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Investigation and Numerical Simulation of the Acoustic Target Strength of the Underwater Submarine Vehicle

School of Electronics Engineering, Vellore Institute of Technology, Vellore 632014, India
School of Electrical and Electronics Engineering, SASTRA University, Thanjavur 613401, India
Faculty of Engineering and Architecture, Kore University of Enna, 94100 Enna, Italy
Authors to whom correspondence should be addressed.
Inventions 2022, 7(4), 111;
Received: 13 November 2022 / Revised: 28 November 2022 / Accepted: 29 November 2022 / Published: 1 December 2022
(This article belongs to the Collection Feature Innovation Papers)


Modern weapon systems’ survival hinges on their detection capabilities more than anything else. In the active sonar equation, the acoustic target strength is crucial. Under the assumption of plane wave propagation, the standard target strength equation is used to forecast the reradiated intensity for the far field. The ability of a submarine to remain unnoticed while on patrol or accomplishing a mission is its primary defense. Sonar, sometimes known as sound navigation ranging, is a popular method for locating submarines. This is because saltwater effectively absorbs radio frequencies. Sonar technology is used in more than just the commercial fishing business; it is also used in undersea research. The submarine’s designers consider the reflection of acoustic waves to minimize the amount of space required for such reflections. The Target Strength (TS) metric is used to assess the sonar objects’ size. This manuscript explains and demystifies the Benchmark Target Echo Strength Simulation (BeTTSi) benchmark submarine’s TS analysis. This model’s Pressure Acoustic-Boundary Element Model (PA-BEM) interface has been stabilized, and the model itself is pretty huge acoustically.

