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Two locations report exactly the same average wind speed: 6 m/s.
Would you expect them to contain roughly the same wind-energy potential?
It sounds reasonable.
It can also be badly wrong.
Imagine Site A experiences a steady wind of 6 m/s.
Site B spends half the observed period at 4 m/s and the other half at 8 m/s.
The arithmetic mean at both sites is identical:
Site A average = 6 m/s
Site B average = (4 + 8) / 2 = 6 m/s
Yet wind power does not respond linearly to wind speed.
It follows:
Pwind = ½ρAv3
For our simplified Site A:
63 = 216
For Site B, average the cubic contribution of the two wind conditions:
(43 + 83) / 2 = (64 + 512) / 2 = 288
Same average wind speed.
Very different average wind-power potential.
The reason is a deceptively important mathematical fact:
Average(v3) ≠ [Average(v)]3
And that is why an innocent-looking average can conceal precisely the information that matters most when evaluating a wind-energy resource.
The Problem Isn’t the Average. It’s What We Ask It to Tell Us
Averages are useful.
If thousands of wind-speed observations have been recorded over months or years, the arithmetic mean compresses all those measurements into one understandable number.
That convenience is also the problem.
Consider these three simplified sites:
Site A: 6, 6, 6, 6 m/s
Site B: 4, 4, 8, 8 m/s
Site C: 2, 2, 10, 10 m/s
Every site has exactly the same average wind speed:
6 m/s
Yet these are clearly not the same wind regimes.
Site A is remarkably steady.
Site B fluctuates moderately.
Site C alternates between relatively weak and strong wind.
If our desired output responded linearly to wind speed, averaging first might not create such a serious problem.
Wind energy doesn’t.
Wind Speed Is Cubed
The power available in moving air can be expressed as:
Pwind = ½ρAv3
