Anemometers, and Robinson's cups

A simple machine for measuring something that won't stay still — and a calibration problem its inventor never solved.

The four-cup question

John Thomas Romney Robinson — a Dublin astronomer who ran Armagh Observatory for most of the nineteenth century — unveiled his cup anemometer in 1846. Four hemispherical cups mounted on horizontal arms rotated around a vertical spindle, and the rotation rate was supposed to tell you the wind speed. The device was elegant, robust and easy to read. It was also, in a mathematically precise way, wrong.

Robinson believed the relationship between cup speed and wind speed was fixed: the cups, he calculated, moved at exactly one-third of the wind's velocity. This would have been wonderfully convenient. It would have meant you could calibrate an instrument once and read it forever. Careful testing by the Royal Meteorological Society ↗ and others gradually made clear that the ratio is nothing of the kind — it varies with cup size, cup shape, arm length, and the steadiness of the wind itself. The one-third figure was, in short, a tidily derived wrong answer.

The cups themselves explain part of the problem. A hemispherical cup catches more force on its concave face than the convex back presents to a wind from the opposite direction. That asymmetry is what makes the thing spin at all. But the aerodynamics are sensitive to geometry in ways that resist a single formula. Change the cup diameter slightly, or the arm length, and you shift the relationship between rotation rate and air velocity. The instrument became standard equipment at weather stations around the world before anyone had agreed, in detail, how to convert its readings.

Calibration, not formula

The practical answer was to abandon the idea of deriving a universal constant and instead to calibrate each instrument — or each design — empirically, by swinging it through still air at a known speed or testing it in a wind tunnel. This is slower and less elegant than Robinson's original claim, and it introduced a difficulty that persisted through much of the late nineteenth and early twentieth centuries: anemometer records from different stations, using cups of different proportions and calibrated on different assumptions, could not always be directly compared.

The World Meteorological Organization ↗ eventually worked toward standardizing anemometer exposure and calibration requirements; its guidance on surface-wind measurement specifies the height at which a cup anemometer should be mounted — ten metres above open ground — partly because the relationship between cup-measured speed and the actual free wind changes if the instrument is in a turbulent or sheltered location. Mounting height is not a bureaucratic preference; it is part of the measurement.

The cup anemometer's other known limitation is what engineers now call "over-speeding." When wind gusts, the cups accelerate quickly because the drag on the concave face surges; when the gust drops, they slow more gradually because inertia keeps them turning. The net effect is that a cup anemometer in gusty conditions tends to report a wind slightly faster than it truly is on average. For a synoptic observation — the kind fed into a numerical weather model every few hours — this bias is small enough to live with if the instrument is well-maintained and properly exposed. For turbulence research or wind-energy assessment, it matters considerably.

Later instruments added a second axis: the wind vane measures direction while the cups measure speed, and the two readings together define the wind vector that ends up in a station plot transmitted to a forecast center. Modern sonic anemometers, which measure the travel time of ultrasound pulses between fixed transducers, carry no moving parts and sidestep the over-speeding problem entirely. They remain more expensive and more complex to maintain, which is why the rotating cup — Robinson's design, modified and calibrated far beyond its original theory — is still the standard at the majority of surface weather stations on earth.

Robinson's mistake was assuming that a clean mechanical relationship could be read off from first principles. What he built instead was a reliable, repairable instrument with a messy transfer function — one that had to be understood through measurement, not mathematics. That turned out to be enough.