**3. The theory of Sonics: A quick review**

In 1918, the Romanian scientist George Constantinescu published *The Theory of Sonics* [25]. This book presents a new theory on the use of waves in the production, transport, and conversion of mechanical energy, as well as experimental validation. Constantinescu applied his theory to longitudinal waves of pressure propagating

**Figure 6.** *Basic principle of the theory of Sonics [25].*

*Sonic Boom Mitigation through Shock Wave Dispersion DOI: http://dx.doi.org/10.5772/intechopen.85088*

through liquids, which fill metallic ducts. These ducts act as "wave guides" (see **Figure 6**). Piston, 1, oscillates in a sinusoidal manner and creates longitudinal waves of pressure, a. These waves propagate through liquid, b, which fills duct, 2, and actuates driven piston 3. Pistons 1 and 3 are going to oscillate with the same frequency. Crank drives, 4, assure the continuous motion of pistons. This method of power transmission relies on liquid compressibility. The phase difference between pistons 1 and 3 depends on the ratio of duct length and wavelength. If this ratio is an odd number, pistons 3 and 1 oscillate in opposition (i.e., the phase difference is equal to π). The amount of power that can be transmitted is proportional to the pressure of liquid within duct. Finally, George Constantinescu demonstrated that sonic waves act like alternative current and built many wave generators and sonic engines with power of tens of kW. Frequencies of sonic waves used for power transmitting can be from several tens to tens of thousands of Hz.

#### **4. New solution for sonic boom mitigation**

This new solution was proposed for the first time in a previous paper of authors [26]. It consists in dispersion of shock wave during its generation by an aircraft in supersonic flight having as a consequence extension of "N" wave (sonic boom) on a much larger area at ground level. In this way, the impact of sonic boom on community is much reduced.

This solution offers to aircraft designers the possibility to create supersonic aircraft with a larger space in fuselage and transportation of a higher number of passengers.

#### **4.1 The bases of the new solution**

The new proposed solution for sonic boom mitigation is based on the following observations:


The thickness of shock wave is extremely small. This thickness depends by Mach number as presented in **Figure 7** [27]. For this reason, when the shock wave hits the ground, a sudden increase of local air pressure is produced.

According to Observation 1, in normal circumstances, the shock wave cannot be eliminated because it is a physical effect governed by natural laws. However, if circumstances are changed, for example, the steady-state is substituted with a transient state; the effect of sonic boom on ground surface will be much reduced.

Taking as example the oblique shock wave created by a wedge having the semiangle α (**Figure 8**), the semi-angle β of the shock wave is given by Eq. (1) [28]. Looking to Eq. (1), one can see that β is depending on the semi-angle α and the speed of aircraft given by the Mach number, M:

$$\cot a = \tan \beta \left[ \frac{(k+1)M^2}{2(M^2 \sin^2 \beta - 1)} - 1 \right] \tag{1}$$

Wingspan: 23.5 m Height: 6.7 m

*Aerion supersonic business jet [24].*

**Figure 5.**

**Figure 6.**

**116**

*Basic principle of the theory of Sonics [25].*

Fuel quantity: 26,800 kg

**3. The theory of Sonics: A quick review**

*Environmental Impact of Aviation and Sustainable Solutions*

Looking to the lengths of cabin (9.1 m) and aircraft (51.8 m), one can see at a glance one of the most important drawbacks of this solution: The space for passengers is extremely low due to the need of the aircraft fuselage to be very thin and long.

