User manual

Velocity Transformation
The velocity transformation is geometric. First, transform the four path velocities into a
velocity vector, (u, v, w), in the frame of the MMP. Recall that the Cartesian co-ordinate frame of
the MMP is defined to have the +x-axis pointing forward, the direction in which the sting of the
ACM points. The +y-axis points to port and the +z-axis points up. The following results from
the geometry:
()
2
XX
VV
u
−+
−
−
=
(
)
2
XX
VV
v
−+
−
+
=
()
2
2
Y
U
Vu
w
−
−
+⋅
=
(
)
2
2
Y
D
Vu
w
+
+
−
⋅
=
Use w = w
U
for an upward (odd numbered) profile and w = w
D
for a downward (even numbered)
profile. It is important to make this distinction rather than just combining the +Y and -Y
measurements as the +X and -X measurements are combined to measure the horizontal velocity
because the trailing Y-path is contaminated by the sheet-flow wake of the central post of the sting
when the MMP is profiling. The leading acoustic path is in relatively clean flow.
Note that w is the sum of the ambient vertical flow field and the vertical motion of the
profiler. The vertical motion of the profiler can be removed, to a reasonable level of accuracy, by
subtracting the pressure rate, dP/dt, which can be determined from the CTD measurements. The
geometry of the acoustic paths and the near zero tilt of the profiler mean that u and v, the
horizontal components of the velocity, are relatively uncontaminated by the vertical motion of the
profiler.
The horizontal speed and direction of the flow, in the MMP frame, are given by:






=+=
−
u
v
vuS
VH
122
tan θ
θ
V
is measured in the usual mathematical sense, positive counter-clockwise from the positive x-
axis of the MMP frame. θ
V
will typically be close to 180° with the sting pointing into the flow.
The direction of flow in the true north Cartesian earth frame is:
HVT
θ
θ
θ
+
=
8-30