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APPENDIX
1.
Remarks on Error resulting from deviation of radiation angle from the reference value
Hull movement causes deviation of radiation angle
from the reference value.
Generally, the balanced array shown in Fig. 10.1 is
often adopted in the Doppler sonar in order to
reduce the error caused by various hull movements.
The following discusses this tolerance in
comparison with the single beam method.
1.1
Error caused by hull movement
The speed error caused by a deviation angle such as rolling and pitching is indicated by Fig.10.4.
An explanation how this is calculated is shown below.
(1) Vertical velocity
Only the velocity in the horizontal direction is important for ship. Vertical velocity is also caused
by swell and other factors, and appears in the form of an error.
When the horizontal velocity is assumed as U, as shown in Fig. 10.2, the Doppler shift frequency
f
with respect to beam N1 is expressed by the following equation 10.1.
d1
2f
0
f
=
(Vcos θ
d1
C
Similarly, Doppler shift frequency f
respect to N2 is expressed by the following
equation 10.2.
2f
0
f
=
(-Vcos θ
d2
C
Assuming that θ
balanced array.
f
= f
– f
=
d
d1
d2
The vertical velocity components cancel each other, without affecting the Doppler shift frequency.
Thus, the Doppler shift frequency is double that of the single beam method.
(2) Trim and heel
When there is an offset of δ with respect to the vertical line as shown in Fig. 10.3, the Doppler shift
frequencies occurring to the beams N
are expressed by the following equations,
respectively:
2Vf
0
f'
=
(cos θ cos δ – sin θ sin δ)
d1
C
2Vf
0
f'
=
(cos θ cos δ + sin θ sin δ)
d2
C
The error due to balanced array is obtained
from Eq. 10.4.
= 100 (cos δ – 1) %
ε
δ
The error in single beam method is expressed by Eq. 10.5.
28
APPENDIX
– Usin θ
)
(10.1)
1
1
– Usin θ
)
(10.2)
2
2
= θ
, we get (10.3) in the
1
2
4f
V
0
cos θ
(10.3)
1
C
with
d1
and N
1
2
(10.4)
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