Some Simplified Momentum Assumption Misconceptions

[MSI]

New: Use this link to go to the latest post on this thread

Some Simplified Momentum Misconceptions:

• And please note this is not to dismiss simplified momentum analysis, it is to help all who use it to understand the assumptions, to encourage that they test a range of assumed input numbers to reveal any sensitivities, and then that they try to test and refine any conclusions.

1. The collision between two vehicles is not the same as a collision between two pool balls.
   
   • More like two crushable rectangular boxes on wheels. And vehicles are not 'balls' or 'points', they are finite dimensioned crushable objects which may behave quite differently during interaction than simple `balls' or `point masses'.
2. The assumption of the impulse of momentum acting though the 'centroid of the damage area' is an assumption which was created for mathematical convenience as part of the development of CRASH.
   
   • The centroid of damage for two vehicles may not be coincident at the assumed `point' of exchange of momentum. The actual area of momentum exchange between two vehicles depends on the impact configuration and sometimes the `centroid of the damage area' may not be a good assumption.
3. The actual exchange of momentum between two vehicles takes place along the collision interface. And that damage, observable after the collision, may not have been created in a single `instant'.
   • Think of it as 50 to 150 or MORE "instantaneous exchanges" as the collision occurs and momentum is exchanged...it takes times, movement and distance to occur....NOT a single instant!
4. The exchange does not take place at a single point or in a single direction or in a single instant, that is a simplifying assumption used by momentum solution procedures for convenience.
   
   • The magnitudes of the forces and the moments change with time for the 50 to 100 milliseconds or more of collision interaction.
5. The collision between two vehicles takes time (50 to 150 milliseconds or more), and during that time, the collision partners can change orientation (Depends on the impact configuration, speeds, etc.).
   
   • So in essence during a collision you have 50-150 or more 'instantaneous exchanges' every millisecond! And programs lump this into a single point/instant/position for mathematical convenience?
6. There may also be a side-slap secondary contact between vehicles (like during intersection collisions) where after the initial contact of the front corners the vehicles 'slap' sides.
   • This obviously must be considered in any momentum solution procedure and obviously it does NOT occur in an instant.
7. The use of a point ('the centroid'), a single direction (PDOF) and an instantaneous exchange time is for mathematical convenience and simplification.
   
   • Variations of these assumptions should be considered and tested as part of any analysis.
8. The assumption for the direction of the momentum vectors at separation should also consider the rotation directions of the collision partners, the amount of rotation, and the end of rotation position (which may or may not be the position of rest).
   
   • A rotating vehicle does not travel in a straight line, it follows a curved path.

These items and others related to accident reconstruction momentum calculations emphasize the need to test and bracket the sensitivity of your assumptions and to focus on the variable which may have the most profound effect on the results of your momentum analysis.

• When CRASH was created for NHTSA it was as a preprocessor for SMAC.
  NHTSA decided CRASH was adequate FOR STATISTICAL STUDIES where they were looking for trends.

NOW 40+ years later 'experts' hide these simplifications behind high end graphics and flashy presentation capabilities in INDIVIDUAL CASES??
Think about that for a moment!...


Sept 2020 NOTE: These comments on Momentum analysis apply to momentum in general when applied to motor vehicle crashes and to programs like PC-CRASH, Virtual Crash, Planar Impact Models, and others:

• There are many great programs out there with amazing options/graphics.
  This is just a word of warning to be very careful as momentum and momentum crash simulation programs include the simplifying assumption of an 'instantaneous exchange of momentum' which requires the user select a subjective 'point and angle' for that instantaneous exchange (begs question: Why isn't it automatic?)
  These programs are useful however they can be very sensitive in many impact configurations. CHECK FOR SENSITIVITIES OF ANY RESULTS!
  Here are some related articles:
  • Nov 2020 Question on Cone of Departure in Momentum from another forum demonstrating issues of 'instantaneous momentum exchange' particularity when there is a sideslap
    • Nov 2020 What is a Sideslap?
  • Nov 2020 PC-CRASH: How Many % May An Investigator Be Wrong with pc-crash? Question posed on another forum
  • Sep 2020 A Negative Coefficient of Restitution? An Irresponsible vCrash Video! Silly Irresponsible video which caused confusion
  • Aug 2020 More Discussion on PC-CRASH type simplified momentum solutions Review of a pay-per-view pc-crash training video
  • Jun 2020 Does Momentum Analysis Requires COM Common Velocity? Some alleged 'experts' run fast and loose with science
  • May 2020 Planar Impact Model assumptions Planar impact models also have issues

[brian]

This is some additional information on item:

• (6) above "There may also be a side-slap secondary contact between vehicles (like during intersection collisions) where after the initial contact of the front corners the vehicles 'slap' sides. This obviously must be considered in any momentum solution procedure and obviously it does NOT occur in an instant".

There's something about sideslaps!

• Rusty Haight sent us some information on the 2007 NYSTARS sideslap crash, (thank you Rusty!) and we did a momentum analysis and SMAC simulation of the collision as a part of our 2008 McHenry Software seminar.

