Classic Example of Sensitivity of Momentum Solutions

General Questions related to the Momentum Based Analysis programs
#pc-crash #virtualcrash #crash
MSI
Site Admin
Posts: 2296
Joined: Thu Jun 18, 2009 12:37 pm

Classic Example of Sensitivity of Momentum Solutions

Post by MSI »

Decided to create a separate topic since I wanted to link to this classic example in our Momentum "Cone of Departure" Question and had to search.
So we made it a separate post. A classic example of problems with the sensitivity of a linear momentum solution which includes the simplifying assumption of an instantaneous exchange of momentum is when it is applied to a t-bone type collision.
  • When a lighter car crosses the path of a heavier car/truck and the lighter vehicle is struck in the side by the heavier vehicle.
    • If the heavier striking car/truck happens to swerve before the impact, either to the left or the right, the degree or two of change of impact angle can result in dramatic changes in the results of a linear momentum solution.
    Why?
    • The swerve by the heavier vehicle will produce a change in the separation angles. The change in separation angles, if all attributed to the smaller vehicle speed
      • Which it will be if the impact angle of the striking heavier vehicle is assumed to be 0 (zero) degrees and/or it the collision is assumed to be a at a 90 degree impact
      Any swerve will dramatically change the linear momentum solution approximated speed for the smaller lighter vehicle.
      The result Depends on the direction of the swerve!,
      The small vehicle will be 'reconstructed' as either
      • Going very fast in the forward or
      • Going very fast in the reverse direction,
        All depends on the direction of any pre-impact swerve by the truck OR if the impact is NOT perfectly 90 degrees.
      Main Point:
      Depending on the difference in the weights of the vehicles
      AND
      • Assumption (or not) for (pre-impact swerve? or not) affecting the impact angle (or not) of the heavier vehicle...
      • Any angularity in the actual impact
      The results can produce very large speeds for the crossing car forward OR backwards!
What calling this ‘classic’ example is meant to illustrate is that when applying a Linear Momentum solution procedure to ANY accident you need to test sensitivities of inputs (angles at impact and angles at separation).
  • If a small change in an angle makes a dramatic change in the results then obviously you need to focus on defining and refining the inputs as well as consider using a more sophisticated solution procedure
  • Test and refine any instantaneous momentum results with something like a SMAC simulation which is essentially like running a mathematical full-scale crash test and can therefore test the effects of swerving the larger heavier vehicle to the left or right.