1. Introduction

Over the last several decades, acoustic dispersion from submerged objects has been the focus of research and inquiry by many acoustics professionals. Only basic geometrical designs were necessary to provide analytical answers to the issues provided by underwater acoustics [1]. Scientists in the fishing sector used empirical methods, which are approaches based on experience rather than a theory [2]. Furthermore, numerical methods are gaining popularity all the time. In addition to traditional finite element approaches, more complex computational methodologies are being developed to address acoustic issues. For example, the underwater acoustics problem was addressed and solved using the point interpolation approach and the smoothed finite element method [3,4,5,6,7].
However, because the frequency range in which these numerical approaches can be used is limited, they are categorized as middle-frequency techniques. On the other hand, high-frequency techniques include, geometrical acoustics, physical acoustics, and a range of other related areas. Planar elements are based on the Kirchhoff approximation, which demands that a scattering item’s dimensions be much greater than the acoustic wavelength [8]. This approximation serves as the basis for the planar element, which is a valuable solution for resolving acoustic difficulties at relatively high frequencies.
Without underwater acoustics, a submarine cannot utilize its stealthy acoustic strategy, as these make detecting and locating a submarine’s location feasible. The working frequency of underwater sonar detection equipment has decreased into the lower frequency domain, increasing the stealth performance requirements for submarines, and this is owing to the rapid development of sonar detection technologies for use underwater [9,10,11,12]. Determining the target size allows for a partial evaluation of the stealth effectiveness of a Submarine Target Strength (STS). Researching the Target Strength (TS) of a generic submarine model and analyzing the results revealed that item geometries and structures significantly impact the TS. Because the rudder substantially affects the submarine’s TS, it is an essential component of the vessel [13]. The hydrodynamic performance of a rudder is a primary element in its design. When evaluating the capabilities of modern underwater sonar-detecting technology, it is vital to consider the stealth capability of the rudder. Song utilized the Finite Element Method (FEM) to investigate how different materials affect the STS of the rudder. He discovered that the FEM had sufficient precision for relatively low frequencies [14]. In addition, the rudder’s shell’s thickness and its profile’s aspect ratio play significant roles in the rudder’s overall structure. Therefore, the design of the rudder can be enhanced by gaining a deeper comprehension of the dynamic relationship between TS and these two factors. These TS-influencing properties of the rudder have never been subjected to a thorough analysis [15,16,17,18].
The primary advantage of employing a submarine for military objectives is the crew’s ability to remain undiscovered. Submarines were developed in response to the need to lower their optical (visible) footprint considerably. On the other hand, other indicators critical to submarine detection were swiftly discovered. Because of the ease with which sound travels through water, it is possible to detect the presence of submarines using only sound under normal diving conditions.
Passive sonars have been the tool of choice for most detection efforts during the last few decades [19]. They are able to pinpoint the source of the submarine’s sonic emissions, and, as a result, tremendous effort was expended to successfully restrict the quantity of radiated acoustic noise created by the submarines. Many navies use active detection sonars because passive sonars have trouble identifying more advanced submarines. Because active sonar detection is critical, the submarine’s tendency to reflect incoming acoustic energy Target Echo Strength (TES) must be reduced to a minimum. This is due to the requirement for active sonar detection [20,21,22].
Not only are procedures for operating submarines constantly updated and improved, but so are the systems for operating sonar. The ever-increasing computing power of computers has dramatically aided sonar technology, resulting in more geometrically exact beams and more complicated data processing procedures [23]. A potential signal-processing method can benefit from the data-synthesis capabilities of a bi- or multi-static network. The fact that this approach has been successfully demonstrated means that the ranges at which a modern submarine may be detected will soon grow dramatically. Submarines must employ TES reduction technologies to maintain their current tactical advantage in the future [24].
Sound transmission in water at distances is characterized by refraction through varying sound speeds with depth (due to temperature, density, and salinity fluctuation) and reflection at water boundaries, as seen in undersea sonar applications.
As a result, sound waves striking a submarine cannot approach from a perfectly horizontal position. More than reducing the TES of a submarine will be required; instead, the TES will need to be dropped across a range of elevation angles. This angular range, also known as the threat sector, is calculated to conduct research on the acoustic propagation of sounds over various sections of the world’s oceans. We then compare a standard submarine design to a derivative submarine with a shape optimized for TES [25].
The primary way a submarine defends itself while at work is by maintaining its cover story. Because of the significant amount of radio signal absorbed by seawater, one of the primary methods used for submarine detection is sonar, which stands for sound navigation ranging. While building submarines, engineers consider how acoustic waves are reflected to determine how to minimize the effective area of the sub’s reflecting surface. The target strength metric is used to determine the size of a sonar target. Most submarines cover their outside surfaces with absorbent materials to reduce the effect of backscatter signals. Figure 1 depicts the COMSOL Simulation model of the proposed acoustic target strength.
The main contribution of the manuscript is highlighted as follows:
  • Implementation of acoustic target strength for underwater submarine vehicles;
  • Comparison of target strength in different acoustic pressure conditions;
  • Analysis of the scattered acoustic sound pressure levels;
  • Examination of the radiation pattern in both polar plot and line graph;
  • Recommendation of appropriate scattered acoustic sound pressure levels for underwater networks based on the targeted performance metric.
The remaining sections of this work will be structured as follows. In Section 2, we discuss the theoretical definition of a model. In Section 3, we provide the design model and methodology. In Section 4, we provide our findings, comparison, and discussion of the obtained findings, and in Section 5, we conclude the paper.

2. Theoretical Definition of a Proposed Model

The Background Pressure Field is utilized to simulate a spherical wave approaching the submarine’s bow from 1000 m away and at an angle of phi equal to 360 degrees. When the waves reach the submarine, they already possess the characteristics of plane waves, which is typical for the region. The ocean attenuation material represents the transmission medium’s intrinsic losses throughout the modeling process. The parameters of this attenuation model are derived from a vast amount of experimental data, giving it a semi-analytical quality. In addition to the role performed by depth, temperature, salinity (in the real world), and pH, additional elements, such as viscosity effects in pure water, the relaxing processes of boric acid, and magnesium sulfate, to name a few, also have an effect. Select the Absorption coefficient option within the Impedance border condition to indicate the presence of a soft material placed on one of the hard surfaces. Figure 2 shows the simulation’s zoomed-out view of the target’s vitality and sweeping angle.
During the modelling phase, a boundary element interface is used to build a model:
In the second stage, we assign geometry and global definitions to the model builder;
The third step is to configure the pressure acoustics and boundary elements to the model and run simulations of possible model configurations.
In fourth place, we have a comparison of the results of various valuations of the performance metrics;
The last stage is collection of the analysis and explanation of the results.
Target strength was calculated using the Helmholtz–Kirchhoff Integral [26,27] and the finite element technique (FEM) for the acoustic–solid coupled model. Target strength is defined by measuring the incident and reflection intensity ratio, and the reference distance is “1 m” in front of the target’s reflection center [28,29,30].
Simple acoustic fields can be obtained using the wave equation and the Helmholtz equation, but a more complex geometrical model, considering underwater habitats’ boundary conditions, is required to obtain the proper underwater setting [31,32,33]. This work uses the finite element method (FEM) in conjunction with the governing equation in acoustic–solid connected modules to solve this complicated computation [34,35,36].

