# Furuno FCV-38 power, Sv, TS and angular position equations

Echoview Furuno FCV-38 power, Sv, TS and angular position equations are derived from equations provided by Furuno. Echoview does not support some variables in the original Furuno equations. Contact Furuno Electric Co., Ltd for further details.

## Power

Under Furuno FCV-38 Version 1 *.nc files, received power is derived as:

Under Furuno FCV-38 Version 2 *.nc files, where the transmit-receive coefficient is recorded in the data file, the received power may be derived as:

Where:

Pr is the received power (W)

A is the received voltage (V), calculated from complex variables read from the data file

The Furuno equation for A is:

Where:

I and Q are complex Furuno variables read from the data file. Contact Furuno Electric Co., Ltd for further details.

TR is a Furuno FCV-38 transmitter/receiver coefficient (dB)

Where:

G0 is the Furuno TransducerGain (dB) read from the data file

Pt is the Furuno TransmittedPower (dB) read from the data file

G is the Furuno system gain (dB)

- G is 24dB for CW data
- G is 27dB for LFM data
V is the Voltage (V) from the Furuno version 2 data file. GainCorrection is the Furuno system gain (dB) read from the Furuno version 2 data file. It is displayed on the Calibration page of the Variable Properties dialog box as GainCorrection and can be modified via an ECS file.

When GainCorrection isnot recordedin the Furuno version 2 data file, the setting isnot displayedon the Calibration page and a value is applied as follows:

- GainCorrection is 24dB for CW data
- GainCorrection is 27dB for LFM data
TransmitReceiveCoefficient is the Furuno transmit-receive coefficient (dB) read from the Furuno version 2 data file.

**Note:** The received power equations are referenced to the netCDF convention Type 6 conversion equations.

## TS

The TS equation is derived from the Furuno FCV-38 TS equation. Contact Furuno Electric Co., Ltd for further details. Echoview TS does not implement the Furuno TS term for D (Directivity index).

Where:

TS is the Target strength (dB)

Pr is the received power (W)

r is the range (m) from the transducer to the ping sample

Where:

c is the sound speed (ms-1) read from the data file

dt is the time (s) between recorded samples read from the data file

i is the sample number i ∈ [0, n-1] where n is the number of samples in a ping

t0 is the sample time offset (s) read from the data file

α is the absorption coefficient (dB/m) read from the data file

ΔTR is the Furuno correction value (dB), determined by calibration, read from the data file

## Sv

The Sv equation is derived from the Furuno FCV-38 Sv equation.

Where:

Sv is the mean volume backscattering strength (dB)

Pr is the received power (W)

r is the range (m) from the transducer to the ping sample. See the description in TS for details

α is the absorption coefficient (dB/m) read from the data file

c is the sound speed (ms-1) read from the data file

τ is the pulse duration (seconds) read from the file

- τ is the nominal PulseDuration for CW data
- τ is 0.005s for LFW data
ψ is the TwoWayBeamAngle (Steradian)

Where:

f is the Frequency (Hz) read from the data file

a is 0.1795 m which is the radius of the Furuno FCV-38 transducer

ΔTR is the Furuno correction value (dB), determined by calibration, read from the data file

## Angular position

Echoview angular position, major-axis angle θ (degrees) and minor-axis angle φ (degrees), are derived from equations for θFuruno, as used with the Directivity index, D. Contact Furuno Electric Co., Ltd for further details.

Where:

c is the sound speed (ms-1) read from the data file

f is the Frequency (Hz) read from the data file

dx is the phase difference in the received signals between the transducer quadrants in the alongship (major axis) direction

dy is the phase difference in the received signals between the transducer quadrants in the athwartship (minor axis) direction

Dch is the distance between phase centers for the Furuno FCV-38 transducer, this is equal to 0.1469m

#### See also

Furuno FCV-38 file format

Raw variables derived from Furuno data files

Calibration settings for Furuno FCV-38 data