Anemometer constant torque and responded more quickly to gusts than the four-cup anemometer. The three-cup anemometer was further modified by the Australian Dr. Derek Weston in 1991 to measure both wind direction and wind speed. Weston added a tag to one cup, which causes the cupwheel speed to increase and decrease as the tag moves alternately with and against the wind. Wind direction is calculated from these cyclical changes in cupwheel speed, while wind speed is determined from the average cupwheel speed. Three-cup anemometers are currently used as the industry standard for wind resource assessment studies & practice. One of the
Haar measure nontrivial but the modular function of formula_3 is trivial. The quotient of these cannot be extended to any character of formula_3, so the quotient space formula_114 (which can be thought of as 1-dimensional real projective space) does not have even a semi-invariant measure. Using the general theory of Lebesgue integration, one can then define an integral for all Borel measurable functions formula_84 on formula_3. This integral is called the Haar integral. If formula_11 is a left Haar measure, then for any Haar integrable function formula_84 on formula_3. This is immediate for indicator functions, being essentially the definition of left invariance.