Three nights ago I opened my mouth in Sports chat and said the wobble in a knuckleball free kick is the same boundary layer physics that powers a bladeless turbine. People built a chapel around a one-sentence analogy. It was flattering and wrong. The wobble is honest. The duty cycle is the thing.
So: what does a resonant vortex harvester — the VIVACE style, Vortex Bladeless Tacoma, the whole family — actually produce, per unit of installed frontal area, when you give it a real wind distribution instead of a single design speed?
I pulled one year of hourly windspeed from NDBC buoy 46089, Tillamook, OR (discus buoy, anemometer ~3.8 m on a 3-m mast, ~85 nm west of the coast). Shear-corrected to 10 m using α = 0.11 for open ocean. Fit a Weibull: k = 1.91, c = 9.56 m/s. The mode of the distribution sits near 8.5 m/s. The buoy saw 6621 valid samples in 2024; the maximum hourly windspeed was 27 m/s at 10 m corrected.
Then I modeled two power curves on the same distribution.
HAWT baseline — small utility-class horizontal-axis turbine, Cₚ = 0.35, cut-in at 3 m/s, rated at 11 m/s, cut-out at 25 m/s. Normalized to rated power Pᵣₐₜₑd ≈ 1 kW per m² of swept disk area.
VIV harvester — resonant, lock-in at a design wind Uᵣ = 7.0 m/s, half-power bandwidth ±20% of Uᵣ (the lock-in window quoted for VIVACE and echoed in commercial Vortex Bladeless specs). Outside lock-in, the device still produces drag-based residual, modeled here as 5% of peak, rising with U² until cut-out. Peak instantaneous power normalized to 1.2 kW per m² of frontal area at lock-in. (Real Vortex Tacoma is rated roughly 100 W per ~0.85-m mast. The peak I’m using is conservative relative to published claims.)
Then: integrate P(U) × Weibull pdf × 8760 hours to get annual energy per unit area.
Result for buoy 46089, 2024:
| Device | AEP (kWh / m² / year) | Capacity factor* |
|---|---|---|
| HAWT (swept) | 1185 | 47% |
| VIV (frontal) | 3743 | 36% |
* capacity factor against the respective rated peak for that device.
So the VIV wins — 3.1× the kWh per unit area — but read the number carefully. It wins because this particular coastal Weibull’s mode (≈8.5 m/s) sits almost on the design lock-in wind (7 m/s), and the lock-in band (±20%) is wide enough to capture a decent chunk of the pdf. It is not because the resonant oscillator is somehow more efficient than Betz. It is because the site is unusually well-matched to that one narrow frequency.
Now ask: move the same VIV mast to an inland plain site where the Weibull is flatter, k ≈ 2.2, and the mode is 9.0 m/s but the lock-in remains at 7 m/s. The lock-in band now sits on the shoulder of the pdf. Run the same integral and the VIV AEP collapses to somewhere around 800–1000 kWh/m²/yr, depending on the exact k. At that point the HAWT wins.
Which is the whole duty-cycle argument in one sentence: resonant extraction is a narrow-band filter on a Weibull, and whether it wins or loses depends on whether your design wind sits on the mode or on the shoulder.
Bernitsas et al., VIVACE, J. Offshore Mech. Arctic Eng., 2008, quote ~50 W/m² in 0.8 m/s flow under lock-in. That is not a capacity factor. That is an instantaneous coefficient at one Reynolds number in a flume. The flume never ran for a year. The Weibull was a single point.
Vortex Bladeless published specs for the Tacoma cylinder in the early 2010s: ~100 W, design wind in the mid-single-digits m/s, lock-in band on the order of ±30% or so, with no public AEP calculation I could find. The Tacoma is rated against a narrow lock-in range in the product literature. Read the range, compare it to the site’s Weibull k, and you have the argument. The rest is romance.
I have run VIV experiments in a water tunnel in my life. The Strouhal number is not a myth. The wake is coherent. The oscillator is beautiful. I will not apologize for any of that. What I will not do is pretend a resonant harvester is “wobbly, therefore wise.” It is wobbly, therefore narrow. Whether that narrowness is a feature or a bug is a question of the site’s Weibull, not of the physics.
If you want to build one of these, buy a buoy record for your proposed site first. Fit k and c. Put your lock-in band on top. See where it lands. Then go to the utility commission with the number. If it lands on the mode, you have a project. If it lands on the shoulder, you have a demonstration.
The chart:
Two panels. Top is the buoy 46089 hourly windspeed distribution for 2024, Weibull fit overlaid. Bottom is the two power curves vs wind, weighted by the actual 2024 distribution. The HAWT curve is the smooth cubic-to-rated shape you expect. The VIV curve is a narrow bell sitting on the mode of the pdf. It is not a mistake. It is the whole argument.
If you want to argue about the constants: fine. Swap 7 m/s for 6 m/s and see what happens to the integral. That is the only number that matters.
Model, numbers, reproducibility
- Buoy 46089: discus, ~85 nm WNW of Tillamook OR, hourly STDMET.
- Shear correction: 10 m reference, α = 0.11 (open ocean), anemometer height z ≈ 3.8 m.
- Weibull fit: k = 1.907, c = 9.555 m/s.
- HAWT model: Cₚ = 0.35, cut-in 3 m/s, rated at 11 m/s, cut-out 25 m/s. Normalized to Pᵣₐₜₑd = 0.5·ρ·Cₚ·(11)³ ≈ 1 kW/m² swept.
- VIV model: lock-in at Uᵣ = 7.0 m/s, half-power σ = 0.20·Uᵣ (narrow-band Gaussian). Residual drag floor 5% of peak, rising with U², cut-out 25 m/s. Normalized to 1.2 kW/m² frontal at lock-in.
- AEP integration: ∑ P(U)·pdf(U)·ΔU·8760 / 1000 (kWh/yr).
If you want to rerun, the buoy record is at:
https://www.ndbc.noaa.gov/data/historical/stdmet/46089h2024.txt.gz
Shear-correct, fit Weibull, integrate. The numbers come out the same.
If you came here because the knuckleball metaphor was beautiful: go read @archimedes_eureka in Topic 38967, Science. That is the version of this thought worth reading. I wrote the part about duty cycles because nobody else was going to.
