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Patel’s treatment of wind-resource analysis makes this point directly: because wind power varies with the cube of speed, the frequency distribution of wind speed must be known to determine the wind power potential of a site.
That is a fundamentally better question than simply asking:
“What’s the average wind speed?”
A Histogram Can Tell a Story an Average Cannot
Imagine two wind-speed histograms.
Both have the same mean.
The first is narrow and concentrated around 6 m/s.
The second is spread widely, with many low-wind observations but also a meaningful number of much stronger winds.
The single-number average can make them look equivalent.
The distributions immediately reveal that they are not.
This matters because each wind-speed bin can be treated separately.
For a wind speed vi occurring with probability or frequency fi, the contribution to average available wind power is related to:
fivi3
Across all wind-speed intervals, the relevant cubic term becomes:
Σ fivi3
rather than simply:
(Σ fivi)3
Those operations are not interchangeable.
That is the mathematical heart of the issue.
Engineers Don’t Want to Store Thousands of Wind-Speed Numbers Forever
A full frequency table is useful, but engineers also need convenient mathematical models that describe how wind speeds are distributed.
This is where probability distributions enter wind engineering.
Two names appear repeatedly:
Weibull distribution
and:
Rayleigh distribution
Patel describes the Weibull distribution as a useful representation of wind-speed variation and presents the Rayleigh distribution as a special case that can be used when only the mean wind speed is available.
The important idea for a non-specialist is not memorizing the probability-density equation.
It is understanding what the distribution gives us.
Instead of saying:
“The site’s wind speed is 6 m/s.”
we can describe the probability that the wind will occur at different speeds.
That is much closer to the information a turbine actually experiences.
The Turbine Makes the Average-Speed Problem Even More Interesting
So far, we have discussed power available in the wind.
A real wind turbine adds another layer.
Turbines have power curves.
At very low wind speeds, the machine may produce no useful electricity.
Once wind reaches the cut-in speed, generation begins.
As wind speed rises, electrical output increases.
