Is a straight line from impact to rest in Momentum correct?

Questions/Topics related to Simplified Momentum Analysis and related computer programs
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brian
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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 vehicle rotation due to the impact the vehicle direction can not be a straight line to the position of rest. 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. It 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) at separation 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 at separation (course angle) has to be to the right of the position of rest. Just how much to the left or right is the question!
(and to further complicate the issue, consideration of possible end of rotation posititions and run out!)
In our CRASH97 paper we suggested using the SMAC trajectory simulation 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.
This 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 does not include a test of those appoximations. A simulation like SMAC provides a test of the 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 appoximations and so have suggested performing a sensitivity analyses (for example using the ‘Monte Carlo Method’ or something similar).
The SMAC simulation program also allows testing and refinement of 'single shot' approximations.
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