Cable Noise/Vibration Estimate (VIV) – 3/4" Duplex SS Cables

```html Cable Noise/Vibration Estimate (VIV) – 3/4" Duplex SS Cables

Estimate of noise/vibration from 3/4" (19 mm) duplex stainless cables moving through seawater

Important: Cable “singing” / vibration is dominated by vortex-induced vibration (VIV). The actual vibration and radiated noise depend strongly on: cable tension, span length, end restraints, any contact points/chafe gear, marine growth/roughness, proximity to leg wakes, and whether thruster wash impinges on the cable. The numbers below are order-of-magnitude engineering estimates for a smooth, bare, circular cable in open flow.

Assumptions used for the estimates

Cable diameter D = 0.75 in = 0.01905 m
Seawater density ρ = 1025 kg/m³, kinematic viscosity ν ≈ 1.05×10⁻⁶ m²/s
Flow approximately cross-flow to cable (worst case for VIV); Strouhal number St ≈ 0.2 (subcritical regime)
Vortex shedding frequency estimate: f ≈ St · V / D
“Noise” discussed qualitatively as structure-borne low-frequency vibration and underwater tonal/broadband components; absolute dB levels are not reliable without a detailed coupled fluid-structure model and acoustic boundary conditions.

1) Expected vortex shedding frequencies vs speed (the “tone” that can drive vibration)

Speed (mph)	Speed V (m/s)	Re = V·D/ν	Shedding freq. f (Hz) (≈ 0.2·V/D)	What it tends to feel/sound like
0.5	0.224	≈ 4,100	≈ 2.35 Hz	Very low-frequency “push-pull” loading; may feel like a slow rumble if it couples into the platform.
1.0	0.447	≈ 8,100	≈ 4.7 Hz	Low-frequency vibration; more likely to become perceptible in structure if a cable/span resonance exists near this band.
1.5	0.671	≈ 12,100	≈ 7.1 Hz	Noticeable excitation band for many cable spans; can become “busy” if multiple spans lock-in.
2.0	0.894	≈ 16,200	≈ 9.4 Hz	Still low-frequency, but forcing is stronger (~V²). Highest likelihood of objectionable vibration if untreated.

Key point: the frequency content is mostly ~2–10 Hz for your 0.5–2 mph range. That is below “audible pitch” for most people, but it can be very effective at producing structure-borne vibration (rattles, creaks, thumps) and a low “rumble” sensation if it couples into the frame.

2) How strong is the forcing on a bare cable? (order-of-magnitude)

A rough estimate of cyclic lift force per unit length on a smooth circular cylinder in this Reynolds regime is: F' ≈ 0.5·ρ·V²·D·C_L,rms, with C_L,rms often on the order of 0.3–0.8 depending on conditions. Using 0.8 as a conservative “could happen” value:

Speed (mph)	V (m/s)	Estimated cyclic force per length F' (N/m)	Same (lb/ft)	Implication
0.5	0.224	≈ 0.39 N/m	≈ 0.03 lb/ft	Often small unless tension/span resonance is “just right.”
1.0	0.447	≈ 1.55 N/m	≈ 0.11 lb/ft	Can become noticeable on long spans with low damping.
1.5	0.671	≈ 3.49 N/m	≈ 0.24 lb/ft	Moderate forcing; VIV lock-in becomes a real concern.
2.0	0.894	≈ 6.20 N/m	≈ 0.42 lb/ft	Highest forcing in your set; untreated VIV is most likely to be objectionable here.

These forces scale with V². So going from 1 mph to 2 mph increases VIV forcing by roughly 4×.

3) Is noise/vibration from the cables likely to be an issue?

At 0.5 mph: often tolerable with bare cable, unless you have long, lightly damped spans and a strong resonance match.
At 1.0 mph: VIV becomes plausible; whether it is “annoying” depends on structural coupling and damping.
At 1.5–2.0 mph: for long underwater spans, a bare 3/4" circular cable is in a regime where VIV lock-in is commonly encountered in offshore practice. This is where mitigation is typically justified.

