The mountain takes 15%. The cold gives half of it back

The power curve on our Atlas product page is built on a formula we print right there beside it: P = ½ × ρ × A × V³ × Cp × η. Everybody reads the V³, because wind speed cubed is the dramatic term. Almost nobody reads the ρ. It is the density of the air, it is not a constant, and 1,300 metres up a mountain in February it is doing something very different from what it does at the coast in May.

Air thins out faster than most people expect.

Atmospheric pressure at 1,300 m is about 867 hPa — 85.5% of the pressure at sea level. Put that through the ideal gas law at the same temperature and density follows it down: at 15 °C, sea-level air is 1.225 kg/m³ and air at 1,300 m is 1.048 kg/m³. The mountain has taken 14.5% of the mass out of every cubic metre of wind crossing your rotor. Power is linear in density, so it has taken 14.5% of the power with it.

That is a real loss and we are not going to dress it up. In the same wind speed, on the same day, a turbine at 1,300 m has about 85% of the energy available to it that the identical turbine has on a beach. It is also the reason a power curve quoted without an air density is an incomplete number — including, until this article, ours.

Air density against temperature, at sea level and at 1,300 m. Pressure from the International Standard Atmosphere, density from the ideal gas law. Both curves are computed rather than measured, and anyone with a calculator can reproduce them.

Which brings us to the part that is easy to miss, because it pushes the other way.

Cold air is heavy air.

Density is inversely proportional to absolute temperature. Cool a parcel of air from 15 °C to −10 °C at constant pressure and it becomes about 9.5% denser. That has nothing to do with altitude — it happens on the beach as readily as on the ridge. But mountains are where you actually spend your winter at −10 °C, and a high site is cold far more of the year than a low one.

So the two effects work against each other, and at a cold high site the arithmetic is a good deal kinder than the altitude figure alone suggests. At 1,300 m the thin air costs 14.5 points of density. At 0 °C the cold has handed back 4.7 of them; at −10 °C, 8.1 of them; at −15 °C, 9.9. On a properly cold day the mountain has given back more than half of what it took.

To match a sea-level turbine working in 8.00 m/s at 15 °C, the same machine at 1,300 m on a −10 °C day needs 8.18 m/s. A shade over two per cent more wind.

What the cold does to the rest of the machine.

Two things get better and one gets worse. The generator’s N42 neodymium magnets get stronger as they cool: remanence in this material carries a temperature coefficient of roughly −0.12% per kelvin, which means it rises as the temperature falls. A magnet at −10 °C is running about 3.6% stronger than the same magnet at +20 °C. Neodymium’s enemy is heat, not cold.

The windings tell the same story from the other end. We publish a Class 200 °C insulation grade for the wire (IEC 60317-13 GR 2), and at an Atlas’s typical output the motor is running at under 7% of its 15 kW continuous rating — it was never going to be thermally troubled in the first place. Copper resistance falls as copper cools, so a cold generator is a fractionally more efficient generator. Nothing on the electrical side of this machine minds winter.

What does mind winter is everything mechanical. Bearing grease stiffens as it cools, and stiffer grease raises the torque needed to break the rotor away from standstill — the 2 m/s start-up figure we publish for the low-wind blade set is a fair-weather number, and a still, genuinely cold morning will want a little more than that to get moving. Ice matters more. A rime deposit adds mass and changes the section the wind is working against, and an iced rotor is simply not a rotor whose output you should be counting on that day.

The part that should worry you more than any of this.

None of the above is the real difficulty with a mountain site. The real difficulty is that you probably cannot find out how windy it is.

Here is a worked example anyone can repeat. PVGIS is the European Commission’s public solar and wind dataset. We like it, we have used it on this blog before, and for a coastal or lowland site it is a sensible place to begin. Ask it for a typical meteorological year at 45.08 °N, 6.70 °E — an Alpine valley at 1,314 m — and it returns 8,760 hours with a mean wind speed of 0.92 m/s and a maximum, across the whole year, of 3.3 m/s. Not one hour above 4 m/s. Not one.

Read literally, that is a site with no wind worth having. It is not. It is a site the model cannot see. The reanalysis grid underneath these figures is tens of kilometres across and its terrain is smoothed to match, so an Alpine valley, the ridgelines above it and the thermal winds that run up and down it twice a day do not exist at that resolution. The series also fails a check we run before quoting any dataset: in September a single wind-speed value repeats for 10.4% of the month’s hours. That is what interpolation looks like. It is not what weather looks like.

We are saying this about a dataset we rate and continue to use. On flat, open, coastal ground it earns its keep. In complex terrain it is the wrong instrument, and a figure from the wrong instrument is worse than no figure at all, because it arrives looking like knowledge.

What to actually do about a high site.

Measure it. A recording anemometer at hub height through a season costs a small fraction of a turbine and is the only thing that will tell you what your own ridge, valley or roofline does. We have made this argument before about ordinary sites. In the mountains it stops being good practice and becomes the whole job.

Then choose the blade set from what you measured rather than what you hoped. We publish three: low-wind at 2–20 m/s, moderate at 4–25 m/s, and high-wind at 5–35 m/s with six blades and a smaller swept area. A high site is not automatically the high-wind case — a sheltered valley floor can be calmer than a coastline — but a ridge or a col can gust well past what the low-wind set is rated for, and that set has to come off before sustained winds above 20 m/s. Fitting it because the site is usually quiet, then leaving it up through the one storm a year that matters, is how blades get destroyed.

And when you do the yield arithmetic, put the density in. Take our published curve, multiply by the density ratio for your altitude and your typical working temperature, and you have a number roughly 8–15% below the brochure and a great deal closer to what you will actually see on the meter.

The mountain takes about 15% of your air.
A cold night gives more than half of it back.
What neither of them will tell you is how hard the wind blows on your own ridge.

Air pressure at altitude is from the International Standard Atmosphere; density is the ideal gas law for dry air with R = 287.058 J/(kg·K). The reference density of 1.225 kg/m³ is the standard value at sea level and 15 °C. The remanence temperature coefficient quoted for N42 neodymium is a published material property, not a measurement of our own. The 2 m/s start-up speed, the three blade ranges, the Class 200 °C wire grade and the power-curve figures in the left-hand column are our own published product-page specifications; the right-hand column is those figures multiplied by a computed density ratio and nothing else. The PVGIS query was made against the v5.2 typical-meteorological-year endpoint at the coordinates given, and the criticism of it here is a criticism of resolution, not of the dataset’s honesty. No customer, order, address or installation is named, described or shown on this page.