1. Introduction
Generally, investigations into protective materials often focus on how to reasonably and scientifically estimate the damage after impact of a small flying object (e.g., fragmentation, meteorite, hail, projectile, etc.) with a high velocity [
1,
2]. Accurately obtaining key parameters such as the hit position, flight speed, and attitude angle can provide some important references for improving the protective performance of the material [
3]. Obviously, a non-contact measurement method should be used to obtain the above-mentioned key parameters. Otherwise, it will lead to serious deviations in these key parameters, thus affecting the accuracy and objectivity of the evaluation of the damage effect [
4,
5]. If a small flying object hits the surface of a target perpendicularly, this will cause the maximum damage to the protective material layer of the attacked target. Obviously, this can provide some scientific reference to improve the performance of the protective material. Generally speaking, the trajectory of small flying objects cannot be completely perpendicular to the protected target surface due to some disturbance factors. Typically, protected objects are often larger in volume, such as protective shelters, aircraft skins, windshields, and shellproof armor. This requires the ability to effectively, accurately, and reliably measure the above key parameters within a large area (e.g., 5 m × 5 m or even larger). Therefore, this presents a greater challenge to existing relevant measurement methods.
So far, many investigations have been carried out in this field. A measurement system based on LED array detection can simultaneously measure the impact coordinates, flight velocity, and incident angle of a high-velocity object. Its detection area is mainly generated by the LED array and the photodetector array, and thus the size of the detection area can be determined by adjusting the number of LEDs and detectors. In this measurement system, multiple detection areas are formed according to a certain structural relationship. When a small flying object passes through these detection areas, it blocks part of the light in the detection areas. Accordingly, this leads to a reduction in the light received by some photoelectric detectors, and then they output several signals correspondingly. Through a time-domain analysis, the time at which the projectile arrives at these detection areas can be obtained from these signals. According to the measurement model, some related parameters, including the impact coordinates, flight velocity, and incident angle of the projectile, are calculated in combination with these time parameters [
6,
7]. However, it is difficult to build a detection area larger than 5 m × 5 m due to the high cost and its insufficient mechanical strength. Similar to the measurement model of the above system, a passive photoelectric measurement system with intersecting detection areas can also realize the above functions. Unlike the above measurement system, it uses the sky background as the light source instead of the LED array; moreover, its detection area can be effectively formed without a support frame [
8,
9]. This system has some advantages such as a high precision, high sensitivity, and low cost, but its detection performance is also easily affected by the environment. More importantly, it is difficult to expand the size of the detection area of systems based on passive detection theory. Additionally, there is also a high-speed photography system which can effectively measure the above parameters. This system generally uses multiple high-speed cameras to capture a series of images of a high-velocity flying object, and then it can measure the spatial position of the small flying object according to the related image parameters. It has several characteristics such as real scene recording, non-contact measurements, and a high measurement accuracy. Through the interpretation and calculation of these sequence images, the impact coordinates, flight velocity, and incident angle of the impact object are effectively obtained [
10,
11]. Moreover, an acoustic target system uses sensor arrays to obtain the shock wave signal generated during the flight of a small supersonic object in order to calculate the impact coordinates. A large test area (up to 20 m × 20 m) can be achieved by increasing the number of sensors and proper array placement. However, this means more inconvenience and costs, and its measurement model requires the flying object to be perpendicular to the target surface. Otherwise, significant theoretical errors will be introduced. It is also more affected by environmental factors, as the wind speed can change the path of the sound waves [
12,
13]. Therefore, it is necessary to develop a novel method to efficiently acquire these parameters over larger detection areas.
In this article, we propose a measurement method to obtain the flight parameters of a small flying object. Firstly, we develop a measurement system based on a multi-dimensional LED detection array and describe its composition and detection principle. Then, the measurement model of the system is derived according to the spatial structure relationship among six laser screens of the LED detection array. Furthermore, we analyze the systematic errors of velocity and impact coordinate measurements. Finally, comparison experiments were performed to show the validity and feasibility of the proposed measurement method.
