# Sonic data to Sv, TS and angular position

This page describes the manner in which variable data is calculated from underlying data for Sonic data files.

## Calculating data point range from Sonic data

For Sv and angular position calculations using Sonic echosounders:

Start range = d * 0.5 (m)
Stop range = d * n (m)

Where:

 d is the sample thickness (m) for the Sonic echosounder. d = 0.0750 m for KFC-500/1000/2000 echosounders (sampling frequency 10 kHz) d = 0.0500 m for KFS echosounders (sampling frequency 15 kHz) d = 0.0375 m for KFC-6000/KSE-300 echosounders (sampling frequency 20 kHz) n is the number of data points read from the file for a ping.

## Calculating Sv, TS from Sonic data

### KFC-500/1000/2000/3000/5000, KFS series

Data files from these echosounders store received power as a single unsigned integer (16 bits) in increments of -0.2 dB from a reference of 20 dB. That is:

Pr = 20 - 0.2i (dB)            where i is the unsigned integer value read from the data file

Sv for any data point is then calculated as follows:

Sv = Pr + 20logR + 2αR - 10log(c * τ / 2) - Ψ - TRFactor

Where:

Pr is the received power (dB) - see note below
R is the range of the data point (meters)
α is the absorption coefficient (dB/m)
c is the sound speed through the medium (m/s)
τ is the pulse duration (s)
Ψ is the equivalent two-way beam angle (dB re 1 Steradian)
TRFactor is the transmit/receive calibration constant (dB)

Notes:

• Verify α, c, τ, Ψ and KaijoTRFactor on the Calibration page of the Variable Properties dialog box
• We do not know against which reference Pr is measured. It is conceivable it is measured re Pt the transmitted power, or some arbitrary unit (1 Watt is not unusual). If the latter, then Pt must be accounted for in the calibration constant KaijoTRFactor.
• It appears that the calibration constant KaijoTRFactor is specific to the transmission frequency being used, as the frequency (wavelength) term expected in the sonar equation is not present.
• TVG is applied to samples with ranges greater than 1 meter.

### KFC-6000/KSE-300

Pr = 20 log10(2.5) - 0.2i (dB)  where i is the unsigned integer value read from the data file

Sv for any data point is then calculated as follows:

Sv = Pr + 20log10 R + 2αR -10log10 (c*τ/2) - TRFactor - Ψ + CalibrationOffsetSv

TS = Pr + 40log10 R + 2αR - TRFactor + CalibrationOffsetTs

where:

Pr is the received power (dB) - see note below
R is the range of the data point (meters)
α is the absorption coefficient (dB/m)
c is the sound speed through the medium (m/s)
τ is the pulse duration (s)
Ψ is the equivalent two-way beam angle (dB re 1 Steradian)
TRFactor is the transmit/receive calibration constant (dB)
CalibrationOffsetSv is a constant used for the offset of Sv.
CalibrationOffsetTs is a constant used for the offset of TS.

Notes:

• α, c, τ, Ψ, TRFactor and CalibrationOffsetSv and CalibrationOffsetTs are displayed on the Calibration page of the Variable Properties dialog box. Many of these settings are read from the data file or a value can be assigned using an Echoview calibration file (ECS).
• We do not know against which reference Pr is measured. It is conceivable it is measured re Pt the transmitted power, or some arbitrary unit (1 Watt is not unusual). If the latter, then Pt must be accounted for in the calibration constant TRFactor.
• It appears that the calibration constant TRFactor is specific to the transmission frequency being used, as the frequency (wavelength) term expected in the sonar equation is not present.
• TVG is applied to samples with ranges greater than 1 meter.

## Calculating angular position from Sonic data

### KFC-500/1000/2000/3000/5000, KFS series

#### Minor-axis and Major-axis angles

Sonic data files store electrical angles as single byte signed integer values with a valid range of -94 degrees to +94 degrees in steps of 1 degree. The following equations handle all angles in radians. Angles displayed in Echoview are in degrees.

Mechanical angles are calculated from the electrical angles as:

α = tan-1(δx / D)
β = tan-1(δy / D)

where:

D = [16π2 - (δx2 + δy2)]1/2
α is the minor-axis mechanical angle
β is the major-axis mechanical angle
δx is the electrical angle in the fore-aft direction (minor-axis); positive indicates fore
δy is the electrical angle in the starboard-port direction (major-axis); positive indicates starboard

#### Sonic angles

Sonic use two different angles, θ and Φ, the angles of a spherical coordinate system, calculated from the electrical angles as follows:

θ = sin-1([δx2 + δy2]1/2 / 4π)
Φ = tan-1(δy / δx)

#### Minor-axis and major-axis angles in terms of Sonic angles

The conversion formulas from Sonic angles θ and Φ to minor-axis and major-axis angles α and β are:

α = tan-1(tan(θ) cos(Φ))
β = tan-1(tan(θ) sin(Φ))

The inverse transformation is:

Φ = tan-1(tan(β) / tan(α))
θ = tan-1((tan(α)2 + tan(β)2)1/2)

Note: The term 4π in the equations above is the product of the wave number (2π/λ) and the center separation of the transducer elements (2λ by design) - where λ is the transmitted signal wavelength.

### KFC-6000/KSE-300

#### Minor-axis and Major-axis angles

Sonic data files store electrical angles as single byte signed integer values with a valid range of -94 degrees to +94 degrees in steps of 1 degree. The following equations handle all angles in radians. Angles displayed in Echoview are in degrees.

Mechanical angles are calculated from the electrical angles as:

α = tan-1(δx / D)
β = tan-1(δy / D)

where:

D = [(SonicArrayCenterDistance*2π)2 - (δx2 + δy2)]1/2
SonicArrayCenterDistance = SonicArrayCenterDistance on the Calibration page of the Variable Properties dialog box
α is the minor-axis mechanical angle
β is the major-axis mechanical angle
δx is the electrical angle in the fore-aft direction (minor-axis); positive indicates fore
δy is the electrical angle in the starboard-port direction (major-axis); positive indicates starboard

#### Sonic angles

Sonic use two different angles, θ and Φ, the angles of a spherical coordinate system, calculated from the electrical angles as follows:

θ = sin-1([δx2 + δ2]1/2 / (SonicArrayCenterDistance*2π))
Φ = tan-1(δy / δx)

#### Minor-axis and major-axis angles in terms of Sonic angles

The conversion formulas from Sonic angles θ and Φ to minor-axis and major-axis angles α and β are:

α = tan-1(tan(θ) cos(Φ))
β = tan-1(tan(θ) sin(Φ))

The inverse transformation is:

Φ = tan-1(tan(β) / tan(α))
θ = tan-1((tan(α)2 + tan(β)2)1/2)