# Assessment of the Sympathetic Detonation of Blasting Caps
## 4 Discussion  
As the main goal of the present study is to evaluate the sympathetic detonation tendency of blasting caps, the main focus is on the correlation of experimental and numerical results. If the experimental approach is a straight forward method that clearly points out the presence of acceptor detonation, the numerical approach is somehow trickier. As previously mentioned, the numerical simulation is based on the use of Lee-Tarver EOS [19]. The Lee-Tarver EOS points mainly at the [PERSON] [19; 20] findings that were later included in [PERSON]'s work [21]. Basically, a stable detonation is achieved when the pressure level reaches a certain value that is specific to each explosive (0.327 Mbar for PETN). Considering this approach, the blasting cap will not be susceptible to sympathetic detonation (in a range of a 0.1 to 0.5 m clearance distance) as long as the pressure recorded by the gauges indicates significantly lower levels (see Table 3). Nevertheless, as experimental tests have proved, the blasting cap detonation manifested at both 100 mm and 200 mm, where, according to numerical simulation, the peak overpressure is less than 0.327 Mbar. the pressure-time curve in Figure 5a is similar to the ones in [PERSON] and [PERSON]'s work [24] at the point that the initiation of the explosive occurs. Additionally, by analyzing Figure 5, it can be observed that the pressure wave shape acting on the blasting cap has a much different profile from the ones usually recorded during a standard gap test. Due to the mismatch between the shock wave's front velocity and donor gas products' front velocity, the first to act on the blast cap is the blast wave, and the gas products pressure shortly afterward, depending on the relative position between the donor and acceptor charges, as can be deduced from Figure 6. The pressure wave profile is also shaped by the reflected blast wave, which is clearly indicated by the numerical simulation. The same outcome can be underlined by theoretical means as well. Therefore, using far-field experimental data (images recorded when the blast wave has already traveled over a 0.6 m distance), the Sedov-Taylor model [25; 26], and [PERSON]'s observations [27], one can predict the distance between the incident blast wave and the gas products' border. Useful data regarding the position of the blast wave and the gas products' border can be extracted by solving Equations (5)-(10) [25; 26; 27; 28; 29]. In Figure 7, a comparison between experimental results and the application of Equations (5)-(10) for two values of the expansion dimensionality factor is presented. \[R_{s}(t)=at^{b} \tag{5}\]  
\[a=\left[\frac{E_{d}/\left(\tau_{0}^{b-n}\right)}{\rho}\right]^{1/\left(n+2 \right)} \tag{6}\]  
\[b=\frac{s+2}{n+2} \tag{7}\]  
\[l_{0}=\left(\frac{3m}{2\pi\rho}\right)^{1/3} \tag{8}\]  
\[\tau_{0}=\frac{l_{0}}{\
u_{TNT}} \tag{9}\]  
\[R_{f}(t)=R_{max}\left(1-e^{-kt}\right) \tag{10}\]  
where \(R_{s}(t)\) indicates the shock front radii; \(a\) and \(b\) are coefficients; \(E_{d}\) is the TNT release energy during detonation (usually 4.1 MJ/kg); \(l_{0}\) denotes a length scale; \(\tau_{0}\) denotes a time scale; \(m\) is the TNT mass; \(\rho\) is the TNT mass density; \(\
u_{TNT}\) denotes the TNT detonation velocity (6940 m/s); \(s\) indicates a factor characterizing the rate of energy release: instantaneous energy release (s = 0) and constant-rate energy release (s = 1); \(n\) is the expansion dimensionality: planar expansion (\(n\) = 1), cylindrical expansion (\(n\) = 2), and spherical expansion (\(n\) = 2). Figure 6: Pressure wave profile (200 mm case). expansion (\(n=3\)); \(R_{f}(t)\) indicates the fireball radii; \(R_{max}\) is the fireball stopping radii (0); and k denotes the drag coefficient. It must be stated that the Sedov-Taylor equation can be applied only to the mid-field region according to Equation (11) [28].