In 1918, the Romanian scientist George Constantinescu published *The Theory of Sonics* [25]. This book presents a new theory on the use of waves in the production, transport, and conversion of mechanical energy, as well as experimental validation. Constantinescu applied his theory to longitudinal waves of pressure propagating

#### *Environmental Impact of Aviation and Sustainable Solutions*

During the travel of the three shock waves to ground, "N"-shaped wave is formed through coalescence hitting the ground as sonic boom. This "N" wave is composed by a high-pressure zone, where maximum pressure is +P0 followed by a

In normal case, the shock wave thickness δ is extremely small as presented in **Figure 7**, and the footprint length d of the "N" wave at ground level is about two

For simplicity, assume an aircraft wing having the wing LE as a wedge, which

Vibration of wing LE surface is done in this case by an elastic membrane, which is stretched over the wing LE. Between the wing and membrane, a thin layer of hydraulic liquid is introduced. When pressure pulses of a certain frequency ν are injected in liquid through perforations in wing LE, the membrane begins to vibrate with the same frequency ν. The pressure pulses can be produced by a sonic equipment as presented in **Figure 6**. In this case, the driven piston 3 from **Figure 6** is

For reaching of a high vibration amplitude, the injection frequency of pulses must coincide with the first resonance frequency of membrane. The resonance frequency of membrane depends on the value of stretching tension of that mem-

In **Figure 9**, one can see that when semi-angle α increases, the shock wave semiangle β increases, and the shock wave is dispersed on a larger area D > d. Due to dispersion, the thickness of shock wave at ground (S) is much larger than the thickness of the shock wave (δ) in the absence of vibration (S >> δ). Extension of shock wave on a larger area at ground level makes the maximum pressure p0 < <P0

According to observation 2, if the Mach number is between 1 and 1.8 (the case of the most supersonic business jet ongoing projects), a small variation of semi-angle α

**4.2 Mechanical dispersion of shock wave using elastic membranes**

can be continuously vibrated with a certain frequency, ν (**Figure 9**) [26].

and the impact of sonic boom on community to be much reduced.

depression zone where minimum depression is P0.

*Sonic Boom Mitigation through Shock Wave Dispersion DOI: http://dx.doi.org/10.5772/intechopen.85088*

times larger the aircraft length.

substituted by the elastic membrane.

brane over the wing LE.

**Figure 9.**

**119**

*Dispersion of shock wave by vibrating surfaces [26].*

A transient state could be produced in two ways:

a. Increasing and decreasing of aircraft speed (Mach number, M)

b. Increasing and decreasing rapidly the semi-angle α.

The first way (a) is impossible due to inertia. Really, it is obviously for everybody that the aircraft cannot be accelerated and decelerated rapidly because the thrust of engines cannot be increased and decreased rapidly.

The second way (b) is affordable if the supersonic aircraft is equipped with an equipment for dispersing of shock wave during flight over populated areas.

In this case the dispersion of shock wave, i.e., variation of angle β, is produced through periodical variation of semi-angle α of aircraft surfaces, which generate the shock waves, i.e., nose, wing leading edge (LE), and horizontal empennage LE.

During horizontal flying of a supersonic aircraft, its nose produces a conical shock wave, and the wing and horizontal empennage are producing oblique shock waves.

Therefore, three booms should be heard at ground level, but the second and the third booms are very close, and practically only two booms are heard.

During the travel of the three shock waves to ground, "N"-shaped wave is formed through coalescence hitting the ground as sonic boom. This "N" wave is composed by a high-pressure zone, where maximum pressure is +P0 followed by a depression zone where minimum depression is P0.

### **4.2 Mechanical dispersion of shock wave using elastic membranes**

In normal case, the shock wave thickness δ is extremely small as presented in **Figure 7**, and the footprint length d of the "N" wave at ground level is about two times larger the aircraft length.

For simplicity, assume an aircraft wing having the wing LE as a wedge, which can be continuously vibrated with a certain frequency, ν (**Figure 9**) [26].

Vibration of wing LE surface is done in this case by an elastic membrane, which is stretched over the wing LE. Between the wing and membrane, a thin layer of hydraulic liquid is introduced. When pressure pulses of a certain frequency ν are injected in liquid through perforations in wing LE, the membrane begins to vibrate with the same frequency ν. The pressure pulses can be produced by a sonic equipment as presented in **Figure 6**. In this case, the driven piston 3 from **Figure 6** is substituted by the elastic membrane.

