Delta-v (\(\Delta v\))#
Description#
\(\Delta v\) is the change in speed over collision duration and widely used in collision databases, where it is typically calculated from post-collision measurements [Gabauer2006]. Introduced in the 1970s [Carlson1979], it uses the difference in speed to estimate the probability of a severe injury or fatality:
A more complex formula for two actors taking the masses into account is given by
for which also probabilistic studies have been done [Shelby2011]. An extended \(\Delta v\) measure, which is additionally considering the mass as well as the driving angles of the collision participants, has been discussed by Laureshyn et al. [Laureshyn2017].
Joksch [Joksch1993] presents a model connecting \(\Delta v\) to the probability \(P\) of a two vehicle collision leading to a fatality using
This connection provides an easily interpretable measure.
Properties#
Run-time capability#
Yes
Target values#
70 km/h [Shelby2011] (deadly collisions), 40 km/h [Ryb2007] (higher mortality rate)
Subject type#
Any, but requires data basis for the target values depending on the involved traffic participants
Scenario type#
Mainly collisions
Inputs#
Assuming one traffic participant: \(v_1(t_\mathit{aftercol})\) and \(v_1(t_\mathit{beforecol})\).
Assuming two traffic participants: velocities \(v_i\) and masses \(m_i\) for \(i \in \{1, 2\}\) over time
Output scale#
\(\left(-\infty,\infty\right)\), velocity (m/s), ratio scale, or \(\left[0,1\right]\), probability, ratio scale
Reliability#
High reliability for collisions, greatly reduced for near-miss scenarios
Validity#
High, if used to estimate injury severity of a collision [Gabauer2006]; very low if used for non-collision scenarios
Sensitivity#
High for severity component of criticality, as it is often associated with a high \(\Delta v\), might also depend on DMM and MM
Specificity#
Medium, non-criticality of collisions can be partially evaluated, but other factors influence non-criticality, e.g. impact angle and torsional rigidity of the vehicles
Prediction model#
None if used a-posteriori.
Otherwise:
Time window#
Duration of collision
Time mode#
Linear time