PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

An underwater vehicle shape with reduced acoustic backscatter
Tom AVSIC
thyssenkrupp Marine Systems GmbH, Germany

ABSTRACTIn some underwater applications, acoustic backscatter might have undesired consequences, such as
interferences in underwater communications or echoes in the sonar image. Acoustic backscatter of anunderwater object is classically reduced by applying appropriate absorbing materials on the surface.
Absorbing materials convert the acoustic energy into heat and their thickness is usually on the order of aquarter wavelength. In some cases, the application of absorbing materials might have unacceptabledrawbacks on other design criteria. For long-distance acoustic propagation (by way of the acoustic channel
propagation,) it can be shown that undisturbed sound travels nearly horizontally within a limited verticalangle of no more than ± 20° from the horizontal plane. Hence, for long-distance applications, the acoustic
backscatter can be reduced by proper shaping of the vehicle’s lateral outer hull. In case the outer hull is not
opaque enough to shield the vehicle’s inner structures (with potentially high backscatter risk), reflective
material can be applied. The working mechanism of reflecting materials is the impedance mismatch andhence, reflecting materials can be much thinner than absorbing materials. This conference contribution willaddress the worldwide sound spreading in the ocean and show the guidelines for a geometric outer hull
shaping.
Keywords: underwater sound propagation, target strength, scattering

1. INTRODUCTION
During the last decades, considerable effort has been made to reduce the radiated acoustic noise ofsubmarines – especially of the diesel-electric types. Such ultra-quiet submarines are difficult to detectby passive sonars alone; therefore, new multi-static active sonar techniques were developed which
dramatically increased the acoustic detection ranges of the nowadays submarines. This technologicaldevelopment motivates the reduction of the target echo strength (TES) for new ly built submarines. A
technique to reduce the backscattering towards the sonar system is based on specular reflection. The
idea for this technique is known now for nearly 100 years (3). Later on, the technique was adopted toreduce the radar cross-section and is often called the stealth technique.
Although this technique is successfully used for radar cross-section (RCS) reduction, it was neverused consequently on an underwater vehicle to reduce its target echo strength (sonar cross-section).
The question arises: why this technique is used for RCS reduction but not for TES reduction. Is thistechnique possibly inappropriate for TES reduction?
This TES reduction technique involves three interacting domains, which need to be considered inan overall concept. These are: the sonar system, the sound propagation and the reflectivity of thesubmarine. The sonar signal is transmitted by a sonar system – most often directed into a certain spatial
direction or domain. The sound propagation through the sea determines the signal paths and thepotentially disturbing reflections from the sea surface and the sea floor. The submarine itself willreflect and/or scatter the sonar signal, which has to travel again through the sea to arrive at a sonar
system where it could be detected.
The first part of the paper is a general analysis of worldwide sound propagation in the sea anddetermines the long distance angular propagation sector of the sonar signal. The second part calculates
the reflection of different geometrical shapes for the previously derived long distan ce angularpropagation sector. Hence, appropriate design criteria can be derived for a TES reducing shape. Finally,
the TES of a classical shaped submarine (with and without anechoic material) is compared to a stealthshaped submarine.

