Radar Method of Measuring the Velocity of the Fragments

Abstract

Thousands of debris dangerous to personnel are generated during controlled explosion of warheads containing explosives. To ensure the safety of people, it is necessary to define a zone in which people can stay without risking their lives. A major focus of modern engineering is to maximize the safety of operating technical equipment. In order to implement the above, it is necessary to determine the kinetic energy of the fragments, for which the safe level is below 17 joules (like for air gun). Simultaneous registration of the velocity of such a large amount of fragments is a significant research problem. The article presents a comparison of the two methods of measuring the velocity of splinters formed during detonation of the fragmentation generator. The first common method is to use a chronometer and aluminum foil. The second method, new for this application, is to use a Doppler radar. It allows you to measure the velocity at any moment of the path traveled by the splinter. The article also describes attempts to measure the velocity with both methods, using different variants of Doppler radar settings. Difficulties resulting from the measurements were described, as well as the methods of their elimination.

1. Introduction

The evaluation of the effective range of potential metal fragments generated during work with warheads and explosives is an essential element determining the safety of personnel. The currently applied numerical calculation methods allow for obtaining (by performing numerical simulations) the characteristics of the splitting of the fragments and the distribution of their velocity.

Nowadays, a few different numerical methods are used in the analysis of fragmentation. The authors of the work [1] used different solvers and computer hydrocodes to study the fracture behavior of a 25 mm steel shell. Other scientists [2] investigated the velocity distribution of fragments created by the explosion of a cased charge with two numerical simulation techniques: 2D simulations, 3D simulations using the smoothed-particle hydrodynamic (SPH) method. The numerical simulation of the fragmentation process varying the mechanical characteristics of the shell and type of explosive filling was successfully carried out by the authors of the paper [3]. The SPH method was used by the researchers [4] to investigate numerically the fragmentation process of a cylindrical metal casing. Another research [5] studied the fragmentation calculations of a 120 mm high explosive shell when it was loaded with an advanced HMX-plastic explosive.

Finally, the simulation results should be compared with the real field verification of the quality of fragmentation of the case during stationary tests. However, tests of such type are very costly and time consuming [6,7,8,9,10,11,12,13,14].

In this paper [15], a combined numerical–experimental approach was used to investigate the fragmentation of the warhead. The authors from the Military Institute of Armament Technology (Poland) conducted the experimental tests with the aim of gathering data, which will be useful for the verification of the subsequent simulations. During the experiments after the detonation of the explosive, the fragments of the ruptured shell were collected. The number and the mass distribution of the fragments were examined. Then, numerical simulations were conducted with the same explosive fragmentation geometry as in the experiments. The correctness of the conducted simulations and the applicability of the used numerical technique were verified by comparing the numerical results, especially the fragments’ number and their mass distribution, with the conducted experimental tests’ outcomes. The reasonable agreement between the examined parameters was achieved, which shows that the technique can be used in the future to predict the behavior of fragments [15]. According to the authors’ conclusions, the analysis and comparison of the results obtained from the stationary tests and from the simulation show that the mean total number of fragments created and the number of fragments in the particular mass ranges are very close. The highest differences occur in the number of fragments of the lowest mass range. The differences result from the fact that during stationary tests, it is very hard to recollect such small elements, and that is why the full mass of the casing was not recovered. However, with the increase in fragment mass, the agreement between the simulation results and the experiment rises [15]. The chosen simulations’ results of fragmentation are shown in Figure 1 and Figure 2 and the comparable results of the experimental fragmentation (Figure 3).

With reference to the research results obtained by the authors of the publication [15], the most important aspect is the experimental verification of the velocity of the splinters generated during stationary shell detonation, which at a later stage allows for determining their effective energy, and it compares with simulation results. Obtaining the possibility to compare the velocities of fragments in the experiment and simulations is an important aspect of the verification of the adopted numerical model. In order to be effective, the fragment (splinter) formed as a result of detonation must have appropriate kinetic energy (the kinetic energy of the effective fragment should not be less than 78 joules [16]). For example, fragmentation into large but relatively slow fragments, while also having some advantages, is generally not desirable. Smaller splinters, but in large numbers, are more effective. In addition, they minimize the risk that the targets will be missed [16,17,18,19,20,21]. This article presents a new approach to the problem of recording the velocity of splinters.