2. Materials and Methods
In this research, we develop a measurement system with a six-screen detection array to obtain the three-dimensional velocity vector and the impact coordinates of a small flying object. The proposed system is mainly composed of a laser detection array, a signal-processing device, and a computer, as shown in
Figure 1. In this system, the laser detection array consists of six detection units. The detection principle of a single detection unit is shown in
Figure 2. When a small flying object passes through a detection area (also called a laser screen), a part of the reflected laser is received by a receiving device equipped with an optical lens, filter, slit diaphragm, photodiode, and signal-processing circuit. This causes the photocurrent of the photodiode to suddenly change. After the circuit processing, a trigger signal is generated [
14,
15]. Different wavelengths of lasers can distinguish adjacent LED detection arrays combined with narrow band filters [
16]. In order to output the trigger signals in the effective detection area, this system must have sufficient sensitivity, which mainly depends on the laser power, the size of the flying object, and the height of the trajectory. Therefore, we can adjust the laser power and the amplification factor of the signal amplification circuit to ensure the detection performance of the flying object in the effective detection area.
Similarly, when the small flying object passes through the six LED detection arrays, six trigger signals are correspondingly generated. There is a certain spatial geometry relationship of the six LED detection arrays. The arrival time series can be obtained by a time estimation algorithm [
17,
18], and it contains several time parameters when the measured target arrives at the detection areas in turn. Finally, the flight velocity and impact coordinates of the small flying object can be calculated using the measurement model with the structure parameter and arrival time series, and it will be described in the following text.
Make a series of assumptions as follows. LS
1, LS
2, LS
3, LS
4, LS
5, and LS
6 are six LED detection arrays, respectively, as shown in
Figure 3. Note that LS
1–LS
2, LS
3–LS
4, and
LS5–
LS6 are three pairs of parallel LED detection arrays. In the measurement, the left-hand Cartesian coordinate system is established, and O is the origin of the coordinate system. The positive direction of the
Y-axis is vertical upward, and the
X-axis and
Z-axis are in the horizontal plane. In this coordinate system, there is an invisible target plate which is parallel to the XOY plane. In addition, the laser output points of the six detection units are located on the
Z-axis. LS
1 and LS
2 are placed vertically on the ground (LS
1 in the XOY plane), and
d12 is the distance between them. The angle between LS
3 and LS
1 is α, and that between LS
5 and LS
1 is
β. In the
Z-axis direction, the distance between LS
3 and LS
4 is
d34. Similarly, the distance between LS
5 and LS
6 in the
Z-axis direction is
d56. According to the related general knowledge of the geometric principle, the distances between LS
3 and LS
4 should be calculated to be
d34·cosα, and that between LS
5 and LS
6 should be
d56·cosα. Based on some test conditions, the detection area (about 1.1 m
2) of the laser screen is an isosceles triangle with a height of 2 m and an effective viewing angle of 30°. In addition,
d12,
d34, and
d56 are set to 3 m, 2.4 m, and 2.4 m, respectively. The distances from the output point of laser 3 and laser 5 to
O are
d13 and
d15, which are 0.2 m and 0.4 m, respectively.
After assembling the measurement system, its structure parameters can be known. Accordingly, the plane equations of the six LED detection arrays can also be obtained. The unit normal vectors of LS
1, LS
3, and LS
5 (LS
2, LS
4, and LS
6) are as follows, respectively,
and
Additionally, the velocity vector of the measured object can be expressed as
where
vx,
vy, and
vz are the value of each component of the velocity vector, respectively;
θ and
γ are the pitch and azimuth of the measured flying object, respectively; in addition,
i,
j, and
k are the unit vectors in the positive direction of the
X-,
Y-
, and
Z-axes, respectively.
The arrival time series T, which is [t1 t2 t3 t4 t5 t6], contains the six time parameters when the measured object arrives at LS1, LS2, LS3, LS4, LS5, and LS6, respectively.
Therefore, we can obtain the following equations as follows.
and
where
d12(S) is the distance between LS
1 and LS
2,
d34(S) is the distance between LS
3 and LS
4, and
d56(S) is the distance between LS
5 and LS
6.