For reaching of a high vibration amplitude, the injection frequency of pulses must coincide with the first resonance frequency of membrane. The resonance frequency of membrane depends on the value of stretching tension of that membrane over the wing LE.

In **Figure 9**, one can see that when semi-angle α increases, the shock wave semiangle β increases, and the shock wave is dispersed on a larger area D > d. Due to dispersion, the thickness of shock wave at ground (S) is much larger than the thickness of the shock wave (δ) in the absence of vibration (S >> δ). Extension of shock wave on a larger area at ground level makes the maximum pressure p0 < <P0 and the impact of sonic boom on community to be much reduced.

According to observation 2, if the Mach number is between 1 and 1.8 (the case of the most supersonic business jet ongoing projects), a small variation of semi-angle α

**Figure 9.** *Dispersion of shock wave by vibrating surfaces [26].*

A transient state could be produced in two ways:

*Environmental Impact of Aviation and Sustainable Solutions*

b. Increasing and decreasing rapidly the semi-angle α.

thrust of engines cannot be increased and decreased rapidly.

waves.

**118**

**Figure 8.**

**Figure 7.**

*The thickness of shock wave [27].*

*The oblique shock wave.*

a. Increasing and decreasing of aircraft speed (Mach number, M)

The first way (a) is impossible due to inertia. Really, it is obviously for everybody that the aircraft cannot be accelerated and decelerated rapidly because the

The second way (b) is affordable if the supersonic aircraft is equipped with an

In this case the dispersion of shock wave, i.e., variation of angle β, is produced through periodical variation of semi-angle α of aircraft surfaces, which generate the shock waves, i.e., nose, wing leading edge (LE), and horizontal empennage LE. During horizontal flying of a supersonic aircraft, its nose produces a conical shock wave, and the wing and horizontal empennage are producing oblique shock

Therefore, three booms should be heard at ground level, but the second and the

equipment for dispersing of shock wave during flight over populated areas.

third booms are very close, and practically only two booms are heard.

produces a large variation of semi-angle β. In the function of the Mach number, the variation of β can be even of several times larger than variation of α. This physical effect offers an important advantage: At the ground level, the dispersed shock wave extends on hundreds of meters. For example, if an aircraft is flying horizontally with speed M = 1.3, and the semi-angle of wing LE is α = 5°, the semi-angle β calculated with Eq. (1) is β = 59.96° [29]. If the semi-angle is α = 6°, the semi-angle β calculated with Eq. (1) is β = 63.46° [29]. So, if the variation of wedge semi-angle is Δα = 6° � 5° = 1°, the variation of semi-angle β is Δβ = 63.46° � 59.96° = 3.5°, i.e., much larger than Δα.

Assume M = 1.3, Δα = 1°, and Δβ = 3.5° (0.061 rad). If the aircraft is flying at height H = 15,000 m, shock wave dispersion is given by Eq. (2):

$$S = H \bullet \Delta \beta = \mathbf{15000} \bullet 0.061 = \mathbf{915} \,\mathrm{m} \tag{2}$$

For M = 1.501, if cone angle is α = 12.125°, a variation Δα = 0.025° theoretically produces transforming of oblique shock wave in a detached shock wave (bow shock

Of course, keeping in control of such a process is a fine task, but it can be

Which could be the most effective vibration frequency, ν? This is a difficult question. It is very clear that the effect of a low frequency, say 1 Hz, has no significant influence to shock wave dispersion because the vibration is too slow. Duration of a natural "N" wave is about 0.1 s. Probably, the period T of membrane oscillation should be smaller than 0.1 s, that is, the vibration frequency should be

At this time there is no theory regarding how much could be this frequency. For this reason, experiments are the next necessary step. Some experiments having an

