## 2 Theoretical Approach  
The state-of-the-art in the field describes the characteristics of screening by determining the transmittance, which is a characteristic that just theoretically defines the quality of the smoke. In the case of a real military combat situation, smoke screening time is the only essential data because transmittance value fails to provide all of the required information that a soldier needs to decide, in real-time, the best procedure for obscuring a target. The concealing area and available standing time [20] have been mentioned as essential parameters to evaluate the smoke protection capability associated with a diffusion equation. Other researchers investigated the timing of ignition and burning [19] in relation to effective screening and smoke cloud dissemination. However, no research has been found to date on IR screening time analysis and how we can ascertain this parameter. The IR screening time (ST) is an essential characteristic of the smoke cloud and a mandatory condition for an obscuring system. ST represents the value expressed in seconds for the screening efficiency, which determines the tactical period during which a target can pass through the enemy firing range unnoticed. According to [PERSON], the mathematical expression of the observation probability (\(OP\)) is [21]:  
\[OP=\frac{N_{t}}{N_{50}}=\frac{\
u(\lambda)}{\
u_{t}}\cdot\frac{1}{N_{50}}= \frac{d_{c}}{R}\cdot\frac{\
u(\lambda)}{N_{50}}=\frac{\sqrt{L_{t}\cdot h_{t}}}{ R}\cdot\frac{\
u(\lambda)}{N_{50}} \tag{1}\]  
where \(OP\) is the observation probability, \(N_{t}\)--number of cycles resolved across the target (cycles/mrad), \(N_{50}\)--number of cycles resolved across target critical dimension (cycles/mrad), \(\
u(\lambda)\)--spatial frequency (cycles/mrad), \(\
u_{t}\)--target spatial frequency, \(d_{c}\)--target feature size (m), \(R\)--path length (km), \(h_{t}\)--target height (m) and \(L_{t}\)--target length (m). Assuming that the screening time is inversely proportional to the probability of observation described by [PERSON], a series of parameters were defined that are useful to establish the screening time. As a first step, it is essential to calculate the mass of aerosols (\(m_{a}\)) generated by a certain amount of pyrotechnic composition (\(m_{pc}\)):  
\[m_{a}=m_{pc}\cdot k_{c} \tag{2}\]  
where \(k_{c}\) is the combustion coefficient (%) defined as a relationship between the mass of the residue (\(m_{r}\)), mass of released gases after combustion (\(m_{g}\))--calculate in relation (4) and the initial mass (\(m_{pc}\)) of pyrotechnic composition:  
\[k_{c}=\left(1-\frac{m_{r}+m_{g}}{m_{pc}}\right)\cdot 100 \tag{3}\]  
\[m_{g}=\frac{V_{sp}\cdot m_{pc}}{22.418}\cdot M_{g} \tag{4}\]  
where 22.418 (L/mol) represent the volume occupied by 1 mol of gas at STP (standard temperature and pressure), \(M_{g}\) is the molar mass of gas elements (g/mol), and \(V_{sp}\) is the specific volume of the composition (L/kg) determined in practice. Meanwhile, the gas volume (\(V_{g}\)) generated by a specific pyrotechnic composition mass is equal to:  
\[V_{g}=V_{sp}\cdot m_{pc} \tag{5}\]  
IR screening capacity is characterized by the coverage coefficient parameter (\(k_{oc}\)) of the dispersed volume of the aerosols that is calculated using the ratio between the gas volume, \(V_{g}\) and the total screened volume, \(V\). In the case of the chamber test, \(V\) is the volume of the chamber (\(V_{ch}\) = 0.512 m\({}^{3}\)--that is kept constant) and for the real field test \(V\) is the disseminated smoke volume (\(V_{s}\))--experimental determinate for each charge (Figure S1 from Supplementary Materials):  
\[V_{s}=L_{s}\cdot h_{s}\cdot l_{s} \tag{6}\]  
\[k_{oc}=\frac{V_{g}}{V}=\frac{V_{sp}}{V}\cdot m_{pc} \tag{7}\]  
where \(L_{s}\) is length of the smoke cloud, \(l_{s}\) is the width of the smoke cloud, and \(h_{s}\) is the height of the smoke cloud.