed/direction at a candidate anchorage for a
few weeks, and hang an instrumented test cable (accelerometer at the top) for one season.
If you later deepen sites beyond ~50 ft, re-run f₁ — the lock-in speed shifts as 0.21·f₁ mph, but as shown
in §3 it stays inside your envelope; the strake solution is depth-independent.
```
**Key takeaways in brief:**
- **Bare cable:** Strong vortex shedding at all four speeds (Re 4,000–17,000). Your ~3,900 lbf pretension puts mode 1 at ~5.2 Hz (30 ft span), which lands almost exactly on the shedding frequency at **1.0 mph** → lock-in/strumming, ~½″ cable whip, 12–20 lbf alternating force into each deck corner. At **2.0 mph** it re-locks on mode 2 (~10 Hz). The water-radiated sound is modest (75–90 dB re 1 µPa@1m); the real annoyance is structure-borne hum and rattle, plus fatigue at the sockets.
- **You can't tune it out** — no feasible tension places the natural frequencies outside the shedding band, and every depth puts a lock-in point somewhere in 0.5–2.0 mph.
- **Recommendation: Option 1 (helical strakes)** — they're the only solution that's fully direction-independent with zero moving parts and a graceful failure mode. **Avoid Option 2**: vertical tension legs see tidal current reversals, and a misaligned fixed fairing can *gallop*, which is worse than the VIV you're fixing. Option 3 works but has fouling/jamming risk in the Caribbean.
- **Best package:** strakes + a cheap elastomer pad at the top termination (blocks the structure-borne path entirely). Result: no perceptible noise or vibration at any of the four speeds, and drag stays trivial (<25 lbf/cable at 2 mph vs. 3,900 lbf pretension).