WIND ENERGY SYSTEMS - Cd3wd

Chapter 3—Wind Measurements 3–30
The voltages V H and V V produce integer numbers N H and N V at the output of the A/D
converter. The actual angles being measured are proportional to these numbers. That is, the
azimuth angle α is given by
α = kN H (43)
where k is a constant depending on the construction of the potentiometer and the applied
battery voltage. A similar equation is valid for the elevation angle β.
The basic geometry of the balloon flight is shown in Fig. 18. At some time t i the balloon
is at point P , at an azimuth angle α i with respect to the reference direction (the x axis) and
an elevation angle β i as seen by the balloon tracker located at the origin. The balloon is at
aheightz i above the horizontal plane extending through the balloon tracker. The vertical
projection on this plane is the point P ’. At some later time t j the balloon has moved to point
Q, atanglesα j and β j , and with projection Q ′ on the horizontal plane. The length P ′ Q ′
represents the horizontal distance traveled during time ∆t = t j − t i . The average wind speed
during the time ∆t is
u ij = P ′ Q ′
∆t
(44)
Figure 18: Geometry of balloon flight
If the vertical distance z i is known from the balloon ascent rate and the time elapsed since
launch, the distance r i can be computed from
r i = z i cot β i (45)
Wind Energy Systems by Dr. Gary L. Johnson November 12, 2001