F.W. Bell 7030, Instruction Manual

Page: 67 / 126

F.W. BELL Model 7030 Gauss/Tesla Meter Instruction Manual
Section 6 – Flux Density Measurement 6-17
VECTOR
SUMMATION
(Continued) Vector Magnitude
The vector magnitude is calculated using the pythagorean theorem for an
orthogonal cartesian co-ordinate system, mathematically:
R = X
2
+ Y
2
+ Z
2
Where X, Y and Z, are the readings from channels 1, 2, and 3. R is the
resultant vector magnitude.
Vector Angle
Vector Angles are specified as the angles between the resultant vector and
X, Y, and Z axes. The angles are calculated using the following equations.
θ
XR
= cos
-1
(X/R),
θ
YR
= cos
-1
(Y/R),
θ
ZR
= cos
-1
(Z/R)
Where
θ
xr
,
θ
yr
,
θ
zr
, are the angles between R and the X, Y, and Z axes. X,
Y, and Z are the readings from channels 1, 2, and, 3. R is the resultant
vector sum magnitude computed from above. On the display, vector
angles are indicated as x/r, y/r, and z/r; corresponding to
θ
xr
,
θ
yr
, and
θ
zr
,
respectively.
Vector Summation and Relative Mode Operation
If the relative mode is enabled for individual channels, the instrument will
use those readings when calculating the vector summation. When all three
channels are in relative mode, a vector difference is calculated using the
following equation:
R = (X-X
rel
)
2
+ (Y-Y
rel
)
2
+ (Z-Z
rel
)
2
Where X, Y, and Z are the present readings in relative mode and X
rel
, Y
rel
,
and Z
rel
are the relative settings. R is the magnitude of the difference
vector.
Similarly, the angles are computed using the following equations:
θ
XR
= cos
-1
([X-X
rel
]/R),
θ
YR
= cos
-1
([Y-Y
rel
]/R),
θ
ZR
= cos
-1
([Z-Z
rel
]/R)
Where R is the vector magnitude calculated using the relative readings.