3.1. Multi-Mode Dynamic Electromagnetic Scattering
Figure 6 shows the multi-mode dynamic RCS of tilt-rotor aircraft at an attitude of
, and the wave frequency is 10 GHz.
Figure 7 shows the contribution ratio of each scattering source to the total scattering. The tilt-rotor aircraft flies in helicopter mode from 0 to 0.15 s, in transition mode from 0.15 to 12.15 s, and in airplane mode from 12.15 to 12.3 s. The rotation period of the rotor is 0.15 s, and it takes 12 s for the tilt-rotor aircraft to change from helicopter mode to airplane mode. To make the RCS results clear in the images, the dynamic RCS images were drawn with a non-uniform sampling time interval of 0.000833 s in helicopter and airplane mode, and 0.0267 s in transition mode.
As can be seen in
Figure 6, three distinct periodic features appear in the helicopter mode from 0 to 0.15 s. At the moments of 0.05, 0.1, and 0.15 s, the blade leading edges of the two rotors are perpendicular to the incident direction of the electromagnetic wave, at which time the RCS has a short-lived peak (leading edge peak) in the local range with a value of 17.36 dBsm. Since the angle between the blade’s leading edge and the trailing edge is 2°, the trailing edges are perpendicular to the wave at about 0.024, 0.074, and 1.024 s. And the RCS value at these moments is 17.09 dBsm, which is slightly lower than the leading edge peak. This is because the blade’s leading edge has a small curvature, and its echo characteristics are dominated by face reflection. While the trailing edge is a wedge configuration, the echo characteristics are mainly edge diffraction, which is a weaker scattering source compared to face reflection. In addition, the RCS shows a significant increasing and then decreasing trend in the intervals of [0.013, 0.024] s, [0.063, 0.074] s, and [0.113, 0.124] s, which is mainly caused by the gradually increasing and then decreasing multiple scattering between the lower surface of the forward blades and the upper surface of the nacelles. This multiple scattering leads to the maximum RCS in the helicopter mode, which is 20.81 dBsm.
In the transition mode, the leading edge peak should actually occur every 0.05 s, but due to the artificially changed sampling interval, the graph shows a leading edge peak every 0.4 s. As the transition proceeds, the RCS shows a sharp oscillation feature. And the leading edge peak is gradually obvious, whose value in the interval of [9.23, 12.15] s is much higher than the other sampling points in the local area. The rotors tilt from horizontal to vertical, while the upper surface of the rotors exposed to the radar wave changes from less to all, resulting in a rising RCS amplitude from 12.29 dBsm to 47.61 dBsm. It can be seen from
Figure 7 that with the increase in tilt angle, the contribution of the rotating parts to the total scattering is also increasing. In airplane mode, the total scattering is almost entirely from the rotating parts. In non-airplane mode, the nose contributes more than a quarter of total scattering, and the other parts contribute about one-sixth; the tail contributes 3~5%. The physical mechanisms of the strong specular reflection on the rotor’s upper surface during the transition can be explained using the RCS characteristics of the flat panel.
Figure 8 shows the RCS results of a flat panel scanned by a monostatic radar. The RCS of a flat panel gradually increases as the incident wave angle changes from 0° to 90°. This is because, on the panel surface, the incident wave angle (
) is equal to the reflection angle (law of reflection). When the radar waves come from an angle of 90°, all the reflected waves return in the opposite direction from the incident waves. And at this time, the echo energy received by the receiver radar is the strongest, and the RCS is also the largest. The tilt-rotor can be compared to a flat panel; with the tilting of the rotor, more and more incident waves can return directly along the original path, so the RCS gradually increases. When the rotor tilts to 90°, the rotor disk is completely perpendicular to the incidence direction. Therefore, at this time, the specular reflection on the rotor’s upper surface is the strongest and the RCS is the largest. In the dashed black box of
Figure 6, the RCS first rises and then falls, leading to a special region where the maximum RCS is 24.27 dBsm at 1.85 s (at this moment the tilting angle is 13°). The reason for this phenomenon is that the angle between the side line and axis of the conical hub is 13° in the present aircraft model, and at a tilting angle of 13°, the hubs are perpendicular to the incident wave and become strong scattering sources. Then, as the tilting angle deviates from 13°, the scattering intensity at the hubs decreases, as does the RCS amplitude.
In airplane mode, the upper surface of the rotors is completely perpendicular to the incident wave, creating an extremely strong specular reflection with a mean RCS of 47.71 dBsm. The dynamic RCS only fluctuates periodically in the range of [−0.36, +0.33] dB around the mean value, which is caused by the periodic shading of the rotors on the wings.
