## 4 Conclusions  
The peak pressure value of the air blast wave from a total of 100 records corresponding to the detonation of different explosive charges in the open air was analyzed. These records can be separated into two basic groups: records from open-air detonations of a gelatinous dynamite-type explosive and records from open-air detonations of a TNT-type explosive.  
The most important result achieved was the definition of an air wave attenuation law, overpressure \(S_{b}\) as a function of the scaled distance \(Z\), for the determination of the overpressure peak due to the detonation of explosive charges in the outdoors. The law is simpler than others since it only requires the determination of two empirical parameters that can be determined with a smaller number of samples.  
The model predicts the peak value of the air blast wave \(S_{b}\) (kPa) from the detonation of a given or equivalent TNT explosive charge in the open air that relates to the value of such variable, \(S_{b}\), with the scaled distance \(Z\) (m/kg\({}^{1/3}\)):  
\[S_{b}=396.27\cdot Z^{-1.280}\]  
where \(Z=R/{W_{eq}}^{1/3}\), that is, the distance \(R\) (m) divided by the cubic root of the equivalent TNT mass \(W_{eq}\) (kg).  
Figure 8: Overpressure measured as a function of scaled distance for the detonation of pure TNT and equivalent TNT (dots are actual values while lower and upper lines correspond to Equation (8) and Equation (9) respectively).  
By using a safety coefficient of 1.35, the predicted \(S_{b}\) is higher than actual \(S_{b}\) in more than 90% of the cases:  
\[S_{b}=534.96\cdot Z^{-1.280}\]  
It has been demonstrated that this law is valid in a wide range of the reduced distance, with \(Z\) varying between 5.71 and 86.74 m/kg\({}^{1/3}\), and in a wide range of the air wave, with \(S_{b}\) between 1.42 and 63.8 kPa. In this way, the attenuation law is useful both for the prediction of the air blast wave due to the detonation of charges of a few kgs of explosives (such as the shaped charges used in civil works for the demolition of metallic structures) and for the prediction of the air wave in the case of the detonation of several tens of kgs of explosives (such as explosive detonations by accident or terrorist bombs).  
The model proposed aims to serve as a basis for the design of protection and containment elements, but it is considered necessary to continue testing with full-scale explosives, in order to further limit other parameters involved in the propagation of the resulting wave of a detonation, tests that are difficult to carry out because they are of a destructive nature and because they are controlled materials for which there is authorization for consumption, qualification, and training.  
Conceptualization, R.R. and J.A.M.; methodology, J.A.M. and R.R.; investigation, J.A.M., R.R., M.B.D. and S.A.; data curation, J.A.M.; writing--original draft preparation, R.R., J.A.M. and S.A.; writing--review and editing, R.R. and J.A.M. All authors have read and agreed to the published version of the manuscript.  
This research was carried out in the framework of the project \"_Espccificaciones de diseho y estructurales para apramiento de terminales de transporte con riesgo de ataque terrorista_\" funded by the Spanish Ministry for Science and Innovation (No. Exp. 16-08).  
Not applicable.  
The article provides all data used in this research.  
The authors declare no conflict of interest.