4 m/s as our estimated windspeed, we must scale our estimate down, mul-
tiplying it by (4/6)3 ≅ 0.3. (Remember, wind power scales as wind-speed
On the other hand, to estimate the typical power, we shouldn’t take the
mean wind speed and cube it; rather, we should find the mean cube of the
windspeed. The average of the cube is bigger than the cube of the average.
But if we start getting into these details, things get even more complicated,
because real wind turbines don’t actually deliver a power proportional to
wind-speed cubed. Rather, they typically have just a range of wind-speeds
within which they deliver the ideal power; at higher or lower speeds real
wind turbines deliver less than the ideal power.
Taller windmills see higher wind speeds. The way that wind speed increases
with height is complicated and depends on the roughness of the
surrounding terrain and on the time of day. As a ballpark figure, doubling
the height typically increases wind-speed by 10% and thus increases the
power of the wind by 30%.
Some standard formulae for speed v as a function of height z are:
In practice, these two wind shear formulae give similar numerical answers.
That’s not to say that they are accurate at all times however. Van den Berg
(2004) suggests that different wind profiles often hold at night.