Wind Shear Power-Law Speed at Hub Height

Wind measured at a met tower is not the wind at the hub, and because power is cubic a small error in the shear exponent becomes a large error in the energy estimate. A tower reading 15 mph at 160 ft, extrapolated to a 330 ft hub at an exponent of 0.2, gives 17.34 mph -- and 1.544 times the energy, 54% more, from height alone. That is the economic case for taller towers in one line. THE EXPONENT IS THE WHOLE CALCULATION and it is site-specific. The 1/7 value of 0.14 that gets used as a default belongs to flat open country in neutral stability; over crops, brush, or trees the profile is much steeper and over water much flatter. Assume 0.14 on this tower instead of 0.2 and the hub speed reads 16.60 mph, worth 0.878 times the energy -- a shear exponent wrong by 0.06 costs 12% of the estimate, and on a project financed against that estimate it is not a rounding difference. MEASURE IT INSTEAD. Two anemometer levels on the same mast give the exponent directly, which is worth far more than any table and is the reason met masts carry multiple levels: 13.2 mph at 100 ft against 15 mph at 160 ft is an exponent of 0.272, well above the 0.2 that was assumed, and it takes the hub speed to 18.26 mph. Shear also varies through the day and the year -- nights are typically far more sheared than afternoons because the atmosphere stabilizes -- so a short campaign in one season can mislead in both directions. A power-law extrapolation with a single exponent. Real profiles are not power laws: they change with atmospheric stability, they distort over complex terrain and near forest canopies where the profile can be displaced upward or even reversed, and extrapolating more than roughly twice the measurement height is not defensible for an energy assessment. It does not compute turbulence intensity, wind veer across the rotor, or the inflow angle, all of which affect both energy and loads, and it does not produce an energy estimate, which needs a full distribution and a power curve. A bankable assessment uses measured hub-height data or remote sensing to IEC 61400-12 and an independent energy assessor, which govern.

the power law v2 = v1 x (z2 / z1) raised to alpha; alpha derived from two measured levels is ln(v2/v1) / ln(z2/z1); the energy ratio is the speed ratio cubed.

The power-law wind shear relation by name, with the customary exponents 0.10 over water and smooth ground, 0.14 the open-country default, 0.20 over crops and scattered obstacles, and 0.25 to 0.40 over woodland and suburbs, and IEC 61400-12 named for the hub-height measurement this does not replace. An independent energy assessor governs a bankable estimate.

Extrapolation between two heights on the user's own anemometer readings; no wind atlas or proprietary shear table is reproduced.

Estimate. AHJ and licensed professional govern.

Field names used by the API: measured_speed_mph, measured_height_ft, hub_height_ft, shear_exponent, alt_shear_exponent, second_speed_mph, second_height_ft, hub_speed_mph, speed_ratio, energy_ratio, alt_hub_speed_mph, alt_energy_vs_entered, derived_exponent

• The exponent is measured, not assumed two levels on one mast beat any published tablemet mast practice
• A speed error triples in energy because power goes as the cube of speedfirst principles
• Twice the measurement height is the limit past that a single power law is not defensibleIEC 61400-12