• Above is a snip of a simulation of the collision with the velocity vectors displayed
  We have also posted up a graphic and tabular summary of the results which includes the positions, velocities, momentum and kinetic energy calculations
  Notice how the velocity vectors direction and magnitude changes during the sideslap. Notice also that the time between initial contact and separation from the sideslap is >> instantaneous!

So for a simplified momentum analysis, which angle do you use and how can you assume 'instantaneous' when the tires are skidding and changing the speed between initial contact and separation from the sideslap?
Obviously knowing the answer, you can judiciously pick an angle that 'works'.
However if you 'do not know' the answer you want or 'need' (seems some folks do reconstruction on an agenda rather than as a scientific endeavor (i'll have more on that later!)), then you will need to use a tool such as SMAC to test and refine your simplified momentum analysis.
SMAC is the only tool available which can scientifically and objectively handle collisions which include a sideslap.
Below are some pictures from the 2007 NYSTARS test:
NOTE the movement between initial and secondary 'sideslap' impacts!

OH sequential NYSTARS sideslap.jpg (301.78 KiB) Viewed 7161 times

Lumina Damage reduced.jpg (106.54 KiB) Viewed 7335 times

[brian]

In re-reading my response, one might interpret my message to mean you MUST run SMAC for every accident reconstruction.
That is not what i meant.
The main point of emphasis with respect to Momentum Solutions is to perform a sensitivity study.
Far too often we encounter ‘experts’ who present a single momentum solution to a complicated collision. When we vary some of the assumptions, such as the assumption of exit angle or exit speed, we get a wide variation in the results and a 'proof' of something quite different from what the 'expert' espoused.
A ‘single’ instantaneous momentum solution may not be a valid solution.
So as a minimum, someone using a Momentum Solution should do a sensitivity study to determine the range for their results.
And then present the results as a range of results.
There have also been papers on using a Monte-Carlo solution procedure to determine sensitivity areas. I will post more on that in another post.

[MSI]

Sept 2020:Added to the first part of the thread a NOTE...see the first thread above for the NOTE

[MSI]

NOTE: DEC 16 2020:

• A question on the Momentum "Cone of Departure" came up and we had our response here but decided to split into a separate topic.
  We are doing an evaluation of a referenced full scale test between a tractor trailer and a pickup truck published in article in Collision - Collision Magazine 5(2), Fall 2010 Please see the Momentum "Cone of Departure" Thread for more information.

The following is a continuation of a review of a test in a 2000 SAE Paper we also are doing an evaluation of:
A review of the 2000 SAE paper mentioned above and from the other forum,SAE paper 2000-01-0464, reinforces our point that:

Be extremely careful when applying simplified momentum analysis,

Whether hand calculations or computer programs which use simplified momentum assumptions like pc-crash or virtual crash or planar impact models.
Particularly if there is a sideslap or pre-impact swerve since a careful choice of the impact and exit angles is important and essential.

• If you know the answer you want or need, and that is what they did in the paper, and so adjust things to match, you get good correlation.
  However
  From the paper:
  • The angles from impact position directly to rest positions were -161° and -101° for the Subaru and LTD, respectively.
    A mistaken use of these values can lead to impact velocities that are incorrect by over 20%.
    

When there is a sideslap and you are trying to approximate a collision with a sideslap as an 'instantaneous exchange of momentum'
with a sideslap there can be 300 to 400 milliseconds between the initial impact the the separation
That can not be approximated in an instant!

• That is 300 to 400 'instants"!

Further discussion on the other forum (INCR, join that forum!)
Response on forum:

• For those who hadn't thought of it that way, you can lump multiple close-on collisions into ONE event for most analysis purposes.
  There was an SAE paper that dealt with that on the issue of secondary slap some time ago...hold on, I can find it...2000-01-0464. OMG, 20 years ago.

Our Response:

• time flies when we're having fun, eh!...
  I remember that paper (i'll post below additional information on it) and that test and doing a simulation of the test as part of one of our seminars maybe in 2008?
  I can't recall momentum considerations in the paper or the magnitude of the sideslap.
  will do and see what's up and add to the sideslap forum thread!
  
  And of course in many collisions the approximation of the collision interaction as a single instantaneous momentum exchange is an adequate approximation.
  So in essence that is combining 50-100 'instantaneous exchanges' into the 'cone of departure' of the initial impact.
  My point was realizing and recognizing the simplification can help explain why in some instances lumping them together, particularly when there is a sideslap, .may not always be a good approximation as things may fall outside the 'cone of departure' of the initial impact configuration.
  
  
  Thanks for the memories

I did find a chart from our reconstruction and still trying to find all the other related files, stay tuned...
Please check forum thread What is a sideslap for more information on that crash test
For additional information on the 2000 SAE paper please see:

• What is a Sideslap?

[MSI]

Dec 2020:Always tinkering with these posts (why we prefer a forum to twitter or others)
Edits/refined the first part of the thread...see the first thread above'

Please let us know if you have any questions or comments!

[MSI]

Please see this important link

• The Major Shortcoming of Simplified Momentum Simulation and Analysis