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2. Vertical propagation sector
The sound speed in the ocean is not homogeneous. Compared to the vertical variations, thehorizontal variations are usually small. The vertical sound speed variations have a strong impact on thelong distance sound propagation. Increasing hydrostatic pressure with depth yields an increasing
sound speed with depth and warm water masses near the sea surface increases the sound speed near thesea surface. Hence, a sound speed minimum is found at a certain depth, which is, for tropical andsubtropical climate zones, usually at about 1000 m. In temperate climate zones, this minimum is at alower depth (50 m – 200 m). For polar and subpolar zones, it is usually at the sea surface, due to thelack of warm water masses at the surface on account of the frigid conditions.
The acoustic waves are refracted towards waters with lower sound speed, i.e. towards the depth ofthe minimum sound speed. They overshoot this depth and subsequently, they are again refracted
towards the minimum. The sound is trapped within the sound channel axis and it can travel over very
long distances without coming in contact by the sea surface or the sea floor. This is important, because
every contact with the sea surface or sea floor will reduce the acoustic signal in to the propagation
direction. Consequently, the undisturbed sound propagates within a certain vertical angular range,depending on the sound speed profile.
A basic worldwide sound propagation study has been conducted to determine the range in elevation
angle of long distance sound propagation. The example of the sound propagation in the Ionian Sea (apart of the Mediterranean Sea) is used to explain the procedure. During the summer, a relatively
shallow but very distinct sonar channel is formed, with its axes at about 150 m depth. Due to therefraction of the sound by the inhomogeneous sound speed profile, sound generated by an acoustic
source can travel at multiple but distinct paths to the target. If the ray-tracing method is used tosimulate the sound propagation, these paths are named eigenrays. The eigenrays between the soundsource (sonar) and the target (submarine) - both at 150 m depth - have been computed over thehorizontal distance of up to 120 km (e.g. Figure 1 shows the eigenrays for a horizontal distance of 20
km together with the corresponding elevation angles at the sound source and the submarine ). In the left
panel of the Figure 2, these elevation angles at the submarine are plotted as dots with respect to thehorizontal distance (up to 120 km). The arrival angles of the undisturbed rays are marked with red dots,
the rays with surface reflections are marked with cyan dots and the rays, which also experience bottom
reflections, are marked with blue dots. With every bottom or surface reflection, the blue color is fadedout a bit, to emphasis that with every reflection the sound signal weakens in intensity. The distributionof vertical incident angles of all eigenrays (including surface-reflected but excluding
bottom-reflected), was generated to highlight the propagation sector. For this sound speed profile, theeigenrays impinge onto the submarine within a vertical angle of about ±17°. It is this maximal verticalangle, which defines the vertical propagation sector for this particular region. Including thesurface-reflected but excluding the bottom-reflected rays highlights the fact that the surface reflectedrays often could be used for sonar detection, however the bottom reflected usually not.

Figure 1 – Left: Eigenrays for the Ionian Sea summer profile. Sound source and submarine are both at 150 m
depth and with a horizontal distance of 20 km. Right: Table with the corresponding elevation angles at thesound source and the target (submarine).

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Figure 2 – Vertical incident angle of eigenrays vs. distance (left) and the corresponding distribution of all rays
without any bottom reflections (right). The eigenrays are color coded as red: undisturbed, cyan: surface
reflected, blue: bottom/bottom-surface reflected.

Figure 3 – Worldwide vertical propagation sector
The maximal vertical propagation angle is calculated worldwide on a 5° x 5°
latitude-longitude-grid and displayed in Figure 3. From this figure it can be deduced, that the verticalpropagation sector is not more than ±20°, no matter where in the World Ocean the submarine isoperating. The reverse conclusion is that if the sonar signal is reflected away from the verticalpropagation sector, the scattered signal will not arrive at the sonar system and hence the submarine will
most likely not be detected. If a stealth shape is used to reduce the TES of an underwater vehicle, theshape then has to ensure, that the sonar signal is reflected in a vertical direction either above +20° or
below -20°.
2.1 Eigenray interaction
The sound propagation in the ocean is in general a multipath propagation. Sound transmitted froman acoustic source can reach the submarine via multiple paths. The submarine does not reflect the1937impinging sound in one direction only, but scatters the sound effectively into all directions. The
scattering is not uniform over the possible directions; however, a significant TES contribution may
occur from sound coming from path A and being scattered into path B.
As an example, we could look more closely at the two eigenrays with two turning points in Figure
1 (Ray ID -2 and +2). The first impinges onto the target at a vertical aspect angle of -4.1°, the second
at an angle of +4.1°. Because of the reciprocity of the eigenrays, the eigenrays for the sound travelingfrom the sonar to the target are the same as for the sound travelling back from the target to the sonar. A
large vertical plate as a target would have a small TES for the two aspect angles ±4.1°; however the
specular reflection would bounce the energy from the -4.1°-ray into the +4.1°-ray and vice versa.
Subsequently the plate would have an even higher TES as would be the case for a single ray having
normal incidence. This phenomenon can be denoted as eigenray interaction.
To describe the eigenray interaction mathematically, we start at the sonar equation for the receiving
level (RL) in dB:
RL = SL + TL + TES + TL
where SL is source level and TL the transmission loss (propagation loss). The received acousticpressure (in linear scale) for the acoustic ray i (ray path reciprocity) is:
𝑝𝑖𝑅𝑥 = 𝑝𝑇𝑥 ∙ 𝑡𝑙𝑖 ∙ 𝑡𝑒𝑠𝑖𝑖 ∙ 𝑡𝑙𝑖
And the received acoustic pressure for the incident acoustic ray path i and the reflected acoustic raypath j is:𝑅𝑥
𝑝𝑖𝑗= 𝑝𝑇𝑥 ∙ 𝑡𝑙𝑖 ∙ 𝑡𝑒𝑠𝑖𝑗 ∙ 𝑡𝑙𝑗
The received acoustic pressure for all combinations of acoustic rays i and j can be written using
vector and matrix formalism:
𝑡𝑙 = [𝑡𝑙1 𝑡𝑙2 𝑡𝑙3 ⋯ 𝑡𝑙𝑁 ]
𝑝

