# Customized Approach to Greenhouse Gas Emissions Calculations in Railway Freight Transport
## 3 Mathematical Formulation
### Proposal of a Customized Approach to GHG Emission Calculations in RFT for the AI  
A proposal for a customized approach to the GHG emission calculations in the context of RFT for the AI is presented in Figure 2. The proposed approach is based on the conclusions obtained from the semi-structured interviews and comparative content analysis of available GHG emission calculators. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**No.**} & \multirow{2}{*}{**Source**} & \multirow{2}{*}{\begin{tabular}{c} **Railway** \\ **Transport** \\ **FC** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Transport** \\ **Wehicle** \\ **PGC** \\ **PC** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Own** \\ **Vehicle** \\ **Option** \\ **Optim** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **Restrictive** \\ **Condition** \\ **Implementation** \\ **Transport** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **One-Way** \\ **and** \\ **and** **SO\({}_{\text{2e}}\)** \\ **Outputs** \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} **CO\({}_{\text{2e}}\)** \\ **and** **SO\({}_{\text{2e}}\)** \\ **Compuits** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Total and** \\ **Average** \\ **Emission** \\ **Outputs** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **WtW, WT** \\ **and** **TtW** \\ **Calculation** \\ **Approach** \\ \end{tabular} } \\ \hline
1 & [67] & RPT & NFA & NFA & NFA & NFA & NFA & NFA & NFA \\ \hline
2 & [68] & RPT & NFA & NFA & NFA & NFA & NFA & NFA \\ \hline
3 & [69] & RPT & NFA & NFA & NFA & NFA & NFA & NFA \\ \hline
4 & [70] & RPT & NFA & NFA & NFA & NFA & NFA & NFA & NFA \\ \hline
5 & [71] & RFT & NA & Y & NA & Y & Y &
\begin{tabular}{c} Only total \\ emissions \\ \end{tabular} & Y \\ \hline
6 & [72] & RFT & NA & NA & NA & NA & \
\begin{tabular}{c} Only \\ CO\({}_{\text{2e}}\) \\ \end{tabular} &
\begin{tabular}{c} Only total \\ emissions \\ \end{tabular} & NA \\ \hline
7 & [73] & RFT & NA & NA & NA & NA & \
\begin{tabular}{c} Only \\ CO\({}_{\text{2e}}\) \\ \end{tabular} &
\begin{tabular}{c} Only total \\ emissions \\ \end{tabular} & Y \\ \hline
8 & [74] & RPT & NFA & NFA & NFA & NFA & NFA & NFA & NFA \\ \hline
9 & [75] & RPT & NFA & NFA & NFA & NFA & NFA & NFA \\ \hline
10 & [76] & RFT & NA & NA & NA & \
\begin{tabular}{c} Only \\ CO\({}_{\text{2e}}\) \\ \end{tabular} &
\begin{tabular}{c} Only total \\ emissions \\ \end{tabular} & NA \\ \hline
11 & [77] & RFT & NA & NA & NA & NA & \
\begin{tabular}{c} Only \\ CO\({}_{\text{2e}}\) \\ \end{tabular} &
\begin{tabular}{c} Only total \\ emissions \\ \end{tabular} & NA \\ \hline
12 & [78] & RPT & NFA & NFA & NFA & NFA & NFA & NFA \\ \hline \hline \end{tabular}  
Notes: PC—passenger cars, CB—car bodies, FC—freight containers, CO\({}_{\text{2e}}\)—carbon dioxide equivalent, SO\({}_{\text{2e}}\)—sulfur dioxide equivalent, WtW—Well-to-Wheel approach, WT—Well-to-Tank approach, TtW—Tank-to-Wheel approach, RT—railway passenger transport only, RT—railway freight transport only, Y—Yes, N—No, NA—not available, NFA—not further analyzed due to inapplicability to RFT.  
\end{table} 
Table 1: The content analysis results of RFT emission calculators (authors based on [67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78]). The customized approach to GHG emission calculations for RFT consists of five consecutive user steps. In the first step, the user selects a specific type of transported cargo (PC, CB, or FC) and a specific railway car (RC\({}_{1-32}\)). In the second step, the user selects between dependent or independent traction, or can choose the ratio of dependent and independent traction. Subsequently, information about the selected railway car and information about the selected traction is retrieved from the database of railway cars. In the next steps, the GHG emission calculations are different according to the type of transported cargo (PC, CB or FC).