Obviously, applying elastic membranes on aircraft nose and wing LE implies a difficult technology. Instead of that design, a new one can be seen in **Figures 11** and **12** [30]. This time the membrane is substituted by an elastic fairing made of thin carbon fiber composite fixed by the aircraft nose or wing LE. When the pressure in the air manifold varies (e.g., sinusoidal variation with frequency ν = 10 Hz), local forces appear on elastic fairing determining its vibration. The variation of pressure must be equal to the resonance frequency of elastic fairing for obtaining the maximum vibra-

Testing of such a solution has an acceptable price if the following two methods

*Principal scheme of shock wave dispersion through vibration of elastic fairings induced by compressed air [30].*

achieved if it is controlled by the aircraft onboard computer.

**4.3 Mechanical dispersion of shock wave using elastic fairings**

An important question is the following:

*Sonic Boom Mitigation through Shock Wave Dispersion DOI: http://dx.doi.org/10.5772/intechopen.85088*

over ν = 1/T = 1/0.1s = 10 Hz.

acceptable price are presented at point 5.

tion amplitude with a minimum pneumatic power.

wave).

are applied.

**Figure 11.**

**121**

If a supersonic aircraft has the length of 20 m, the natural ground footprint of the "N" wave is 40 m. One can easily see that through dispersion the footprint is enlarged about 23 times from 40 to 915 m.

However, even larger dispersion distances S can be obtained if through design the semi-angle α of wing LE is taken equally to αlim for detaching of oblique shock wave. For a given supersonic cruise speed M, if the semi-angle α of wing LE is increased through vibration, only a little over αlim, an extremely large variation of shock wave semi-angle β is produced. This is happening because when the semi-angle α is over αlim, the oblique shock wave is detaching as presented in **Figure 10** [26].

The results of calculations using [29] are given in **Table 1**.

As it can be seen in **Table 1**, shock wave dispersion at the ground level is of thousands of meters.

**Figure 10.** *Detaching of shock wave [26].*


#### **Table 1.**

*Variation of β when α = αlim.*

*Sonic Boom Mitigation through Shock Wave Dispersion DOI: http://dx.doi.org/10.5772/intechopen.85088*

produces a large variation of semi-angle β. In the function of the Mach number, the variation of β can be even of several times larger than variation of α. This physical effect offers an important advantage: At the ground level, the dispersed shock wave extends on hundreds of meters. For example, if an aircraft is flying horizontally with speed M = 1.3, and the semi-angle of wing LE is α = 5°, the semi-angle β calculated with Eq. (1) is β = 59.96° [29]. If the semi-angle is α = 6°, the semi-angle β calculated with Eq. (1) is β = 63.46° [29]. So, if the variation of wedge semi-angle is Δα = 6° � 5° = 1°, the variation of semi-angle β is Δβ = 63.46° � 59.96° = 3.5°, i.e.,

Assume M = 1.3, Δα = 1°, and Δβ = 3.5° (0.061 rad). If the aircraft is flying at

If a supersonic aircraft has the length of 20 m, the natural ground footprint of the "N" wave is 40 m. One can easily see that through dispersion the footprint is

However, even larger dispersion distances S can be obtained if through design the semi-angle α of wing LE is taken equally to αlim for detaching of oblique shock wave. For a given supersonic cruise speed M, if the semi-angle α of wing LE is increased through vibration, only a little over αlim, an extremely large variation of shock wave semi-angle β is produced. This is happening because when the semi-angle α is over

As it can be seen in **Table 1**, shock wave dispersion at the ground level is of

**M αlim [°] βbefore [°] βafter [°] Δβ [°] S [m]** 1.300 6.650 68.59 90 21.41 5602 1.501 12.125 65.80 90 24.20 6332

*S* ¼ *H* ∙ Δ*β* ¼ 15000 ∙ 0*:*061 ¼ 915 *m* (2)

height H = 15,000 m, shock wave dispersion is given by Eq. (2):

*Environmental Impact of Aviation and Sustainable Solutions*

αlim, the oblique shock wave is detaching as presented in **Figure 10** [26]. The results of calculations using [29] are given in **Table 1**.

enlarged about 23 times from 40 to 915 m.

much larger than Δα.

thousands of meters.

