sec-points-allocation.tex

% !TEX TS-program = xelatex
% !TEX encoding = UTF-8 Unicode
\documentclass[gap.tex]{subfiles}
\begin{document}
\label{sec:points-allocation}
The available points for each task are \(1000*TaskValidity\). These points are
distributed between distance points, time points, leading points and arrival
points. The distribution depends on the percentage of pilots who reached goal
before the task deadline, compared to pilots who launched, as well as the
chosen goal form. It is expressed in terms of weight factors for each of the
four point categories: Distance weight, time weight, leading weight and arrival
weight. Weight factors are always between 0 and 1. A weight factor of 0.5 for
distance, for example, means that 50\% of the day’s available overall points
are available for distance points.
\begin{align*}
    GoalRatio &= \frac{NumberOfPilotsInGoal}{NumberOfPilotsFlying} \\
    DistanceWeight &= 0.9 - 1.665 * GoalRatio + 1.713 * GoalRatio^2 - 0.587 * GoalRatio^3 \\
    \hgh{LeadingWeight} &= \frac{1 - DistanceWeight}{8} * 1.4 \\
    \pgh{GoalRatio = 0 : LeadingWeight} &= \frac{BestDistance}{TaskDistance} * 0.1 \\
    \pgh{GoalRatio > 0 : LeadingWeight} &= \frac{1 - DistanceWeight}{8} * 1.4 * 2 \\
    \hgh{ArrivalWeight} &= \frac{1 - DistanceWeight}{8} \\
    \pgh{ArrivalWeight} &= 0 \\
    TimeWeight &= 1 - DistanceWeight - LeadingWeight - ArrivalWeight \\
    AvailableDistancePoints &= 1000 * TaskValidity * DistanceWeight \\
    AvailableTimePoints &= 1000 * TaskValidity * TimeWeight \\
    AvailableLeadingPoints &= 1000 * TaskValidity * LeadingWeight \\
    AvailableArrivalPoints &= 1000 * TaskValidity * ArrivalWeight
\end{align*}

\begin{figure}[ht]
    \centering
    \input{gph/points-allocation-hg}
    \caption{Points allocation for hang gliding}
\end{figure}

\begin{figure}[ht]
    \centering
    \input{gph/points-allocation-pg}
    \caption{Points allocation for paragliding}
\end{figure}

\begin{hg}
From the above it follows that in hang-gliding, if nobody reaches ESS, then
a maximum of 900 points are available for distance and 18 points for leading
but, of course, no points for time nor arrival. This is also the maximum
possible number of points for an open distance task.
\end{hg}

\begin{align*}
    numberOfPilotsAtESS = 0 : \\
    \\
    AvaliableDistancePoints &= 1000 * TaskValidity * DistanceWeight \\
    AvailableTimePoints &= 0 \\
    AvailableLeadingPoints &= 1000 * TaskValidity * LeadingWeight \\
    AvailableArrivalPoints &= 0 \\
    \max(AvailableDistancePoints) &= 900 \\ 
    \max(availableLeadingPoints) &= 18 \\
    \max(availableTotalPoints) &= 918
\end{align*}
\end{document}