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:

\[\Delta v(A_1) = \|v_1(t_\mathit{aftercol})\|_2-\|v_1(t_\mathit{beforecol})\|_2.\]

A more complex formula for two actors taking the masses into account is given by

\[\Delta v(A_1, A_2, t) = \frac{m_2}{m_1+m_2}(\|v_2(t)\|_2-\|v_1(t)\|_2),\]

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

\[P(A_1) \approx \left(\frac{\Delta v}{31.74\text{m}/\text{s}}\right)^4.\]

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