Figure 9 reveals the micro-Doppler effects of tilt-rotor aircraft from helicopter mode to transition mode to airplane mode. When the aircraft has a translational velocity in the direction of the radar line of sight, the micro-Doppler will have an overall translation on the frequency shift axis, which is not considered in this paper. A positive micro-Doppler frequency shift is generated when the forward blades are perpendicular to the incident wave, and a negative shift is generated when the retreating blades are perpendicular to the incident wave. In helicopter mode, the maximum micro-Doppler frequency shift is kept at 16,425 Hz, and the scintillation period is 0.05 s. There is always a bright scintillation band distributed around the zero frequency, which is caused by the non-rotational parts of the tilt-rotor aircraft. In the transition mode, at the moment of 0.15 s, the maximum micro-Doppler frequency shift is 16,425 Hz, which is the same as that of helicopter mode. After the rotors start to tilt, the maximum micro-Doppler frequency shift decreases according to the law of
until it drops to 0 Hz at the moment of 12.15 s. But the time interval between the two adjacent scintillation bands stays at 0.05 s.
Figure 10 reveals the influence mechanism of the rotors tilting on the micro-Doppler effect. When the component of the blade linear velocity in the radar line of sight direction changes, the maximum micro-Doppler frequency shift also changes in response. In airplane mode, the micro-Doppler spectrum distribution is characterized by a bright line concentrated near the zero frequency because there is no velocity component in the direction of the radar line of sight. And it is not negligible that, if the forward speed of the tilt-rotor aircraft is taken into account, there will be a micro-Doppler frequency shift.
Figure 11 provides the multi-mode ISAR images of tilt-rotor aircraft. It can be seen that at the attitude of
, the main strong scattering sources of the tilt-rotor aircraft are concentrated in the head, the wings, and the rotor blades, which are perpendicular to the incident wave. In the transition mode, the scattering intensity at the blade tips increases compared to the helicopter mode. When the tilting angle is 90°, the scattering intensity at the upper surface of the rotors increases rapidly and substantially. The results of these ISAR images are all consistent with the trends of the dynamic RCS profiles. And in order to improve the survivability of the tilt-rotor aircraft, it is necessary to focus on the stealth design of the highlighted areas in the ISAR images. However, it should be noted that when the tilt-rotor aircraft flies in airplane mode, it is very difficult to achieve the rotor’s stealth against the radar directly in front of the aircraft. At this time, stealth measures such as morphing rotor structures or radar-absorbing materials can be further considered.
3.2. Effects of Pitch Angle
In fact, tilt-rotor aircraft usually have a certain pitch or azimuth angle relative to the detection radar. Therefore, the effects of pitch angle and azimuth angle on the dynamic electromagnetic scattering of the tilt-rotor aircraft are investigated next.
Figure 12 shows the multi-mode dynamic RCS of tilt-rotor aircraft at the attitude of
and
.
Figure 13 shows the contribution ratio of each scattering source to the total scattering.
As can be seen in
Figure 12, at a pitch angle of 30°, the dynamic RCS still possesses a significant periodic characteristic in the helicopter mode, and there are three cycles in 0.15 s. Due to the larger area of the lower surface of the rotors exposed to the radar incidence, the blade leading edge peak increases to a value of 20.81 dBsm. However, when the blade’s trailing edges are perpendicular to the incident wave, the RCS is reduced by 5.74 dB compared to the pitch angle of 0°. In addition, in the intervals of [0.013, 0.024] s, [0.063, 0.074] s, and [0.113, 0.124] s, the multiple scattering between the lower surface of the forward blades and the upper surface of the nacelles still becomes stronger first and then weaker, so the RCS increases first and then decreases.
In transition mode, the blade leading edge peak is no longer obvious, and the RCS increase is only 2.32 dB after the conversion from helicopter mode to airplane mode. And in the dynamic RCS profiles, there are two special zones where the RCS first increases and then decreases. “Zone1” is caused by the nacelles, and “Zone2” is caused by the hubs. These two components are both first gradually perpendicular to the direction of the incidence and then away from the direction during the tilting process, thus causing the two special zones.
In airplane mode, the RCS oscillation is much larger than that of the pitch angle of 0°, which is in the range of [−11.72, +7.25] dB around the mean value of 14.11 dBsm. The periodic features of the rotors’ scattering still exist in this mode, but the rotors are no longer the dominant scattering sources.
From the perspective of the contribution ratio of each scattering source to the total scattering, at different tilt angles, the contribution ratio of each source remains basically unchanged, and the contribution of the rotating parts is the largest. The tail contribution has been significantly improved compared to the state of 0° azimuth and pitch angle, accounting for about one-seventh.
Figure 14 reveals the multi-mode micro-Doppler of tilt-rotor aircraft at the attitude of
and
. It can be seen that the scintillation period remains unchanged in all modes, which is always 0.05 s. But the patterns of the maximum micro-Doppler frequency shift have changed significantly. Since the pitch angle is 30°, the angle between the incidence and the rotor disk is 30° in helicopter mode, and the maximum micro-Doppler frequency shift of helicopter mode needs to be multiplied by
, which is 14,224 Hz. In transition mode, the angle between the incidence and the rotor disk is equal to the tilting angle minus the pitch angle. So, after the rotors start to tilt, the maximum micro-Doppler frequency shift is
At the moment of 4.15 s, we have . From 12.15 s to 12.3 s, the angle between the incidence and the rotor disk is kept at 60°; hence, the maximum micro-Doppler frequency shift of the airplane mode is 8213 Hz.