2. Materials and Methods

The measurements of the velocity of the fragments were carried out during an experiment of the fragmentation of a stationary steel shell. A 70 mm shell was mounted on a tripod, which was surrounded by large plates—witnesses allocated at various distances. Depending on the needs, they were made of plywood, steel, or aluminum. A replacement fuse was screwed into the shell and detonated remotely. During the fragmentation of the shell, a cloud of debris spread around, striking the witness plates. Individual impacts and punctures can be observed on the plates. The plates usually stick to each other to form a full circle around the fragmented projectile. Traces on the plates made it possible to estimate the size of the fragments, their number, propagation, and arrangement per square meter. By adjusting the distance of the plates from the projectile and changing their thickness, it was possible to estimate the effective radius of destruction of the fragments in a practical way. However, in this case, several fragmentations had to be carried out, which was associated with a high cost of research. Alternatively, a circle of plates can be divided into several parts, and each part can be placed at a different distance from the fragmented projectile. From the scientific and research point of view, determining the velocity of the fragments with their known mass would allow determination of the kinetic energy. To measure the velocity of standard objects, such as projectiles, the most commonly used are appropriate induction gates, optical gates, or a Doppler radar. However, there are difficulties in measuring the velocity of the fragments that are not present in the case of measuring the velocity of the projectile. When measuring the velocity of the projectile, the direction of the flight path is well known. Moreover, the projectile is the only object that moves during the measurement. In the case of a series of projectiles, the time difference between the individual shots is long enough for undisturbed measurement.

In the case of determining the velocity of the fragments, the process becomes more complicated. The debris spreads out simultaneously in different directions. It is impossible to use gates or a Doppler radar directly close to the fragmented shell. The equipment would be damaged by the detonation wave and debris.

Until now, the velocity of fragments was measured using a chronometer and aluminum foils. It is based on delivering two signals to the chronometer: starting and stopping time measurement. The moment of detonation of the shell is the start of the measurement of time, and the moment the fragment hits the plate, the measurement of time is stopped. Knowing additionally the distance from the shell to the plate, it is possible to calculate the average velocity of the fragment on the flight path.

The measurement is started by two leads attached to the head and connected to a chronometer. They are isolated from each other. Upon detonation, the high temperature melts the insulation between them, causing an electrical short circuit. The chronometer interprets this as a signal to start the measurement. The individual boards are covered with aluminum foils, insulated from the steel board with a laminate. One wire is connected to the steel plate, and the other wire to the aluminum foil. When the aluminum foil, laminate, and board are punctured by a splinter, the foil is shorted with the board, and the circuit is closed, and the timer interprets it as a signal to stop the time measurement. An illustrative diagram is shown in Figure 4.

The method described above is quite simple but considerably inaccurate. Generally, after fragmentation, the plates are covered with splinters’ holes, and it is impossible to estimate which splinter stopped the time measurement. The aluminum foil method does not solve this basic problem and only allows for calculating the average velocity of the splinter. In conclusion, the method with aluminum foils is not accurate enough.

Taking the above into account, the authors decided to use Doppler radar technology for the velocity measurement of the splinters. Two Weibel’s Doppler radars were used during the tests. The first radar (SL-528PE) was located in the bunker about 4 m from the fragmented shell. It was directed towards the most distant plate. The second radar (SL-520P) was placed in the bunker behind the plate. It was directed with a mirror towards the fragmented shell through a small window in the plate (Figure 5).

The radar could not be allocated directly at the detonating object because of the possibility of damage of the equipment. The window in the plate reduced this possibility to the minimum. The configuration scheme is shown in Figure 6.

3. Results

During the stationary detonation test, the 70 mm steel shell was used. The shell was surrounded by four quarter circles made of steel plates with four different radii: 5, 9, 14, 21 m. On each quarter circle, one aluminum foil was stuck and connected to the chronometer. The shell filled by the explosive was detonated by using a blaster and a replacement fuse (Figure 7).

After the detonation, the measurement results were recorded and then analyzed. Both radars recorded the velocities of the splinters. Radar 2 emitted the radiation through the mirror and was able to record the fragment, which moved in a straight line, and registered the velocity of the splinters (directly from the radar point of view). Radar 1, observing the plate from the inside, recorded much more debris, which distorted the velocity chart. Due to its hardware limitation, the chronometer only measured time in three quarter circles.

The velocity versus time graphs (Figure 8, Figure 9, Figure 10 and Figure 11) and the corresponding data in the tables (

Table 1. Recorded data for a separated single splinter (radar 1).

Time (s)	Radial Velocity (m/s)	Range (m)
0.001	1,590,889	1623
0.002	1,528,398	3183
0.003	1,468,089	4681
0.004	1,409,963	6119
0.005	1,354,019	7501
0.006	1,300,257	8828
0.007	1,248,678	10,102
0.008	1,199,281	11,326
0.009	1,152,067	12,502
0.010	1,107,035	13,631
0.011	1,064,186	14,717
0.012	1,023,519	15,760
0.013	985,034	16,764
0.014	948,732	17,731
0.015	914,612	18,663
0.016	882,675	19,561
0.017	852,919	20,429

and

Table 2. Recorded data for a separated single splinter (radar 2).