3. Design Model and Methodology

We used COMSOL Multiphysics, version 5.6, in this investigation to simulate the target strength computation. The parameters for performing the simulation are detailed below. Variables evaluated were the target model, vehicle shape, hull thickness, frequency, and sweeping angles of incident acoustic waves. The submarine geometry of BeTSSi is shown in Figure 3.
When measured concerning the wavelength, the dimensions of this model are unacceptably large. Stabilized formulation is used for boundary elements in the physical theory of pressure acoustics. If this way is followed, there is a 100% chance that the iterative solver will converge. When the excitation frequency approaches 800 Hz without remaining stable, iterative solutions call for a significant increase in the number of iterations they perform.
Submarines use an anechoic coating on their hulls to reduce signal scatter. It is possible to make this absorption coefficient dependent on the measurement frequency; in that case, it will use the value specified by the alpha n parameter. It is expected that 40 gigabytes of random access memory (RAM) will be required for the analysis, and it will take around 30 min to finish. Because COMSOL relies on virtual memory, the time required to complete a task will lengthen if insufficient RAM is available.

4. Results and Discussion

Target strength (TS) is a critical component in underwater stealth systems. Several studies focus on weakening the target to limit the likelihood of detection. However, the objective strength can be influenced by various factors, including the vehicle’s geometries and structures, sonic reflection coefficients, and the material utilized for the outer hull coating, to name a few. We present the results of a calculation of target strength concerning the geometry of the vehicle, the thickness of the hull, and the frequency of acoustic waves incident upon the vehicle in this inquiry. The most challenging component is the demand for enormous amounts of memory and rapid calculation due to the size of the vehicle and the high frequency of the incident acoustic waves. To address this issue, we included a scaling mechanism for the vehicle, which minimizes the model’s overall size. In addition, we have increased our computer’s capability to improve the accuracy of our calculations. The target strength (TS) is estimated using an acoustic–solid coupled model and the finite element technique (FEM). According to the findings, the personified area and, hence, the TS develops in proportion to the model’s size. Greater thickness hulls can be predicted to have a higher TS. Finally, the frequency would impact TS due to the activation of individual auditory modes.
Figure 4 illustrates the total acoustic pressure at the underwater surface areas. Take note of the virtually flat pressure waves and the fact that the “dark” side of the source has far lower acoustic pressure. This is a highly comprehensive acoustical model, as seen by the staggering amount of wavelengths that have been considered.
Figure 5 illustrates the radiation pattern that would be observed at a distance of one hundred meters from the submarine. To illustrate this, an arrow has been drawn in the general direction that the sound will move. It is important to note that the scattered signal at this frequency has intricate lobes and is extremely position-dependent.
Figure 6 shows a cross-sectional image of distributed acoustic pressure through the midsection of the submarine. Figure 7 depicts a plot demonstrating the dispersed sound pressure level in the region as another way of presenting the data.
The target strength (TS) is computed by the following Equation (1):
T S = 20   log 10 [ P s P i n d l i s t 1 m ]
where P s is the scattered pressure at the listening point, P i n is the background pressure at the submarine and d l i s t is the distance from the submarine to the listening point. We have used d_source in the simulation of the COMSOL tool as the distance to the listening point, and this equation has been modified in the variable definition.
Figure 7 shows the sound pressure level polar plot around the submarine; that is, the radiation pattern. Note the peaks right below the submarine and at the reflection angle from the source. Sound pressure levels and the resulting radiation pattern surrounding the submarine are seen in Figure 8 below. Take heed of the peaks directly below the submarine and at the reflection angle from the source. Sonar equipment can operate in either an active or passive mode. The distinction between active and passive sonar is that active sonar employs an active source to generate an acoustic signal that is subsequently reflected on the submarine. In contrast, passive sonar includes the sensor reflecting the sound emitted by the submarine while it operates. Active sonar can be utilized in monostatic (source and listening point in the exact location) and bistatic (source and listening point in distinct locations) configurations in the COMSOL acoustic simulation model. The goal strength for a bistatic system is represented in Figure 9.

