# How to calculate current speed and direction from three beam ADCP velocity components

FollowThe raw velocity measurement is a vector in the direction along each of the beams, which are referred to as Beam coordinates. Beam coordinates can be converted to a Cartesian coordinate system (XYZ) by knowing the beam orientation relative to the head. Furthermore, the flow can be presented in Earth-normal coordinates (ENU; East, North and Up). In order to get the information referenced to Earth coordinates (ENU) it is therefore necessary to detect the instrument’s orientation in space. The preferred coordinate system may be specified in the deployment software.

For midlife instruments (Aquadopp, AquaPro, AWAC, Vector, etc.) the ASCII converted raw data for the velocities are given in the .v1, .v2 and .v3 files. Depending on your chosen coordinate system the content in each file is as follows:

.v1 is beam 1, or the X-axis (in XYZ), or East (in ENU)

.v2 is beam 2, or the Y-axis (in XYZ), or North (in ENU)

.v3 is beam 3, or the Z-axis (in XYZ), or Up (in ENU)

In Beam coordinates, a positive velocity is in the same direction as the beam points. Beam 1 is marked with an “X” on the head. In XYZ coordinates, a positive velocity in the X-direction points in the direction of the X-axis arrow. The X-axis points in the same direction as Beam 1. In ENU coordinates, a positive east velocity points toward east. This is also a right-handed orthogonal system. The velocity data unit is m/s.

The speed, or magnitude of the velocity vector, for ENU components can be calculated as follows:

Speed = sqrt(Veast^2 + Vnorth^2 + Vup^2)

The angle, given in interval [-π, π]:

Angle = atan2(Veast,Vnorth)

To get the direction in Earth coordinates [0,360] the following transformation can be done:

Direction = 180 + 180/pi*(atan2(-Veast,-Vnorth))

0 degrees points towards North, 90 degrees towards East, 180 degrees towards South, and 270 towards West.

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