# Source Level calculations of an Underwater Cylindrical Acoustic Array

nauman
TL;DR Summary
Calculations of Source Level of Cylindrical Array of multiple transducers with each transducer with known Transmit Voltage Response 'TVR'
Hi all

I am trying to calculate Source Level 'SL' of a underwater acoustic Cylindrical Array with multiple Transducers. The array has 03 Rings with 32 transducers in each Ring. The spacing between each ring is around 0.18m whereas Dia of each Ring is about 1m. Each transducer is being driven with separate Power Amplifier.
What i know about SL of individual transducer is that if we apply Vrms to a transducer having a 'TVR' of X dB, transducer SL will be calculated as:

SL = 20LOG10(Vrms)+X dB

On the basis of this SL calculations, I want to know how can we calculate 'SL' of complete cylindrical array (32x3 elements) in 'Omni Directional' Mode if we know TVR and Vrms applied to each Transducer? Here 'Omni Directional' means same level of transmission in all directions simultaneously.

Thanks

Mentor
Summary:: Calculations of Source Level of Cylindrical Array of multiple transducers with each transducer with known Transmit Voltage Response 'TVR'

Hi all

I am trying to calculate Source Level 'SL' of a underwater acoustic Cylindrical Array with multiple Transducers. The array has 03 Rings with 32 transducers in each Ring. The spacing between each ring is around 0.18m whereas Dia of each Ring is about 1m. Each transducer is being driven with separate Power Amplifier.
What i know about SL of individual transducer is that if we apply Vrms to a transducer having a 'TVR' of X dB, transducer SL will be calculated as:

SL = 20LOG10(Vrms)+X dB

On the basis of this SL calculations, I want to know how can we calculate 'SL' of complete cylindrical array (32x3 elements) in 'Omni Directional' Mode if we know TVR and Vrms applied to each Transducer? Here 'Omni Directional' means same level of transmission in all directions simultaneously.

Thanks
Can you post a sketch of the setup? Which way do the transducers face, axially or radially? Which direction do you want the main transmitted power lobe to be in? Can you post a link to the datasheet for the US transducers you are using?

nauman
Can you post a sketch of the setup? Which way do the transducers face, axially or radially? Which direction do you want the main transmitted power lobe to be in? Can you post a link to the datasheet for the US transducers you are using?
Hi
I do want to do theoretical calculations only as actual array is not in my hand. The sketch of array is attached here, it consist of 96 customized 'Twin-Transducers'. Only estimated TVR values of these transducers are known.

#### Attachments

• Cylindrical Array.jpg
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It looks to me like you have transducers embedded in a cylindrical wall, so transducers on the far side cannot be seen directly. Each elemental transducer will have a radiation pattern that I believe you are describing as isotropic when it is actually semi-isotropic because of the cylindrical wall.
1. Is that correct ?

2. Will the transducers be driven synchronously in phase, or will the phase be controlled individually to synthesise a maximum EIRP beam?

3. You give the dimensions of the array element distribution on the surface of the cylinder, but no idea of the range of frequencies involved that will determine the wavelength in the water.

Basically, as a phased beam radiator; 4 rings of 32 transducers = 4 * 32 = 128, but only half are visible, so 64 elements = 26 are in line of sight.
Each doubling of the energy in the beam will give a 3 dB increase, so 26 elements will give you a; 6 * 3dB = 18 dB array factor to add to the SL in dB of an individual sensor.
If the sensor has an SL of a dB, the array will give a maximum SL of; a + 18 dB.

For n = 96 / 2 = 48;
Array factor = ( 10 * Log10( 2 ) ) * Log2( n )
Change of base …
10 * Log10( 2 ) = 10 * Log( 2 ) / Log( 10 ) = 3.0103 dB
Log2( n ) = Log( n ) / Log( 2 ) = 5.585
Additive array factor = 3.0103 * 5.585 = 16.81 dB

nauman
Thanks for reply. I am attaching another picture of array for clarification purpose.

1a. It is a complete cylindrical array immersed in water and can transmit evenly in all directions and open on all sides i.e. no cylindrical wall.
1b. I do not have radiation pattern of 'Twin Transducer' but most probably it will have cosine shape beam pattern due its shape.
1c. These transducers are backbaffeld i.e. transmitting from front phase only.

2. As per my understanding, in ODT Mode i.e. Omni Directional Transmission Mode, no phase adjustments will be applied and all transducers should be simultaneously driven (synchronously). In RDT Mode i.e. Rotational Directional Transmission Mode, Cylindrical Array can be divided into equal sectors e.g. 3 sectors and for each sector independent transmit beamforming can be applied using proper phase adjustments.

3. Array operates in frequency range of 6-9 KHz

My confusion is that if i drive all Transducers simultaneously in ODT Mode i.e. without any phase adjustments, should i include"Array Factor or Gain" in SL calculations? In my understanding, Array Gain should be added only when doing beamforming using phase adjustments.