Substituting (1) to (3) into (5) to (7) and transforming the result into a matrix form, we can obtain the velocity vector, which is as follows.
with
Furthermore, the relationship between the velocity vector and the target position vector is as follows.
In (10),
r is written as
where (
x0,
y0,
z0) are the coordinates of the measured object at the initial time.
If
P1 (
x1,
y1,
z1),
P3 (
x3,
y3,
z3), and
P5 (
x5,
y5,
z5) are the intersection points of the trajectory and LS
1, LS
3, and LS
5, respectively, then the position vectors of the three points are
By eliminating (
x0,
y0,
z0), we can obtain the following equations, which are
and
In (13) and (14), t13 is the deviation between t1 and t3, and t15 is the deviation between t1 and t5.
Let the plane equations of the LED detection array LS
1, LS
2, ... , LS
6 be
The coefficients of the plane equation can be obtained if the structural parameters of the system are known. By substituting
P1 (
x1,
y1,
z1) into the equation of LS
1, the following equation can be obtained as follows.
Substitute
P3 (
x3,
y3,
z3) and
P5 (
x5,
y5,
z5) represented by
P1 into the plane equation of LS
3 and LS
5, as shown below.
and
Equation (19) can be obtained by combining (16) to (18), and it is
In addition, Equation (19) is written in the matrix form as follows.
By solving (
x1,
y1,
z1), the position vector can be obtained, and thus the target position coordinates at any given time can be solved as follows.
The distance between the target plate and the XOY plane is set to
DT. Furthermore, the time parameter when the small flying object hits the target plane is set to
tT. Thus, the impact coordinates (
xt,
yt,
zt) of the measured object on the target plate can be expressed as
with
4. Discussion
In
Section 3.1, we performed the simulation of the impact points within the dispersion range in the target plate, and then it was observed that the errors of
xT and
yT are not greater than 1.5 mm and 1.7 mm, respectively, when |
v| is set to 900 m/s. In addition, when |
v| is set to 700 m/s, the error of
xT and that of
yT are not greater than 1.3 mm and 1.5 mm, respectively. According to the test requirements [
19,
20], the measurement method is feasible if the relative measurement error of |
v| is less than 2‰ and the measurement errors of
x and
y are less than 3 mm, respectively [
10]. The simulation results show that the system can theoretically achieve the measurement of |
v| and impact coordinates of the small flying object at different pitches and meet the above test requirements.
As can be seen from
Table 3,
Table 4 and
Table 5, in the three groups of shooting experiments at three pitch angles (i.e., −30°, −15°, and 0°), through using our proposed system and high-speed camera system, their maximum deviation of |
v| is 0.66 m/s, their maximum deviation of
xT is 1.8 mm, and their maximum deviation of
yT is 1.9 mm. Additionally,
Table 6,
Table 7 and
Table 8 show that the maximum deviation of |
v| is 0.64 m/s through the proposed system and high-speed camera system, the maximum deviation of
xT is 1.9 mm, and the maximum deviation of
yT is 1.6 mm in the three groups of firing experiments using projectiles with a reference velocity of 700 m/s at different pitch angles (i.e., −30°, −15°, and 0°).
Similarly, we can also use the experimental setup to perform another investigation. In the experiment, 50 projectiles are fired with the reference velocity of 900 m/s (or 700 m/s) at different azimuth angles (i.e., −20°, 0°, and 20°), respectively; however, the pitch angle is constant and set to 0°. In the proposed system, the absolute velocity of |
v| and the impact coordinates (
xT,
yT) can be measured, and they are compared with the measurement data from the high-speed camera system. To avoid an excessive length of our article, measurement data related to the investigation are not listed in
Section 3.2. Thus, we give the related results directly as follows. The maximum value of |
v| is not more than 0.42 m/s, and the maximum value of
xT (or
yT) is not more than 1.5 mm. Therefore, this indicates that the proposed measurement method is feasible, and its measurement accuracy is high enough.