𝑅𝑥

= 𝑝

𝑇𝑥

𝑡𝑒𝑠11
∙ 𝑡𝑙 ∙ [ ⋮
𝑡𝑒𝑠𝑁1

⋯
⋱
⋯

𝑡𝑒𝑠1𝑁
⋮ ] ∙ 𝑡𝑙 𝑇
𝑡𝑒𝑠𝑁𝑁

The tl i and tes ij values must be complex valued to account for travel-time variations (between the
different ray paths) and the correct phase changes of reflections (e.g. the water-surface reflections
reflect the phase of the signal).
To deduce the reflectivity levels within the ray interaction matrices (𝑡𝑒𝑠𝑖𝑖 ) , multipath TES
combinations were calculated for the vertical incident and reflected angles ranging from -20° to +20°.
Results for four different geometrical shapes with identical cross section area of 30m×6m (namely thecylinder, flat plate, corner backside and foreside) are shown in Figure 4. The dots in the center of eachpanel mark the positions where to pick-up the 𝑡𝑒𝑠𝑖𝑖 levels of the ray interaction matrix whichcorrespond to the eigenrays shown in Figure 1. The energetic (incoherent) mean of the 𝑡𝑒𝑠𝑖𝑖 levels is
indicated by a line in the color bars. The cylinder has a remarkably uniform scattering of the acoustic
intensity over the entire vertical angular sector (note the uniform color over the entire panel in the
Figure). Besides the normal incidence case (0°, 0°), the flat plate shows high bi-static TES levels at the
specular reflection axis (from the lower right corner to the upper left) whereas the foreside of thecorner reflector show very high monostatic TES levels (from the lower left to the upper right corner).
The backside of the corner reflector (roof shape) has comparably low TES levels over the entire
angular range considered.
The concept of eigenray interaction is used to ensure that the TES reduction efforts on a submarine
covers the entire vertical propagation angle. It enables one to combine the sound propagation effects
with the scattering characteristic of the submarine (or more generally that of an arbitrary acoustic
target). This is especially important in oceanographic regions where the sound propagation ischaracterized by a wide angular (vertical) spread.
An inclined flat surface is able to reflect the sonar signal away from the vertical propagation sector,
if its inclination from the vertical is sufficiently high (more than ~30°). In addition, its dimensions
have to act as a reflector and not as an acoustic scatterer.

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2.2 Hydroacoustic materials for TES reduction
Hydro-acoustic materials can be used as coating materials to reduce the TES of a submarine. Most
self-evident is simply to cover the outer hull with an echo reduction material. However, echo reduction
materials for low sonar frequencies are very thick, bulky and often heavy. TES reduction can also be
obtained with transmission loss (TL) materials. In case there is an object with high TES behind asemi-transparent surface with low TES, then coating the semi-transparent surface with a TL material
leads to shadow/shield the object with the high TES (1).
The TL material is relatively thin and at the same time suitable also for very low sonar frequencies.
It achieves 10 dB transmission loss up to 150 m diving depth, while the thickness is less than 20 mm.
The nearly neutral buoyancy for seawater may allow an implementat ion on existing submarines.
The echo reduction (ER) material can be used on large surfaces with high reflectivity. This is in
general at the pressure hull, which is not semi-transparent but fully reflecting and also at the sail (if its
sides have nearly vertical orientation). However, for low frequencies the required material thickness is
unfortunately high. A thickness comparable to a quarter of (the sonar signal) wavelength is usuallyused for absorbing materials. For 1 kHz, this results in an absorber thickness of 375 mm.