Thanks & Regards

#### Attachments

1c. These transducers are backbaffeld i.e. transmitting from front phase only.
I assume you mean the “front face”.
1a. It is a complete cylindrical array immersed in water and can transmit evenly in all directions and open on all sides i.e. no cylindrical wall.
The elements form a cylindrical wall behind which there are baffles. The elements transmit from their front surface only, so elements on the far side of the array will not radiate on the near side of the array.

1b. I do not have radiation pattern of 'Twin Transducer' but most probably it will have cosine shape beam pattern due its shape.
Are the pairs driven differentially as a dipole? How do you know which pair is a pair? I notice the rings of elements are staggered = feathered, probably to reduce side-lobes.
If a ring is driven in phase, then because the 6 elements in each column are staggered, each alternate column will be connected in reverse.

nauman
I assume you mean the “front face”.
Yes, You are right.
The elements form a cylindrical wall behind which there are baffles. The elements transmit from their front surface only, so elements on the far side of the array will not radiate on the near side of the array.
Ok, You are right.
Are the pairs driven differentially as a dipole? How do you know which pair is a pair? I notice the rings of elements are staggered = feathered, probably to reduce side-lobes.
If a ring is driven in phase, then because the 6 elements in each column are staggered, each alternate column will be connected in reverse.
What i know for sure about this array is that it has total of 96 channels (96 Twin Transducers) each driven with separate Power Amplifier (i.e. total of 96 Power Amplifiers). Furthermore, there are 32 vertical staves arranged in a 1m dia circle with 03 Twin Transducers in each vertical stave as highlighted in the figure in my previous post also.

#### Attachments

It appears that a twin transducer is a two square dipole, one above the other, in the same stave.

The individual vertically staggered staves of six elements, will appear to be seven continuous rings formed about the vertical axis. Each ring will radiate an amplitude of A = ai·sin(t);
The coefficients ai for the rings will be [ +½, –1, +1, –1, +1, –1, +½ }
The top and bottom rings radiate half the power since those rings are half populated.
The negative sign gives a 180° phase reversal.

Without phase control to synthesise a beam, the radiation pattern will be symmetrical about the vertical axis. The signal wavelength, ring separation = transducer pitch, and ring diameter = 1m, will determine the angle of the main lobes in the conical pattern. (Depending on depth, there may also be a reflection from the water surface).

To find the beam pattern when all transducers are driven synchronously, you will need to integrate the radiation from all parts of the near side, of 7 rings, over an arc with a fixed azimuth. That will include, or be multiplied by the two dimensional cosine response of the individual dipole transducers.

nauman
Without phase control to synthesise a beam, the radiation pattern will be symmetrical about the vertical axis. The signal wavelength, ring separation = transducer pitch, and ring diameter = 1m, will determine the angle of the main lobes in the conical pattern. (Depending on depth, there may also be a reflection from the water surface).
Should i include Array Factor/Gain in SL calculations if i drive all 96 transducers simultaneously (without any phase control) in Omni Directional Transmission Mode?

Gold Member
Summary:: Calculations of Source Level of Cylindrical Array of multiple transducers with each transducer with known Transmit Voltage Response 'TVR'

Hi all

I am trying to calculate Source Level 'SL' of a underwater acoustic Cylindrical Array with multiple Transducers. The array has 03 Rings with 32 transducers in each Ring. The spacing between each ring is around 0.18m whereas Dia of each Ring is about 1m. Each transducer is being driven with separate Power Amplifier.
What i know about SL of individual transducer is that if we apply Vrms to a transducer having a 'TVR' of X dB, transducer SL will be calculated as:

SL = 20LOG10(Vrms)+X dB

On the basis of this SL calculations, I want to know how can we calculate 'SL' of complete cylindrical array (32x3 elements) in 'Omni Directional' Mode if we know TVR and Vrms applied to each Transducer? Here 'Omni Directional' means same level of transmission in all directions simultaneously.

Thanks
For a circular mode, the array is going to produce a circularly symmetric beam, so we need only consider the vertical plane directivity. This will be controlled by the pattern of a vertical stack of four transducers (not three due to the staggering I think). We then find the directive gain from D=vertical beamwidth of one transducer/vertical beamwidth of a stack of four. Here we define beamwidth to the half power points. This will be the directive gain relative to one transducer.

You might wonder about the transmitter power being shared among transducers. In the circular mode, a distant receiver obtains power from many transducers, but the transmitter power is shared among the same number, so there is no net gain.
Regarding the number of transducers being usefuly employed for one direction, let's assume for discussion that this will be a third of the stacks. As a simplified model, let's assume that the transmitter power will be shared between the three sectors, giving a loss of 3 times, but each sector is displaying directivity of 3 in the horizontal plane, so there is no overall effect caused by the number of transducers working for us in a particular direction.

