## 2 Experimental Setup Using the Explosive Driven Shock Tube
### Control of the Projectile Flight Trajectory
#### 2.2.1 Projectile Flight Trajectory and Dispersion of Impacts in Free Air  
The experimental setup consists of nine polyurethane plates with dimensions of 1000 mm \(\times\) 1220 mm \(\times\) 50 mm attached to the same number of 80 mm thickness hardboard panels. They are arranged to form an octagon with a diameter of 2150 mm as shown in Figure 3. The polyurethane allows a good visibility of the projectile's impact point. A total of 23 tests are carried out [27]. A detonator and a rear-detonated C4 spherical explosive charge are used to accelerate the selected projectile. A distance of 910 mm separates the charge from the target. Steel spheres with diameters of 5, 7, and 8 mm are used. A steel bar is used for the fixation of the detonator-projectile configuration. An SA5 photon fastcam digital camera is positioned at a distance of 2150 mm from the center of the explosion. The HSC is configured with a frame rate of 50,000 fps and a shutter speed of 1/1,000,000 s\({}^{-1}\). A view from the top enables to track a part of the projectile's trajectory. Two 1500 W light emitting diodes are used to increase the illumination of the setup.  
A typical result at different time steps of the flight trajectory of a 7 mm diameter projectile is shown in Figure 4. First, the projectile is accelerated by the blast wave generated by the explosive. The projectile's initial trajectory is hidden by the flash of the detonation. After its passage through the opaque gas cloud, the first appearance of the projectile is captured as shown in Figure 4a. A straight trajectory visualized by the yellow dashed line can be tracked. A straight trajectory can be seen as shown in the images corresponding to Figure 4b,c. At the end of its straight flight in the air, the position of the projectile impact on the target is recorded.  
Figure 2: Image of the experimental setup using the EDST showing the instrumentation used to visualize the passage of the blast wave front and the projectile at the exit of the tube.  
In a first step, the raw form of the projectile's position (in pixel per frame) versus time is extracted from the images. All the images are processed using an image processing software which enables the determination of the projectile's velocity. The fragment tracking software FTS developed at the Royal Military Academy of Brussels is used [28; 29]. The tracking software uses images generated by a HSC to determine the displacement and the velocity data as function of time for a particular projectile during its flight. The coordinates of the impact points are recorded after each detonation. Figure 5 summarizes the dispersion of all impacts on the target. The area of all impacts is 100 mm \(\times\) 100 mm. The dots represent tests where the projectiles hit the target in a single point. The special symbols, i.e., squares and diamonds, represent tests where the projectile respectively broke up into two and three parts due to the explosion itself.  
In conclusion, the test campaign reveals two main results. The first resides in the capability of the projectiles to maintain an oriented path until impact on the target. The second is that the dispersion of impacts is circumscribed within an area which corresponds to the cross sectional area of the EDST. This means that the EDST can be used for further testing avoiding collision with the shock tube.  
Figure 4: Typical flight trajectory of a 7 mm diameter projectile attached to the front surface of a detonator after being propelled by the explosion (Video S1): (**a**) first appearance of the projectile after its passage through the opaque gas cloud, (**b**) projectile’s trajectory after detonation, (**c**) the projectile maintains a straight flight trajectory till impact on the target.  
Figure 3: Schematic representation of the experimental setup showing the different instruments used to track the projectile flight trajectory.