Figure 4: Multi-static TES combinations for vertical incidence angles and vertical reflected angles ranging
from -20° to +20° respectively. Results for four different geometrical shapes with identical cross section areaof 30m×6m are shown (namely the cylinder, flat plate, corner backside and foreside). The dots mark thepositions where to pick-up the 𝒕𝒆𝒔𝒊𝒊 levels of the ray interaction matrix for the eigenrays shown in Figure 1.
The energetic (incoherent) mean of the 𝒕𝒆𝒔𝒊𝒊 levels is indicated by a line in the color bars. Sonar signal: asweep in frequency from 2.7 kHz to 3.3 kHz

3. TES of a classical submarine
Often, the TES calculations assume fully reflecting objects, i.e. reflection coefficients of unity.
However, a submarine’s outer hull is not completely reflecting and numerous scattering objects ofdifferent sizes and shapes can be found beneath the hydrodynamic casing. Hence, it is not adequate toconsider solely the outer hull for the entire TES calculation.

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The TES calculation and TES reduction techniques are emphasized on a geometrical model
submarine named BeTSSi (2) (Figure 5). BeTSSi has features of a modern submarine without sharing
specific similarities with any particular submarine class. That makes it an ideal neutral candidate to
study TES behaviour and reduction. BeTSSi’s overall model-length is 62 meters and themodel-diameter of the pressure hull is 7 meters. The casings of the bow, upper deck, sail and stern aremodelled as 10 mm steel. These areas are modeled with flooded sea-water. That means that themedium in front and behind the steel casing is seawater. In such conditions, a 10mm steel plate isnearly transparent for low sonar frequencies. Obviously the objects lying within the flooded areas,such as the bulkheads, torpedo tubes, masts and tanks, become important for any accurate TES
calculation. The arrangement of the bulkheads forms several significant corner reflectors, which inturn increases the resulting TES over a wide angular range.

Figure 5: The fictive geometrical submarine “BeTSSi” used for exemplary TES calculations.
We assume an active sonar source with a transmitting frequency of 1 kHz and 3 kHz. The TES of
the uncoated submarine is shown as the blue curves in Figure 6. The overall TES value is somewhere
between 10 dB and 25 dB. Several sharp peaks/highlights of high TES are present: The bow peak (at 0° aspect angle) arises from the bulkheads of the ballast tanks in the bow
 The beam peaks (at 90° and 270° aspect angle) are due to the large cylindrical pressure hull.
 The 180° peak is due to the bulkheads in the sail and the submarine’s stern.
Besides these distinct peaks, an area of intermediate levels can be found. Here, multiple reflections
between the along ships’ and athwart ships’ bulkheads are responsible for the relatively high TES
levels - especially at 3 kHz.

Figure 6: Monostatic TES of a stealth-shape submarine (green) compared to the coated (red) anduncoated (blue) submarine model BeTSSi. Left: 1 kHz, right: 3 kHz.

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4. Coating concept for TES reduction
For a reflecting object, the main effect on the spatial TES characteristics comes from its geometricshape. A flat plate, if large compared to the acoustic wavelength, will reflect the sound in a narrow
beam whereas a sphere will distribute the reflected sound over a wider angular range. This matter offact can be used, together with hydro-acoustic materials, to develop a coating concept for TES
reduction for the model submarine geometry BeTSSi.
The first coating step is to apply the TL material onto the bow casing. This will decrease thetransparency of the bow and hence the TES contribution of the large flat bulkheads behind the casing
is reduced. Even if the reflectivity of the bow’s outer shell is increased, the TES of the bow peak will
be reduced. The TES-calculation predicts a reduction of the bow peak of more than 10 dB, as shown in
Figure 6 (red curves). The pressure hull is already fully reflecting, therefore applying TL material on
its surface will not reduce the beam aspect peak. The beam peak may be reduced by applying the ER
material (with an assumed reflection loss of 10 dB) to the pressure hull and the sail. In the case of the
BeTSSi model, the 90°/270° peaks could be reduced by 8 dB. In addition, the submarine stern was also
coated with the TL material, which reduced the peak at 180° by more than 15 dB. The overallmonostatic TES value could also be reduced slightly at 1 kHz and significantly at 3 kHz.