Figure 15 provides the multi-mode ISAR images of tilt-rotor aircraft at the attitude of
and
. It can be seen that when the pitch angle is 30°, the surface areas of the tilt-rotor aircraft exposed to the electromagnetic rays are larger, resulting in an increase in the scattering intensity at the belly, the tail wings, and the wing–fuselage junctions. Because of the V-shaped construction, the contribution of the tail wings to the total scattering is dominated by edge diffraction. The wing–fuselage junctions produce multiple scattering due to the presence of angular structures, which should be avoided as much as possible in the stealth design of tilt-rotor aircraft. Furthermore, at this pitch angle, the rays do not have the opportunity to irradiate vertically on the rotor disk, so the scattering intensity at the blade’s surface does not differ much in different modes.
3.3. Effects of Azimuth Angle
Figure 16 shows the multi-mode dynamic RCS of tilt-rotor aircraft at the attitude of
and
.
Figure 17 shows the contribution ratio of each scattering source to the total scattering.
Due to the azimuth angle of 45°, the rotational phase of the two rotors in the direction of the radar line of sight is no longer symmetrical. As shown in
Figure 16, in the helicopter mode, there are six cases in which the blade leading edge is perpendicular to the incident wave. These cases are distributed at the moments of 0.01875 s, 0.03125 s, 0.06875 s, 0.08125 s, 0.11875 s, and 0.13125 s, and the RCS values alternate at 7.99 dBsm and 13.53 dBsm. These two values are less than the blade leading edge peak at the state of the 0° azimuth angle because the leading edges of the two rotors are no longer perpendicular to the direction of the incident wave at the same time, resulting in a reduction in the total scattering intensity. Therefore, when the rotational phase is not symmetrical relative to the incident wave, the influence of the periodic rotation of the rotors on the total scattering is weakened.
In transition mode, the dynamic RCS still fluctuates dramatically, but it is difficult to directly find out the effects of the rotors’ periodic rotation only from the RCS profiles. And the RCS increase is only 0.92 dB after the conversion from helicopter mode to airplane mode. During the tilting process, the hubs are perpendicular to the incident wave at about 2.63 s, which will produce a peak value in the local area, so the RCS increases first and then decreases near this moment.
In airplane mode, the RCS oscillation is in the range of [−15.15, +7.79] dB around the mean value of 12.49 dBsm. And except for the numerical differences, the overall features of the dynamic RCS are similar to those at the state of 30° pitch angle.
In addition, due to the change in azimuth angle, the incident wave cannot be vertically incident on the rotor disk plane, so the contribution of the rotating parts to the total scattering is greatly reduced. The multiple scattering between the various components is enhanced, and the scattering intensity of the tail is still maintained at a very low level.
Figure 18 reveals the multi-mode micro-Doppler of tilt-rotor aircraft at the attitude of
and
. It can be seen that with the change of azimuth angle, there is a time difference of 0.0125 s between the two rotors’ micro-Doppler scintillation characteristics. However, due to the constant rotation period of the rotors, the scintillation period is always maintained at 0.05 s. In the helicopter mode, the maximum micro-Doppler frequency shift is the same as that of the state of
, which is 16,425 Hz. This is because only the azimuth angle is changed, and in fact, the angle between the incident wave and the rotor disk is kept at 0°. In the transition mode, at the state of
and
, the angle between the incidence wave and the rotor disk can be expressed as
, where
is the tilting angle. So, the maximum micro-Doppler frequency shift is
When the rotors tilting is finished, the is kept at 45°; hence, the maximum micro-Doppler frequency shift of the airplane mode from 12.15 s to 12.3 s is 11,614 Hz. Moreover, due to the particularity of the 45° azimuth angle, both positive and negative frequency shifts appear on the micro-Doppler spectrum, which means that there are forward and retreating blades perpendicular to the direction of the incident wave at the same time.
It can be seen from the above analyses that the tilt-rotor aircraft has rotors that can be converted from a horizontal state to a vertical state, so its micro-Doppler shift can produce a large and continuous variation between zero shift and maximum shift, which is a feature not found in other types of vehicles. By observing the range of micro-Doppler shift variation, it is possible to identify whether the vehicle is a tilt-rotor aircraft. In addition, the tilt-rotor aircraft can fly at any tilt angle of the rotor. And in order to maintain a stable flight attitude, there is a certain relationship between the tilt angle of the rotor and the flight speed. That is, at a certain tilt angle of the rotor, the tilt-rotor aircraft can only safely fly at a certain range of speed. Therefore, according to the measured micro-Doppler shift, the tilt angle of the rotor can be calculated through the shift variation functions. And furthermore, the flight mode can be confirmed and the flight speed estimated.
Figure 19 gives the multi-mode ISAR images of tilt-rotor aircraft. The strong scattering sources of the tilt-rotor aircraft at the state of
and
are mainly distributed in a point-like manner, concentrated in the parts of the nose, the hubs, the blade tips, the tail wings, and the fuselage side. The scattering intensity of each part at different tilt angles is relatively consistent, and there is no case where the scattering intensity of one part is much larger than that of other parts. It also shows that the tilt-rotor aircraft can maintain a more stable electromagnetic scattering level when the radar wave is incident from an oblique direction in the horizontal plane.