Campbell-scientific CR9000X Measurement and Control System Instrukcja Użytkownika Pobierz pdf (Strona 223)

100

101

Section 6. Data Table Declarations and Output Processing Instructions

For deviations less than 40 degrees, the error in this approximation is less than

1%. At deviations of 60 degrees, the error is 10%.

The speed sample may be expressed as the deviation about the mean speed,

ss'S

Equating the two expressions for Cos (

θ‘) and using the previous equation for

;

−=+(')/ /(')Θ

iii

UsS

(')

(') / (')'/ '/ΘΘ

iiii

U S sS sS

22 2=− − +

(')Θ

Solving for , one obtains;

Summing over N samples and dividing by N yields the variance of

Θu.

Note that the sum of the last term equals 0.

(( )) ( ')/ ( /) (( ') ')/

ΘΘ ΘuNUSsNS

iii

22 2

21==−−

∑∑

) /Θ sNS

∑

(( ') '

The term, , is 0 if the deviations in speed are not

correlated with the deviation in direction. This assumption has been verified in

tests on wind data by CSI; the Air Resources Laboratory, NOAA, Idaho Falls,

ID; and MERDI, Butte, MT. In these tests, the maximum differences in

σσ

()((')/) ()(( /))

ΘΘ ΘuNuUS

==−

∑

212 12

21 and

have never been greater tan a few degrees.

The final form is arrived at by converting from radians to degrees (57.296

degrees/radian).

()(( /)) ( /)

ΘuUS US=− =−21 811

12 12

6-39

1 2 ... 218 219 220 221 222 223 224 225 226 227 228 ... 441 442

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