Time-To-Collision (TTC)

time to collision (ttc)

The time that remains until a collision between two vehicles would have occured if the collision course and speed difference are maintained (https://resolver.tudelft.nl/uuid:8fb40be7-fae1-4481-bc37-12a7411b85c7: a time-based analysis of read user behaviour in normal and critical encounters)

TTC is the time until a colllision between the vehicles would occur if they kept their present course at their present rates (Intersection Safety Assessment Using Video-Based Traffic Conflict Analysis - The Case Study of Thailand)

Source:

T T C_{i} (t) = \frac{X_{i - 1} (t) - X_{i} (t) - l_{i}}{V_{i} (t) - V_{i - 1} (t)}

where:

$X_{i} (t) :$ Position of vehicle $i$
$X_{i - 1} (t) - X_{i} (t) :$ Relative distance
$V_{i} (t) :$ Speed of vehicle $i$
$V_{i} (t) - V_{i - 1} (t) :$ Relative speed
$l_{i} :$ Length of vehicle $i$

If I understand correctly, this is defined at any point in space-time (even if the objects are not on collision course, but are tracing conflicting trajectories). The minumum value of $T T C$ calculated is $T T C_{m i n}$ .
If the vehicles are on a collision course, the last value of $T T C$ calculated before an evasive action is the $T A$ (Time To Accident (TA)).

[?] Can TTC decrease and increase in an event before an evasive action is taken?

(Intersection Safety Assessment Using Video-Based Traffic Conflict Analysis - The Case Study of Thailand) defines TTC as:

T T C = \frac{S}{C S}

where:

$S :$ conflict distance - relative distance from the position of vehicle taking the evasive action to the potential conflict point
$C S :$ conflict speed - speed of the relevant vehicle while taking the evasive action

Critical TTC values

Generally, TTC lower than the perception and reaction time should be considered unsafe (Application of proximal surrogate indicators for safety evaluation - A review of recent developments and research needs)

Thresholds values according to [[Intersection Safety Assessment Using Video-Based Traffic Conflict Analysis - The Case Study of Thailand]]