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\section{Trade Method, Rationale and Organization}  \label{sec:trade_method}  %Please do not forget to add new symbols to the nomenclature e.g.: \nomenclature{$t_{element}$}{Thickness coefficient of plate \nomunit{[$-$]}}  To rely on a mathematical method to choose the weights for the criteria presented in Section~\ref{sec:trade_criteria}, the Analytical Hierarchy Process (AHP) was chosen. According to this method, the objective for the trade-off is stated first, after which the criteria are listed, followed by the different alternatives. Then, the criteria are compared pairwise and it is determined which criterion of the two compared ones is more important for the objective. Thereafter, a factor is assigned, by how much the importance differs, as can been seen in Table~\ref{tab:criteriafactors}~\cite{AHPtable}.  \begin{table}[htbp]  \centering  \caption{Weight factors for the Analytical Hierarchy Process}  \label{tab:criteriafactors}  \centering  \begin{tabular}{l l l}  \toprule  \textbf{Factor} & \textbf{Meaning} & \textbf{Explanation} \\ \toprule  1 & Equal Importance & Both elements contribute equally to the objective \\ \hline  3 & Moderate Importance & Experience/Judgement slightly favour one element \\ \hline  5 & Strong Importance & Experience/Judgement strongly favour one element \\ \hline  7 & Very Strong Importance & One element is strongly favoured; as demonstrated in practice \\ \hline   9 & Extreme Importance & Highest possible order of affirmation for favouring one element \\  \bottomrule  \end{tabular}  \end{table}  %\subsection{Sensitivity Analysis}  %To analyse the sensitivity of different criteria, the factors have to be altered.  After choosing the factors, the criteria are compared in a matrix showing their relation. Thereafter, the same approach is taken for the alternatives. They are compared pairwise with the same factors for each criterion simultaneously. Thereby, they can be compared either qualitatively or quantitatively. Since at this stage of the project no exact values are known yet, all comparisons are done qualitatively, meaning that they are assigned a value based on the expectation for the respective alternative in this criterion or category. The alternatives are also ordered in matrices, one for each criterion.  %% Do we want to include the code or not??  In order to facilitate this process a Python program was written. This program asks the user to compare all of the criteria two by two. Then all these comparisons are put into a matrix and its eigenvalue is computed. This yields a vector with the weights of the different criteria.   The part for the options is written in the same way; they are compared two by two and these values are put in a matrix. The eigenvectors of these matrices are the rankings of the options for each criteria. If the matrix of these eigenvectors is multiplied with the weights, the ranking of the options is obtained.  diff --git a/Chapters/7b.Trade_Criteria.tex b/Chapters/7b.Trade_Criteria.tex  new file mode 100644  index 0000000..39105ec  --- /dev/null  +++ b/Chapters/7b.Trade_Criteria.tex 
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\section{Trade-Off Criteria}  \label{sec:trade_criteria}  %Please do not forget to add new symbols to the nomenclature e.g.: \nomenclature{$t_{element}$}{Thickness coefficient of plate \nomunit{[$-$]}}  In order to perform a trade-off and thus find the ideal configuration and subsystems, criteria have to be defined that are deemed favourable for the respective components. Therefore, the requirements as well as performance and stakeholder needs are considered.  This section describes the criteria that are important in the configuration trade-off process. Firstly, the criteria for the entire system and thus the configurations that were defined beforehand are outlined. Thereafter, the separate criteria for the individual subsystems are named. To keep the trade-off practical for the top-level configuration, only four main criteria are considered.  \subsection{Criteria for the Complete Configurations}  For the entire aircraft, the following criteria are particularly important:  \begin{itemize}  \item[]\textbf{L/D} The aircraft should produce lift efficiently, since cruise and climb have to be performed with minimum power. This is important since the aircraft is newly developed and electric and power consumption should be kept at a minimum. Also, the drag should be kept low. To judge the efficiency and many flight performance characteristics, the lift per drag ratio should be investigated.   \item[]\textbf{Complexity} A more complex design introduces additional costs and efforts to realize the design. In order to stay within the proclaimed boundaries, a less complex design is favourable. Also, increased complexity will make production more difficult and may lead to the need for subcontractors.  \item[]\textbf{Maneuverability} During the race, the aircraft has to perform demanding and complex maneuvers. To allow for a fast lap time and safe operation, the pilot has to be fully in control at all times. Since many maneuvers, such as knife-edge-turns, require a fast roll rate, but only fewer maneuvers take place in vertical direction, the maneuverability in lateral direction was deemed more important than in longitudinal direction. This was considered in the criteria comparison.  \item[]\textbf{Propulsive Efficiency} Propulsive efficiency defines the use of the available resources, and thus allows to judge the performance in terms of demand. Also, for the same origin of electricity, a better propulsive efficiency can yield information on the expected sustainability of a system. Since the race is short and demands full power over its time, propulsive efficiency was deemed less important compared to the other criteria. It would have a far higher value when considering a long range or long time mission.  \end{itemize}  \subsection{Criteria for the Subsystems}  Since the subsystems perform different tasks, different criteria are important. Weight, complexity and performance, however, are always crucial, whereby performance is to be considered with respect to the individual subsystems too, for example, either deliver as much power per energy consumed (propulsion unit) or provide structural integrity and shield the pilot (fuselage). The trade-off criteria are shown in Table~\ref{tab:subsyscriteria}. The cost of a subsystem is often corresponding to the complexity of the design, which is considered in cases where it is complicated to determine cost influences of a certain design, such as for the control system, or where the complexity greatly influences the manufacturability. These aspects are closely related. Also, the readiness of technology is considered in subsystems that are likely to make a jump in its development over the next 10 years and or that are not ready nowadays to a point where they are fully applicable. On top of that, safety is considered when the system can potentially directly harm the pilot.  \begin{table}[htbp]  \centering  \caption{Criteria for the trade-off of the subsystems}  \label{tab:subsyscriteria}  \centering  \begin{tabular}{l l p{0.16\textwidth} p{0.16\textwidth} p{0.16\textwidth} p{0.16\textwidth}}  \toprule  \textbf{Subsystem} & \textbf{Criteria 1} & \textbf{Criteria 2} & \textbf{Criteria 3} & \textbf{Criteria 4} & \textbf{Criteria 5} \\ \toprule  \textbf{Power} & Weight & Cost & Performance & Readiness of Technology & Sustainability \\   \rowcolor{grey} \textbf{ Propulsion} & Weight & Cost & Performance & Readiness of Technology & Power Consumption \\   \textbf{Fuselage} & Weight & Cost/Complexity of Design & Drag & Structural Integrity & Safety \\  \rowcolor{grey} \textbf{Landing Gear} & Weight & Cost/Complexity of Design & Drag & Structural Integrity & Safety \\   \textbf{Empennage} & Weight & Cost & Performance & Size & Complexity of Design \\   \rowcolor{grey} \textbf{Wing} & Weight & Cost & Performance & Size & Complexity of Design \\  \textbf{Control} & Weight & Cost/Complexity of Design & Performance & Usable for pilot & Safety \\ \bottomrule  \end{tabular}  \end{table}