5. Conclusions

We compared the target strength over three different vehicle geometry magnifications, three different hull thicknesses, the standard acoustic impedance, and a variety of incident acoustic wave frequencies and sweeping angles as part of this research. We also examined the frequency and angle of arrival of the sound waves. To represent the findings of the far-field computation, which relied on the Hamz–Kisshoff integral theory, we used COMSOL Multiphysics, a finite-element analysis program. According to the findings, altering the characteristic acoustic impedance was a critical component of stealth technology. The intensity of the target can be substantially reduced by adding the coating. If the undersea vehicle is more prominent in size, more force will be applied to the target. If the sonar system works at a higher frequency, it is more likely to be noticed. As a result, the anti-high-frequency shielding will be incorporated into the ship’s design for the underwater vehicle.

Author Contributions

K.S.: Conceptualization, Data curation, Formal Analysis, Methodology, Software, Writing—original draft; R.A.: Visualization, Investigation, Formal Analysis, Software; R.C.V.: Supervision, Writing—review & editing, Project administration, Visualization; F.A.: Supervision, Project administration, Visualization; G.P.: Data Curation, Investigation, Resources, Software, Writing—original draft, Methodology. All authors have read and agreed to the published version of the manuscript.


This research received no external funding.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data will be made available on request.

Conflicts of Interest

The authors declare no conflict of interest.


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Figure 1. COMSOL Simulation model of proposed acoustic target strength.
Figure 1. COMSOL Simulation model of proposed acoustic target strength.
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Figure 2. The simulation’s zoomed-out view of the target’s vitality and its sweeping angle.
Figure 2. The simulation’s zoomed-out view of the target’s vitality and its sweeping angle.
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Figure 3. Submarine geometry of BeTTSi.
Figure 3. Submarine geometry of BeTTSi.
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Figure 4. The total acoustic pressure that was measured at the submarine.
Figure 4. The total acoustic pressure that was measured at the submarine.
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Figure 5. The pattern of radiation one hundred meters distant from the submarine.
Figure 5. The pattern of radiation one hundred meters distant from the submarine.
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Figure 6. Cross-section of the distributed acoustic pressure.
Figure 6. Cross-section of the distributed acoustic pressure.
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Figure 7. A cross-section at the level of scattered sound pressure.
Figure 7. A cross-section at the level of scattered sound pressure.
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Figure 8. The polar plot of the sound pressure.
Figure 8. The polar plot of the sound pressure.
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Figure 9. The static target strength of the submarine from a bistatic perspective for a receiver that is located at the same distance as the source.
Figure 9. The static target strength of the submarine from a bistatic perspective for a receiver that is located at the same distance as the source.
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Sathish, K.; Anbazhagan, R.; Venkata, R.C.; Arena, F.; Pau, G. Investigation and Numerical Simulation of the Acoustic Target Strength of the Underwater Submarine Vehicle. Inventions 2022, 7, 111.

AMA Style

Sathish K, Anbazhagan R, Venkata RC, Arena F, Pau G. Investigation and Numerical Simulation of the Acoustic Target Strength of the Underwater Submarine Vehicle. Inventions. 2022; 7(4):111.

Chicago/Turabian Style

Sathish, Kaveripakam, Rajesh Anbazhagan, Ravikumar Chinthaginjala Venkata, Fabio Arena, and Giovanni Pau. 2022. "Investigation and Numerical Simulation of the Acoustic Target Strength of the Underwater Submarine Vehicle" Inventions 7, no. 4: 111.

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