deletions | additions       diff --git a/Methodology Measurements TTC.tex b/Methodology Measurements TTC.tex  index e7ba1e9..4d09656 100644  --- a/Methodology Measurements TTC.tex  +++ b/Methodology Measurements TTC.tex 
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Time-to-collision (TTC) is one of the most popular surrogate safety measures. It is a method of quantifying proximity to danger. Time-to-collision measures the time, at a given interaction-instant $t_0$ until two road users collide, if they collide based on the motion prediction model. In the simplest form, e.g. constant velocity, time-to-collision is the ratio of differential velocity and differential distance. A TTC value of 0 seconds is, by definition, a collision. TTC is particularly useful as it has the same dimensions as some important traffic accident factors such as user reaction time and breaking time. Larger values of observed TTC thus provide greater factors of safety for these driving tasks.  Time-to-collision is measured instantaneously: a new value of TTC may exist for every interaction-instant. A pair of users may thus have a series of TTC observations evolving over time.\subsubsection{Post-encroachment time}  While TTC and motion prediction model collision potential, other surrogate safety measures aim to measure collision proximity from crossing, but not necesarily colliding movements. Trajectory data is detailed enough to provide gap acceptance time (GT) and post-encroachment times (PET). These are measures that broadly characterise how aggresively merging and crossing tasks are performed, respectively. As such, there is generally only one of these measures for the entire common time interval of a pair of road users.  For the crossing zone defined by the intersection of the two trajectories of a pair of road users, the post-ecnrochment time measure the time between complete departure of the first arriving vehicle, and first arrival of the last arriving vehicle. If PET < 0, a collision ensues. As such, higher PETs demonstrate safer behaviour.  Gap acceptance time similarly measures arrival and departure of a road user at a common crossing zone, but in this case, the crossing zone occurs inline during a merging task, usually followed by following behaviour.