# SimEx: A Tool for the Rapid Evaluation of the Effects of Explosions
## 2 SimEx Capabilities
### Other Calculation Assistants
#### 2.2.4 Damage to People  
SimEx includes an assistant for estimating damage to people using the widely accepted probit (_probability unit_) functions [58,59] provided by the TNO's Green Book [9] and summarized in Table 3. For each type of injury or cause of death (eardrum rupture, lung injury, etc.), a probit function is defined that depends on the blast parameters: side-on, dynamic or reflected peak overpressure (depending on the body position), impulse per unit area, etc. For primary injuries, lethality due to lung damage is evaluated together with the probability of eardrum rupture. For tertiary injuries, lethality is evaluated for shock-induced body displacement and subsequent direct impact, either with the head or the whole body [29].  
\begin{table}
\begin{tabular}{l c} \hline
**Effect** & _Probit Function_ \\ \hline Primary injuries & \\ \hline Eardrum rupture & \(\Pr=-12.6+1.52\ln p^{\circ}\) \\ Death due to lung damage & \(\Pr=5-5.74\ln\biggl{(}\dfrac{4.2}{p_{\text{ef}}^{\circ}/p_{1}}+\dfrac{1.3}{i/ (p_{1}^{1/2}m^{1/3})}\biggr{)}\) \\ \hline Tertiary injuries & \\ \hline Death due to displacement & \(\Pr=5-2.44\ln\biggl{(}\dfrac{7380}{p^{\circ}}+\dfrac{1.3\times 10^{9}}{p^{ \circ}i}\biggr{)}\) \\ and whole-body impact & \(\Pr=5-8.49\ln\biggl{(}\dfrac{2430}{p^{\circ}}+\dfrac{4\times 10^{8}}{p^{ \circ}i}\biggr{)}\) \\ \hline \end{tabular}
\end{table}
Table 3: _Probit_ functions used to estimate the probability of different types of primary and tertiary injuries. \(\Pr\) is the _probit_ value, \(p^{\circ}\) [Pa] the peak overpressure, \(p_{\text{ef}}^{\circ}\) [Pa] the maximum effective overpressure, depending on the relative orientation of the person with respect to the shock wave, \(p_{1}\) [Pa] the atmospheric pressure, \(1/A\) [Pa \(\cdot\) s] the impulse per unit area and \(m\) [kg] the weight of the person [9].  
Figure 7: Interface of the primary fragment calculation assistant showing the initial deceleration chart, which provides the fraction of the initial velocity, \(u/u_{\text{f}}\), achieved at a certain distance (contour lines), given the fragment mass, \(m_{\text{f}}\), and material (e.g., lead), and the atmospheric conditions (e.g., ISA mean sea level). Fragments are assumed spherical.  
The appearance of the interface is shown in Figure 8. All necessary parameters can be selected on the left: size, type, and geometry of the explosive charge, as well as the body position relative to the incoming pressure wave, which determines whether side-on, dynamic, or reflected pressure is used to compute the peak overpressure and impulse. The rest of the window presents the results both numerically and graphically, using overpressure-impulse diagrams on the left and CW-S diagrams on the right, with primary injuries shown above and tertiary injuries below. Overpressure-impulse diagrams display the characteristic overpressure-impulse-distance curve for the selected charge weight to facilitate the interpretation of results [60], while CW-S diagrams include a diagonal dashed line indicating the approximated position of the fireball radius, corresponding roughly to an scaled distance \(Z=d/W^{1/3}=1\) m. Above this line, the Freidlander waveform is not valid, and the blast wave parameters are increasingly imprecise [1].