# How does a Pulse-Coherent system use lags to determine maximum velocity range?

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

v = c * delta_phi / ( 4 * pi * f * delta_t )

where c is the speed of sound, delta_phi is the measured phase shift, f is the acoustic frequency, and delta_t 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 delta_phi / delta_t.

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

VR = c / ( 4 * f * delta_t )

This is the formula used to calculate the velocity range reported in software. Everything but delta_t is easily found in the header.

delta_t 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, but for pulse-coherent instruments they contain the lag information.

The shorter of these two lags (i.e. the lower number in counts) is used to calculate the velocity range. So, for instance, if the Nominal Velocity Range is 1 m/s, System 38 is 50 and System 39 is 130 counts. The velocity range calculated using the formula supplied previously is for the beam velocity range (what the instrument is measuring – the velocity along the bi-static axis in the case of the velocimeters).

The final piece of the puzzle is to scale these lags from digital counts to time. This is a simple linear scaling:

timeLag = lagCounts / 480e3

where the scaling factor is the internal sample clock timing. This scaling is only valid for the Vector. Both frequencies of the HR Profiler, Vectrino, etc. all have different sample clock timing, resulting in a different scaling:

Vectrino: timeLag = lagCounts/1e6 Hz

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

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

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