WIND ENERGY SYSTEMS - Cd3wd

Chapter 3—Wind Measurements 3–31
The projection of the balloon flight on the horizontal plane is shown in Fig. 19.
distance A i is given by
The
The distance B i is given by a similar expression:
A i = r i cos α i = z i cot β i cos α i (46)
The projections of P ′ Q ′ on the x and y axes are given by
B i = r i sin α i = z i cot β i sin α i (47)
∆A = A j − A i = z j cot β j cos α j − z i cot β i cos α i (48)
The length P ′ Q ′ is then given by
∆B = B j − B i = z j cot β j sin α j − z i cot β i sin α i (49)
P ′ Q ′ =
√
(∆A) 2 +(∆B) 2 (50)
Figure 19: Projection of balloon flight on a horizontal plane.
The angle δ, showing direction of balloon travel with respect to the x axis, is given by
−1 ∆B
δ =tan
∆A
(51)
An alternative approach is to combine the length and direction into a vector quantity
P ′ Q ′ , where, by using complex arithmetic, we have
Wind Energy Systems by Dr. Gary L. Johnson November 12, 2001