All of our pulse-coherent instruments use a form of the Doppler relationship to estimate velocity from a measured phase shift. Flow velocity is calculated as: 

where c is the speed of sound, is the measured phase shift, f is the acoustic frequency, and is the time lag between the two pulses. This is just a slightly different form of the Doppler relationship, where the expected frequency shift is replaced by  / . 

The phase shift is constrained to +/- pi in simple pulse-coherent operation, meaning the maximum measurable velocity (velocity range) is

This is the formula used to calculate the beam velocity range reported in the software. The beam velocity range refers to what the instrument is measuring – the velocity along the bi-static axis in the case of the velocimeters. Speed of sound can be found in the header (*.hdr extension) or *.sen file, and frequency can be found on header file under Head configuration > Head frequency. 

Time lag () is specified in two fields for the Vector, Vectrino and AquaPro HR. In an exported ASCII header file (*.hdr) these are labelled System 38 and 39 (under “User Setup”). Note, however, that these are listed as “not used” in the Integrator’s Manual, and in most instruments, they are not. For pulse-coherent instruments, they contain the lag information. The smallest non-zero value of these two lags is used to calculate the velocity range. This information is given in number of counts.

To convert these lags from digital counts to time, we use a simple linear scaling that varies according to the instrument: 

Vector: timeLag = lagCounts / 480e3 

Vectrino: timeLag = lagCounts/1e6 Hz

AquaPro HR (2 MHz): timeLag = lagCounts/111,111 Hz 

AquaPro HR (1 MHz): timeLag = lagCounts/55,555 Hz

where the scaling factor is the internal sample clock timing. 

Let's use an example: in a Vector (6000 kHz head frequency) *.hdr file, System 38 is 50 and System 39 is 130 counts, sound speed was measured as 1470.7 m/s.

For the vector, timeLag = 50/480e3 = 1.042e-4

Velocity range will be:

which leads to:

As the Velocity Range refers to the beam velocity, the final vertical velocity range will be:

HorizontalVelocityRange = 0.59/sind(15)~2.3 m/s

VerticalVelocityRange = 0.59/cosd(15)~0.6 m/s