5. Stealth-shape concept for TES reduction
As already proposed in 1922 (3), the TES can be reduced if the outer shape is modified according to
the rules known today from the radar cross section reductions. Such a shape needs an opaque surface towork as intended. Therefore, a TL material would need to be applied nearly over the entire outer hull.
The TES calculations with these types of shapes show very promising results. One such result is shownin Figure 6 (green curves) in comparison to the uncoated and coated BeTSSi model results. The beam
aspect peak could be reduced by 12 dB to 25 dB at 1 kHz and 3 kHz; the bow and stern peaks could be
reduced by 15 dB and 25 dB respectively. Note that, beside the few sharp TES peaks, the stealth-shapeconcept is able to reduce the TES over the wider angular range. This property is not observed with thisintensity for the coating concept and it will be even more pronounced for the muti-static scenario.

6. Comparison of the multi-static TES
New multi-static active sonar techniques were developed which dramatically increased the acoustic
detection ranges of the nowadays submarines. Due to the reflecting nature of the stealth -shape concept,
it is often believed that this concept would not perform in a multi-static sonar scenario, as has beensometimes observed with stealth-shaped airplanes. However, the stealth-shape concept proposed bythyssenkrupp Marine Systems reflects the acoustic energy into the vertical sector such that further
sound propagation over long horizontal distances is no longer possible (without high attenuation).
Figure 7 compares the multi-static target echo strength for the three mentioned submarines: thestealth-shaped submarine and the coated and uncoated BeTSSi model submarine. The azimuthal
receiver aspect angle relative to the submarine is plotted on the x-axis and the transmitter aspect angle
on the y-axis. The TES levels for all receiver/transmitter aspect angle combinations are color-coded.
The upper panel shows the TES levels for a sonar frequency of 1 kHz and the lower panel for 3 kHz.
On the left side, the TES levels of the original BeTTSi model submarine and on the right side the TES
levels of the stealth-shaped submarine are displayed. In the center the TES levels of the coated BeTSSi
model submarine are shown. At the diagonal from the upper left corner to the lower right corner, themonostatic TES levels are depicted again. The high TES levels from the lower left corner to the upper
right corner represent the specular reflection of the broad side of the submarine. It can be seen that withthe coating concept, the monostatic TES levels could be reduced - however the overall multi-staticlevels of the coated BeTSSi model differ not greatly from the uncoated BeTSSi model. Here clearly theadvantages of the stealth-shape concept are highlighted. The stealth-shape concept achieves asignificant reduction of the TES levels for virtually all multi-static transmitter/receiver aspect angle
combinations.

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Figure 7: The multi-static target echo strength with respect to the transmitter and receiver aspect angle for thethree submarines: uncoated BeTSSi model, coated BeTTSi model and the stealth-shaped submarine.

7. Summary
The degree of reflection of acoustic signals is denoted as the “target echo strength” (TES).
Concerning the “visibility” of submarines, this backscatter phenomenon is of the utmost importance. A
correct prediction of the TES is fundamental for an efficient TES reduction concept. With the use ofhydro-acoustic materials, which are applied as a cover over the outer hull of the submarine, two TES
reduction concepts were presented. The first concept is a classical coating concept, where different
surfaces are covered with absorptive and reflective material without changing the outer shape of thesubmarine. The second concept uses only a thin reflective material, however strongly changes theouter shape in accordance with the known stealth technique for reducing the radar cross section.
Both concepts - the coating and the shaping concept - reduce significantly some very distinct
monostatic TES peaks. However switching from the monostatic to the multi-static case scenario, theability to reduce the overall TES levels - for any combination of transmitter/receiver positions - is only
observed from the standpoint of the submarine form-shaping concept.

REFERENCES
1. Avsic, T. Taking the next step in stealth submarine development, Proceedings of the 22th
International Congress on Sound and Vibration, Florence, Italia, 12–16 July, (2015).
2. Gilroy, L., De Jong, C., Nolte, B. and Schäfer, I., BeTSSi II Benchmark Target Strength Simulation,
available: http://www.dwt-sgw.de/wt-aks/arbeitskreis-akustik/veranstaltungen-2014/
3. Knox Samuel Lippincott Griswold, Submarine construction, Patent US1500997A (1924)1942