Is a Straight Line From Impact to Rest in Momentum Correct?

General Crash Reconstruction Tecnhiques
Crash tests, Pole Impacts
brian
Posts: 499
Joined: Tue Jul 14, 2009 10:52 am

Is a Straight Line From Impact to Rest in Momentum Correct?

Post by brian »

Q: Is using an assumption of a straight line approximation between Impact and Rest the correct departure angle for use in Momentum?

A: A lot of effort in the early CRASH research was trying to figure out to get the best approximation on the separation conditions including direction (course angle).
In many simplified momentum solution procedures, the assumption is to use a straight line direction of the vehicle from impact to rest. This assumption of a straight line from impact to rest, particularly for vehicles which rotate as a result of the collision impact, can lead to large errors in momentum analyses.

At separation a vehicle has
  • a speed,
  • an angular velocity and
  • a course angle (direction of the velocity vector).
With consideration of the vehicle rotation due to the impact, the vehicle direction cannot be a straight line to the position of rest.
Consider that if the course angle of a rotating vehicle at separation is assumed towards position of rest, then as the vehicle rotates it will travel in a direction away from the position of rest.
The rotating vehicle generally follows a curved path and with an ‘upstream’ direction:
  • By ‘upstream’ we mean that for a clockwise direction of rotation at separation the vehicle path direction (course angle) has to be to the left of the position of rest so that as it rotates it will travel to the correct position of rest.
    For a counter-clockwise direction of rotation at separation the vehicle direction (course angle) has to be to the right of the position of rest. Just how much to the left or right is the question!
To further complicate the issue, consideration of possible end of rotation positions and run out![/list]
Sometimes referred to as a dogleg trajectory

In our CRASH97 paper we suggested using the SMAC trajectory simulation model to refine the separation conditions:
  • Start with a Marquard approximation of separation speeds and then
  • Use a SMAC simulation to iterate the separation speed, angular velocity and course angle until you get a good match of the position of rest.
    • The CRASH97 research was done in the early days of personal computers (1995-1997) where the idea of iterating SMAC was too time consuming to be practical.
      In 2000 as part of our SMAC2003 research paper we found computers were fast enough to do the whole solution procedure of SMAC (collision and run out to rest positions) with an automatic iteration of SMAC:
      • Start with Marquard/CRASH approximations of the impact speeds and then
      • Iterate SMAC to find a solution.
The point is with simplified Momentum solution procedures the approximation of separation speeds, angular velocities and course angle must be approximated in a 'single shot' which sometimes does not include a test of those appoximations.
A trajectory simulation of the vehicles, like which can be done with SMAC, provides a good test of the eparation speed and angles approximations.

A good way to bracket the effects of approximations is to vary each of the assumptions (exit angle, effective drag, etc) to see which is most sensitive and has the greatest effect on the results.
Papers written recently in SAE on Collision Reconstruction recognize the shortcomings of 'single shot' approximations of separation angles and sensitivities associated with those approximations and so have suggested performing a sensitivity analyses Also the SMAC simulation program also allows testing and refinement of 'single shot' approximations.
Here are some samples of the curved path option, end of rotation designation, etc from CRASH
Crash Traj refinements.jpg
Crash Traj refinements.jpg (60.91 KiB) Viewed 41 times
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