I have assumed that we are receiving at a distant location; if close to the array we will find that the beam is initially cylindrical, before splaying out to the calculated beamwidth in the vertical plane.

Gold Member
In short, it looks as if the directive gain is the array factor of a stack of 4 vertical transducers, which will likely be 4 in power terms, or 2 in SPL terms.

Gold Member
If we look at the unidirectional mode, here the transducers are phased to produce a single beam. From the point of view of a distant receiver, we might expect to obtain most of our signal from a quarter of the transducers. This is because those not pointing directly at us will have less radiation in our direction. If they have a cosine pattern, then at 45 degrees they will radiate 0.7 of the field, or half power.
As there are 32 stacks of transducers, we now expect our received field to be the sum of 8 stacks. This gives a power increase of 8^2 = 64. However, the transmitter is sharing power to 8 stacks, so the directive gain is 64/8 = 8 in power terms, or SQRT 8 in terms of SPL = 2.8.
This directive gain in the horizontal plane is now multiplied by the directive gain of one stack in the vertical plane, which as discussed earlier might be 4. So the directive gain in total is 4 x 8 = 32 in power terms or SQRT 32 = 5.6 in terms of SPL.

nauman
In short, it looks as if the directive gain is the array factor of a stack of 4 vertical transducers, which will likely be 4 in power terms, or 2 in SPL terms.
Thanks for reply. Accordingly, the net SL of cylindrical array in far field in 'ODT' Mode will be:

SL = 20LOG10(Vrms)+X dB+20LOG10(4 or 3) where 4 or 3 be no of Twin Transducers in vertical stave

As we know for this typical array,

X (TVR of twin transducer) = 144 dB
Vrms (Voltage across each Twin-Transducer) = 200 Vrms

The net SL of array in 'ODT' Mode will be = 46 dB + 144 dB + 12 dB = 202 dB

However, the problem is that SL claimed for this array in 'ODT' Mode is 217 dB. This 'confusion' was the reason this post was created in first place.

The array has 03 Rings with 32 transducers in each Ring. The spacing between each ring is around 0.18m whereas Dia of each Ring is about 1m.
We need to stop talking of three rings since each ring is made from twin transducers, with one above the other. That makes 6 rings of transducers. Since the transducers are staggered by half of a twin, that makes 7 rings with the top and bottom rings being half-populated.

Next we look at the square transducers and try to find out what their dimensions are. The 0.18m separation suggests the transducers are 0.09 m = 90 mm apart.
32 transducers are spaced around a 1 m diameter cylinder. Circumference = 3.1416 m
3.1416 m / 32 transducers = 0.098 m = 98 mm.
There is a disagreement of the dimensions, so the dimensions are wrong, or the transducers are not square.

The horizontal radiation will be zero since all twin transducers cancel with their twin. The vertical radiation is zero since the elements have a cosine radiation pattern.

Speed of sound in water is 1480 m/s;
Frequency range 6 kHz to 9 kHz. Mean frequency = 7.35 kHz.
Wavelength in water is; 1480 / 7350 = 201.4 mm.

At what angle will the main lobe lie? Vertical separation of same phase transducers is 198.0 mm, wavelength = 201.4 mm. There lies a problem. The main lobe will be very close to vertical, almost totally defeated by the cosine response.

nauman
We need to stop talking of three rings since each ring is made from twin transducers, with one above the other. That makes 6 rings of transducers. Since the transducers are staggered by half of a twin, that makes 7 rings with the top and bottom rings being half-populated.

Next we look at the square transducers and try to find out what their dimensions are. The 0.18m separation suggests the transducers are 0.09 m = 90 mm apart.
32 transducers are spaced around a 1 m diameter cylinder. Circumference = 3.1416 m
3.1416 m / 32 transducers = 0.098 m = 98 mm.
There is a disagreement of the dimensions, so the dimensions are wrong, or the transducers are not square.
I think i could not explain the 'Twin Transducer' properly. I have attached another photo of 'Twin Transducer' for further clarification. It is for certain that each 'Twin Transducer' have common cable which indicates that both units in 'Twin Transducer' are internally connected some how. In my opinion, when we apply common voltage signal to both units of 'Twin Transducer', a cosine beampattern will be formed of a 'Twin Transducer' so we should consider 'Twin Transducer' as single transducer from cylindrical carray point of view.

The single block appearing above and below alternately in each 'stave' as shown in 'Cylindrical Array4.jpg' in my previous post is not a transducer and is acting only as spacer.
The 1m dia is only approximate and can vary few cms.

#### Attachments

The twin_transducer.jpg in post #8 shows the twin ceramic squares with the cut corners.
Please provide a web link to the device you are attempting to interpret and describe.
Without accurate information I am wasting my time.

nauman
Please provide a web link to the device you are attempting to interpret and describe.
Sorry, it is a customized transducer and i could not find this type of transducer on internet, otherwise i would have shared its data sheet in my first post. 