**Figure 10.**

**Table 1.**

**120**

*Detaching of shock wave [26].*

*Variation of β when α = αlim.*

For M = 1.501, if cone angle is α = 12.125°, a variation Δα = 0.025° theoretically produces transforming of oblique shock wave in a detached shock wave (bow shock wave).

Of course, keeping in control of such a process is a fine task, but it can be achieved if it is controlled by the aircraft onboard computer.

An important question is the following:

Which could be the most effective vibration frequency, ν? This is a difficult question. It is very clear that the effect of a low frequency, say 1 Hz, has no significant influence to shock wave dispersion because the vibration is too slow. Duration of a natural "N" wave is about 0.1 s. Probably, the period T of membrane oscillation should be smaller than 0.1 s, that is, the vibration frequency should be over ν = 1/T = 1/0.1s = 10 Hz.

At this time there is no theory regarding how much could be this frequency. For this reason, experiments are the next necessary step. Some experiments having an acceptable price are presented at point 5.

#### **4.3 Mechanical dispersion of shock wave using elastic fairings**

Obviously, applying elastic membranes on aircraft nose and wing LE implies a difficult technology. Instead of that design, a new one can be seen in **Figures 11** and **12** [30]. This time the membrane is substituted by an elastic fairing made of thin carbon fiber composite fixed by the aircraft nose or wing LE. When the pressure in the air manifold varies (e.g., sinusoidal variation with frequency ν = 10 Hz), local forces appear on elastic fairing determining its vibration. The variation of pressure must be equal to the resonance frequency of elastic fairing for obtaining the maximum vibration amplitude with a minimum pneumatic power.

Testing of such a solution has an acceptable price if the following two methods are applied.

#### **Figure 11.**

*Principal scheme of shock wave dispersion through vibration of elastic fairings induced by compressed air [30].*

*Environmental Impact of Aviation and Sustainable Solutions*

The components of experimental equipment no. 1 are:

• Electromagnet that is fed by an alternative current (AC).

wave is schlieren photographed for various values of Mach number.

ness, depending on vibration frequency and Mach number.

to the resonance frequency of lamella, and the shock wave is schlieren

When electromagnet is powered with an alternative current at the frequency ν equal to the resonance frequency of lamella, the lamellae vibrate at the maximum amplitude. Vibration frequency can be changed if the mass of the two steel pieces is changed. When the weight of steel piece increases, the resonance frequency of lamella decreases and vice-versa. Another role of steel piece is to increase the

Firstly, the shock wave is observed in the window of supersonic aerodynamic tunnel for various speeds when electromagnet is not actuated. The position of shock

After that, the electromagnet is actuated by the AC having a frequency ν equally

photographed for the same Mach number as before (when electromagnet was not

For every measurement, the shock wave should have variable taper and thick-

The test equipment no. 2 is more complex than test equipment no. 1. It should normally be used as a second step if good measurements are registered during using

This equipment is presented in **Figure 14** [26]. The components of experimental

• Two steel lamellae having at their end steel pieces.

*Sonic Boom Mitigation through Shock Wave Dispersion DOI: http://dx.doi.org/10.5772/intechopen.85088*

attraction force of electromagnet on lamella.

• Wedge simulating a cone or wing LE.

• Membrane made of elastic material.

• Central support.

actuated).

**5.2 The test equipment no. 2**

of equipment no. 1.

equipment no. 2 are:

• Hydraulic liquid.

**Figure 14.**

**123**

*Test equipment no. 2 [26].*

**Figure 12.** *View of a wing with elastic fairings at LE for dispersion of shock wave [30].*