Time (s)	Radial Velocity (m/s)	Range (m)
0.002	1,626,465	3413
0.003	1,549,289	5001
0.004	1,474,893	6513
0.005	1,403,522	7952
0.006	1,335,423	9321
0.007	1,270,839	10,624
0.008	1,210,017	11,864
0.009	1,153,202	13,045
0.010	1,100,640	14,172
0.011	1,052,577	15,248
0.012	1,009,256	16,278
0.013	970,925	17,268
0.014	937,828	18,222
0.015	910,211	19,145
0.016	888,320	20,044

) are shown below for the chosen detonation, additionally comparing radars 1 and 2.

In order to compare the measurements made with the chronometer (Figure 12) and the radar, the average velocities of the individual flight sections were calculated. The comparison results for the chosen splinter are presented below (

Table 3. The chronometer and the radar average velocities.

	Range
	5 m	9 m	14 m
Chronometer average velocity (m/s)	1688.0	1692.0 *	1485.3
Radar average velocity (m/s)	1668.8	1569.8	1448.35

* Questionable result—should be rejected.

).

4. Discussion

The images recorded by radars 1 and 2 (Figure 8 and Figure 9) show comparatively the distribution of the recorded flight paths of the splinters depending on the width of the recording field.

Significantly, the negative values of the fragment velocity are observed on radar 1. The cause of the signal in the negative velocities, also known as the image spurious signal, is the finite image rejection in the downconverting mixer. Depending on the model of Weibel’s radar, it will have different requirements for the suppression of this image signal, but in all cases, it is suppressed enough for the processing software to identify it as a spurious signal and not create a false track for it. For velocity radars and their fairly simple measurement scenarios, the requirements for the image suppression are quite low (>20 dB compared with the real signal). For larger instrumentation radar systems (like radar 1), the typical performance is in excess of 30 dB, which is more important in these cases as they support scenarios more likely to have many targets occurring at once—some of which might have opposite velocities potentially overlapping with image spurious signals, which might degrade their signal-to-noise ratio and detection probability.

The results recorded by radar 2, thanks to the application of the limited field of view (through the window cut out in the cover), more accurately express the flight paths of the selected fragments. These differences are visible in the comparison of Figure 10 and Figure 11. In the case of the velocity recording signal of the selected fragment from radar 1 (Figure 10), a significant dispersion of the values of the measurement points can be seen on the basis of which the radar software traced the trend line of the fragment’s velocity versus time.

The signal for recording the velocity of the selected fragment from radar 2 (Figure 11) contains the values of the measuring points with a small dispersion in relation to the plotted trend line of the fragment’s velocity versus time. On the basis of the obtained results, it can be concluded that the measurement configuration with radar 1 can be used for the general assessment of the propagation of fragments in the selected angular zone limited by the concave surface of the witness’s plate signal reflection, while the station with radar 2 can be used for the selective measurement of fragments whose velocity is determined continuously, and enabling them to be captured (after using an bullet trap) will allow for determining their kinetic energy.

Regarding the averaged values of the velocity of the splinter (Table 3) for the various measurement methods, it can be concluded that the results are comparable for both 5 and 14 m distances. It should be taken into account that the aluminum foil and the radar most probably measured the velocity of two different fragments (with the differences no more than 1%). Additionally, the differences may be generated during the moment of the start of the measurement time. For the Doppler radar, the moment of starting the measurement is the flash at the moment of detonation. For the chronometer, the measurement starts after the insulation is melted down (which occurs later than the flash). The questionable result of the average velocity calculated by the chronometer for the 9 m distance may be related to the fact of premature electrical short circuit between the foil and the plate.

5. Conclusions and Advice

Doppler radar measurement is a more accurate method compared with the contact method. It allows the measurement of the splinters’ velocity along the entire flight path. In order to reduce the interference caused by other debris, the window in the plate can be reduced proportionally. An interesting solution would be to place the tube from the head to the hole with the mirror. Doppler waves would affect only the objects in the tube, which should improve the quality of velocity recording. Importantly, the radar measurement will allow for experimentally measuring the kinetic energy of the fragment. A bullet trap placed behind the mirror would catch the fragment, which can then be weighed. It is important for the estimation of the kinetic energy and the precise determination of the effective radius of splinters. However, the most important achievement, according to obtained results of experimental research, is the possibility to compare them with the results of numerical simulations. Of course, other noncontact measurement methods can be used for speed measurements, such as the laser method, photonic Doppler method, and high-speed photography; however, this requires many comparative tests with the currently used method to determine the accuracy of measurements and the possibility of protecting measuring devices against splinters.

On the basis of the obtained results, it is possible to refine the numerical model of the fragmentation process so that it can be used to determine safety zones with the required accuracy.