Pathfinder DVL Guide
April
2018
EAR-Controlled Technology Subject to Restrictions Contained on the Cover Page.
Page 35
which decreases the distance the pulse has to travel and this partly offsets the change in travel time.
This error is difficult to calculate because one needs to know the actual speed of sound profile in the
water column. A couple of examples are given below:
Example 1
: A linearly changing temperature from 15°C at the instrument to 4°C at 250m depth will cause
the “slant range” measurement to read high by about 1% at an altitude of 250 meters.
Example 2
: A step change in temperature of 10°C at a depth of 50 meters will increase the “slant range”
measurement a little less than 1% when operating at 100m altitude.
Bottom Slope
Pathfinder DVLs multiply the measured “slant range” of each beam by the Cosine of the Janus angle
(normally 30°) to indicate the vertical distance. While a simple solution is to average the four beam values
obtained for altitude, this is not the preferred method. The equation for this is shown as (1) below. This is
reasonably accurate when there is no bottom slope, but a better algorithm is shown in (2) below for bot-
toms that are sloped.
4
4
3
2
1
h
h
h
h
h
+
+
+
≈
(1)
h
h h
h
h
h h
h
h
h
h
h
h
1
1
1
1
1
1
=
+
+
+
=
+
+
+
1
2
3
4
1 2
1
2
3 4
3
4
(2)
Where h is the altitude and the h
1
, h
2
, h
3
, h
4
are the four beam “slant ranges” projected into the vertical.
This equation is exact if the bottom is a plane surface.
Pitch & Roll
Pitch and/or roll of the instrument causes the h components shown in (1) above to change. Because it is
complicated to compute the h components for all combinations of pitch, roll, and bottom slope, the worst-
case relative error as calculated by equation (1) above is used and is approximately:
θ
β
βφ
φ
2
2
2
1
2
2
1
tan
1
−
±
+
≈
∆
h
h
where
β
is the bottom slope in radians,
φ
is the instrument tilt in radians, and
θ
is the beam Janus angle.
This method is used in the case that tilts and bottom slope are in the same direction. Note that the error is
second order in the bottom slope and tilt parameters. An 8-degree tilt will cause the simple four-beam av-
erage to be 1% long. A 14-degree bottom slope will cause it to be 1% short (when the beam Janus angle is
30
0
).
Resolution
The Pathfinder DVLs provide two additional altitude outputs in the
. The first
is called “Slant Range” which is actually a range to the bottom in the Z-axis. It is a combination of
the four slant ranges per equation (2) above. The second is called “Vertical Range” where the instrument
pitch and roll are used to calculate the altitude. This is the most accurate output for altitude since it
compensates for the orientation of the instrument.