4) Mitigation options (your list) and recommendation

Option	VIV reduction (typical)	Drag penalty	Pros	Cons / gotchas	Fit for “waves & cross-currents”
1) Helical strakes	Often 60–90% reduction in VIV amplitude / coherence	High (commonly +50–100% drag on that member)	Simple, passive, works regardless of flow direction; very common offshore	Drag hurts your low-power propulsion; collects growth; bulky; can complicate handling/maintenance	Good
2) Fixed “wing” snap-on fairing	Can be 80–95% if perfectly aligned	Low when aligned	Best hydrodynamics when aligned; can reduce both VIV and drag	If yaw/cross-flow occurs, can stall, lose effectiveness, and sometimes create its own unsteady loading	Poor to fair (only if you truly maintain direction)
3) Freely rotating wing fairings	Commonly 80–95%+ reduction over a wide range of directions	Low (often less than bare cylinder when working correctly)	Best overall for variable flow direction; widely used for offshore risers	More complex; needs robust rotation hardware; fouling/jamming risk; design details matter	Best
4) Other	Varies	Varies	Can be very effective if you change the problem (materials/layout/damping)	May require redesign	Depends

Recommendation for your use case (low-speed propulsion + variable cross-flow):
Prefer (3) freely rotating wing fairings on the long, continuously submerged cable runs. If you want the simplest, most robust passive approach and can accept extra drag/power, then (1) helical strakes are the next-best choice.

5) Estimated residual noise/vibration with mitigation (relative, practical expectations)

Because absolute acoustic levels are highly installation-dependent, the table below gives expected relative outcomes (how “noticeable” it is likely to be) and a rough residual vibration amplitude in terms of cable diameter D, assuming the system is otherwise well-built (no loose fittings).

Speed (mph)	Bare cable (no treatment)	With helical strakes	With rotating wing fairings
0.5	Low likelihood of objectionable VIV. Typical cross-flow vibration (if it occurs): ~0.05–0.3 D. Main content: ~2.35 Hz.	Usually minimal. Residual: ~<0.05–0.1 D.	Usually negligible. Residual: ~<0.05 D.
1.0	Moderate VIV risk on long spans; may be felt as low-frequency rumble if coupled. Typical: ~0.1–0.6 D during lock-in. Main content: ~4.7 Hz.	Generally low. Residual: ~<0.05–0.15 D.	Generally very low. Residual: ~<0.05–0.1 D.
1.5	Moderate to high chance of lock-in depending on tension and damping. Typical: ~0.2–1.0 D possible in “worst practical” cases. Main content: ~7.1 Hz.	Usually reduced to low to moderate (but drag penalty increases power needed). Residual: ~<0.1–0.25 D.	Usually low. Residual: ~<0.05–0.15 D.
2.0	High risk of objectionable vibration on long spans if untreated. Typical: ~0.3–1.0 D (sometimes higher locally). Main content: ~9.4 Hz.	Typically moderate or better (but highest drag/power cost here). Residual: ~<0.1–0.3 D.	Typically low. Residual: ~<0.05–0.2 D.

6) “Other solutions” that often matter more than people expect

Avoid thruster wash on cables: even if your cruising speed is 1 mph, local jet velocities near a prop can be much higher, pushing you into a much louder/higher-frequency excitation regime.
Add damping at terminations: purpose-designed dampers or viscoelastic elements at cable ends can dramatically reduce transmitted vibration into the platform.
Increase tension (carefully): moves cable natural frequencies and can reduce response, but may also bring a mode into lock-in; this is a tuning problem, not a guaranteed fix.
Change member type: a jacketed cable, faired rod, or an integrated streamlined tie can reduce both drag and VIV.
Marine growth control: roughness changes VIV behavior; a “partially fouled” cable can be worse than clean in some regimes.

7) Practical takeaway

In your 0.5–2 mph range, a 3/4" bare cable will shed vortices at ~2–10 Hz. That is prime territory for felt vibration if it couples into the structure.
If you want to minimize both vibration and propulsion power, rotating wing fairings are typically the best match for variable directions from waves/currents.
If you want the simplest robust solution and can accept a drag penalty, use helical strakes.

If you can provide (a) approximate underwater span lengths for each cable run, (b) cable tension range, (c) whether any runs are in the wake of the 4-ft legs, and (d) how close the thrusters are to the cables, I can refine the estimate toward a “likely/not likely” VIV lock-in map and a better sense of how much vibration would reach the living platform.

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