# Sonar calculator algorithms

This page details the algorithms used in Sonar Calculator. The equations used by Mackenzie (1981), Chen and Millero (1977) are discussed by the National Physical Laboratory website (2018) Simple Equations [Online] Available at http://resource.npl.co.uk/acoustics/techguides/soundseawater/content.html.

Where:

c = speed of sound (m/s),

α =  absorption coefficient (dB/m)

T = temperature (°C)

S = salinity (ppt)

D = depth (m)

P = pressure (kPa)

f = frequency (kHz)

### Speed of sound in salt water (Mackenzie, 1981)

Mackenzie (1981)

#### where  -2 < T < 30

25 < S < 40

0 < D < 8000

### Speed of sound in salt water (Leroy, 1969)

Leroy (1969)

#### where -2 < T < 23

30 < S < 40

0 < D < 500

### Speed of sound in fresh water (Del Grosso and Mader, 1972) where  0 < T < 95

D = 0

### Speed of sound (Chen and Millero, 1977)

Chen and Millero (1977). The Sonar calculator Pressure (kPa) is converted to units of bar for calculations. Where:

c(S, T, P) = Speed of sound (m/s) is a function of salinity, temperature and pressure.

T = Temperature with a valid range* of 0 to 40 degrees Celsius.

S = Salinity with a valid range* of 0 to 40 ppt.

P = Pressure with a valid range* of 0 to 1000 bar.

*Valid range is sourced from Wong and Zhu (1995).

Coefficient

Numerical value

Coefficient

Numerical value

C00

1402.388

A02

7.166E-5

C01

5.03830

A03

2.008E-6

C02

-5.81090E-2

A04

-3.21E-8

C03

3.3432E-4

A10

9.4742E-5

C04

-1.47797E-6

A11

-1.2583E-5

C05

3.1419E-9

A12

-6.4928E-8

C10

0.153563

A13

1.0515E-8

C11

6.8999E-4

A14

-2.0142E-10

C12

-8.1829E-6

A20

-3.9064E-7

C13

1.3632E-7

A21

9.1061E-9

C14

-6.1260E-10

A22

-1.6009E-10

C20

3.1260E-5

A23

7.994E-12

C21

-1.7111E-6

A30

1.100E-10

C22

2.5986E-8

A31

6.651E-12

C23

-2.5353E-10

A32

-3.391E-13

C24

1.0415E-12

B00

-1.922E-2

C30

-9.7729E-9

B01

-4.42E-5

C31

3.8513E-10

B10

7.3637E-5

C32

-2.3654E-12

B11

1.7950E-7

A00

1.389

D00

1.727E-3

A01

-1.262E-2

D10

-7.9836E-6

### Absorption coefficient (Francois & Garrison, 1982) where:       This algorithm applies to all oceanic conditions and 200 Hz < f < 1 MHz.

Note: The Francois & Garrison (1982) algorithm calculates the absorption coefficient in units of dB/km. Echoview displays the calculated absorption coefficient units in dB/m as recommended by MacLennan et al (2002).