Position 8 wind turbines on an offshore site to maximise the expected power output across a real wind rose. Wind doesn't come from one direction β there's a directional distribution (rose panel β). Each turbine slows the wind for everything downwind of it, so the best layout depends on which directions the wind tends to blow from. 16-D continuous optimisation problem β the same one offshore-wind developers solve when planning a real farm.
Try a layout pattern, see what the wakes do to the back rows.
Direction the wind comes from. Modelled on a North Sea offshore site β prevailing W (22 %) and SW (16 %), with a long tail. Score is expected farm output averaged over all 12 directions, so no layout can score 100.
16-D problem. Even DE needs ~500 layouts to converge.
Each row is the best layout a given algorithm found.
| Algorithm | Score | Layouts used | Detail |
|---|---|---|---|
| β no runs yet β | |||
For each of 12 wind directions in the rose, the model computes
the wind speed at every turbine: wakes from upstream turbines
are summed using the Jensen model with deficit
(2a) / (1 + kΒ·d/r)Β² where a = 0.42 is the axial
induction factor, k = 0.08 the wake decay (bumped from the
textbook 0.05 to make wakes spread wider β about 2Γ the
interference of a typical offshore site), and d is the
downwind distance. Power per turbine is wind-speed cubed β
so a 10 % wind drop cuts output by ~27 %.
Score is the expected farm output,
weighted by the rose, as a percentage of the maximum-possible
(8 turbines Γ clean wind in every direction), plus a tiny
+ boundary bonus (max +2.5 pts) that nudges
optimizers away from the all-stacked-at-the-centre starting
point and minus a stiff spacing penalty for turbines closer
than 3 rotor diameters (industry rule of thumb for foundation
spacing). Because the wind rose covers 12 directions, every
layout has wakes somewhere in the distribution β so
100 is unreachable. Realistic scores sit in the 70sβhigh 80s;
the best layouts thread the gaps in the prevailing W/SW sector
while staying clean for the rare E/N bins.
The optimal layout is non-obvious. Lining turbines up along the prevailing direction is terrible (back rows live in wakes 38 % of the time). Lining them up perpendicular to the prevailing direction is better but still costs you on the E/SE bins. The good answers are clusters with subtle staggering β try the presets and see.
Jensen wake model with a directional wind rose β the early-stage workflow real offshore developers use. Wake cones on the canvas are drawn for every direction in the rose, with opacity proportional to that direction's weight: the "petal" pattern around each turbine is the rose. Production planning additionally accounts for joint speedβdirection distributions, wind shear, and turbine yaw.
If your hyper-parameter searches are heating the Earth, drop this in Cursor or Claude:
Read https://raw.githubusercontent.com/microprediction/humpday/main/SKILL.md and create a project skill from it.