Momentum "Cone of Departure" Question

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MSI
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Momentum "Cone of Departure" Question

Post by MSI »

Dec 16, 2020 this Question, from another forum, was originally posted to Some Momentum Misconceptions, however once we saw a full scale test on the topic we spun if off to a separate topic.
On our response to this thread (see below) we posted a video so why not bring it to the top,
read through this you'll see why we posted this video:
Question on another forum: (INCR, join that forum!)
  • In a book under Myths and Misconceptions there is a discussion of the Cone of Departure in Momentum analyses. The book describes and gives examples that there is no requirement that the departure angles of two colliding vehicles be within the approach heading vectors.
    My questions is, has anyone seen this happen from an actual crash, staged or otherwise?
    If so, what were the circumstances?
    Any reference location on this topic would be appreciated.
Answer posted to the forum:
  • Newton requires that the SUM of the momentum vectors be the same incoming and outgoing. Newton does NOT care if they are in the "cone of departure" on leaving or not, though...just that the sum is pointed in the same direction. If there is a big enough momentum disparity and the correct angle relationships, the sum can still be in the cone, while one of them is, by itself, NOT directed inside the cone. It is possible. We did it at the Joint Conference a few years ago. Bruno Schmidt and I published an article in Collision - Collision Magazine 5(2), Fall 2010 with the title: Cone of Departure: A Good Idea, but NOT a Law about it.
Our RESPONSE ABOUT "CONE OF DEPARTURE"
  • Great article (quick read looks good) and when i get a chance for a more detailed review i might also create a simulation of the collision example to demonstrate the issue i always harp about (sorry folks!) with respect to simplified momentum collision reconstruction.

    That is:
    Collisions do NOT happen in an instant...actually 50 to 150 or more milliseconds or "instants"
    • and so really a collision is a
      • 50 to 150 millisecond collisions.(and a millisecond is closer to an 'instant' than a full collision!)
      • I hadn't thought of characterizing it as 50-150 instantaneous momentum exchanges, but that is what it is!
      Because simplified momentum interaction tries to approximate a finite collision interaction (50 to 150 milliseconds of collision interactions)
      the "cone of departure" at the initial impact and then the "cone of departure" at the point of separation will be different as the vehicles move, rotate, crush, etc (And let us not forget sideslaps!!)

      Main points:
      • The collision of two vehicles is not instantaneous and they are not point masses.
      • All simplified momentum analyses, which assume instantaneous exchange, whether hand calculations or sophisticated computer programs, are good in many instances
        However
      • They are trying to approximate 50 to 100 'instantaneous' collisions in a single instant.
      Understanding that will help you understand why they don't always seem to 'be in the cone' and therefore make you scratch your head.
    Please also see:
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MSI
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Re: Momentum "Cone of Departure" Question

Post by MSI »

The following is some additional information on the crash test between a tractor trailer and a pickup truck
This was from an article published in Collision -
  • Collision Magazine 5(2), Fall 2010 entitled Cone of Departure: A Good Idea, but NOT a Law
    • In that publication they state
      • A conservation of linear momentum analysis was undertaken using the measured values and incorporating appropriate ranges. This analysis is calculated a Freightliner approach speed of between 33.4 and 34.1 mph. This is slightly lower than was actually measured, consistent with the fact that momentum of the two vehicles is not truly conserved through the crash because of roadway friction during the impact [and sideslap] . The Chevrolet's departure angle was approximately 4 .3 degrees outside of the "cone" defined by the approach vectors for the two vehicles.
        The vector diagram of this crash looks almost like one line, as a result of the huge momentum disparity between the two vehicles (approximately 400 to 1). This means that while the Freightliner’s pre-impact speed can be calculated with high confidence (a narrow range), the Silverado's calculated pre-impact speed will be highly sensitive to small changes in the Freightliner approach and departure angles
      The momentum diagram from the paper:
      Momentum Diagram REDUCED.jpg
      Momentum Diagram REDUCED.jpg (13.24 KiB) Viewed 188 times
    • Conclusion from the paper:
      • The occasionally heard "rule "that both vehicles involved in a collision must depart within the "cone" defined by their approach angles has been shown to not be inviolable. Even the "law" regarding momentum vector equivalence is only an approximation , though it has been shown again to be a good one when roadway friction forces are small compared to the inter-vehicle impact forces.
    • Additional information was obtained from the NAPARS web site REFERENCE SECTION (videos, photographs, etc.).
    • Join and support NAPARS and INCR:
COMMENT ON LINEAR MOMENTUM ANALYSIS:
  • The crash test was somewhat similar to the Classic Example of Sensitivity of Momentum Solutions except the pickup truck is relatively stationary (2 mph at impact) in this test.
    • They also knew/assumed/used that the truck swerved right prior to impact.
      • In many instances the pre-impact behavior of a large vehicle is unknown and can result in dramatic changes in the results if swerving right or left.
    The authors did not provide the details of their actual linear momentum solution:
    • How did they determined the separation velocities (they mentioned angles).
    • Did they use something like the SPIN2 routine? or what procedure did they use to determine the separation velocities?
    • Their momentum diagram includes multiple positions for the Pickup truck however simplified momentum requires the same impact/separation position.
    For some additional discussion on applying simplified momentum to crashes, please see our paper where we worked on approximating the effects of external forces and vehicle movement during a collision in a modification of the CRASH linear momentum solution (and we also added an angular momentum solution).
    In 2003 with the phenomenal increase in computer capabilities we focused our attention on the automatic iteration of SMAC since no need for except to be used for starter speeds for a [url=https://www.mchenrysoftware.com/board/viewtopic.php?f=36&t=583]SMAC simulation (and that is what we did in the 2003 SMAC research)
DOCUMENTATION AND ANALYSIS OF THE CRASH
Videos edited and slowed down/zoomed in to show the sideslap:
The collision partners:
Collision Partners.jpg
Collision Partners.jpg (6.56 KiB) Viewed 208 times
The scene diagram
SCENE Diagram w ADJ Scale.png
SCENE Diagram w ADJ Scale.png (228.08 KiB) Viewed 208 times
We digitized SDM data(Chevy) and Radar Data (Freightlliner) and compared it to msmac3D reconstruction:
Chevy SDM v msmac REDUCED.png
Chevy SDM v msmac REDUCED.png (33.48 KiB) Viewed 194 times
FriegthLiner Speed Comparison REDUCED.png
FriegthLiner Speed Comparison REDUCED.png (24.27 KiB) Viewed 194 times
Impact Sequential:
impact sequential REDUCED.png
impact sequential REDUCED.png (376.07 KiB) Viewed 194 times
More to come...
NEW!! LEASE pricing of msmac3D Software!!
FOR MORE TOPICS see:Forum Index & McHenrySoftware.com
Question? Comment? Please email us (all communications considered confidential)
(c)McHenry Software, Inc ALL Rights Reserved.
MSI
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Posts: 1699
Joined: Thu Jun 18, 2009 12:37 pm

Re: Momentum "Cone of Departure" Question

Post by MSI »

Some additional refinement of the discussion and presentation of the data.
more to come...
NEW!! LEASE pricing of msmac3D Software!!
FOR MORE TOPICS see:Forum Index & McHenrySoftware.com
Question? Comment? Please email us (all communications considered confidential)
(c)McHenry Software, Inc ALL Rights Reserved.
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