Japan Radio Co. JLN-740A, Instruction Manual

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C-1
Appendix C Error due to the deviation from
the irradiation angle reference value
APP C
Appendix C
Error due to the deviation from the
irradiation angle reference value
The causes of occurrence of deviation from the reference value are classified into two: hull motions,
and manufacturing or installation of the oscillator. In general, in Doppler log, to minimize the errors
caused by various hull motions, symmetrical sequence (dual beam) is often applied as shown in Figure
1 a).
The following section discusses the tolerance values by comparing the dual beam system with the
single beam system.
C.1 Errors by hull motions
Figure 4 shows the speed errors that are caused by the deviation angle of rolling and pitching. This
condition is explained below.
1
Vertical speed component
Although a speed component in the horizontal direction is the only important factor for a ship, a
vertical speed component occurs due to a cause such as ocean swell, causing an error. See
Figure 2. Doppler shift frequency f
d1
for
beam N
1
will be as follows when the
horizontal speed component is V and
the vertical speed component is U.
f
d1
= 2f
0
C (Vcos
θ
1
– Usin
θ
1
) (1)
In the same way, Doppler shift frequency fd
2
for beam N
2
will be:
f
d2
= 2f
0
C (-Vcos
θ
2
– Usin
θ
2
) (2)
When
θ
1 =
θ
2, the following expression
is established for dual beam:
f
d
= f
d1
– f
d2
= 4f
0
V
C cos
θ
1
(3)
As a result, vertical components are canceled out, not impacting the Doppler shift frequency
and a Doppler shift frequency twice that of the single beam system is obtained.