Jan 13, 2021: This message I repeated in a few posts so decided to split it off as a separate topic:
These comments apply to any crash analysis in general and simplified momentum analysis in particular which include a major simplifying assumption when applied to motor vehicle crashes.
The major shortcoming when applying some simplified momentum solutions in equations or simulations:
There are many programs out there with good options & graphics:
A word of caution to be very careful as momentum and some simplified 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 assumed instantaneous exchange
begs question: if so easy, why isn't it automatic?
These programs are useful however they can be very sensitive in many impact configurations.
ALWAYS CHECK FOR SENSITIVITIES OF ANY RESULTS!
Simplified momentum equations and programs which include this simplifying assumption require the user to pick a point and angle/direction to instantaneously exchange the momentum of a vehicular crash.
The full exchange of momentum in any vehicular crash takes 50-150 milliseconds (or more).
These programs/equations which include the simplifying 'instantaneous exchange' assumption consider a crash a SINGLE 'instant' (less than 0.001 second!) AND require the user select some subjective point and angle for the momentum exchange.
See SAE 97-0949 and others which demonstrate the movement between point of impact (POI) and point of separation(POS) in collisions.
Here is a simple illustration from the 1997 paper which is based on real world tests.
Also see RICSAC97 SAE 97-0961 and other 'real world' tests which demonstrate vehicle move and rotate between POI and POS.
sample POI to POS movement.png (33.58 KiB) Viewed 2953 times
This also means DO NOT use these simplified momentum solution procedures for side-slap collisions
Main point: Real world collisions take time (50-150 ms or more) and have changes in positions and orientations
When applying a momentum solution with the simplifying assumption it is very subjective and random HOW and WHERE a user places/sets the LOCATION and the ANGLE/DIRECTION for the INSTANT of the momentum to be "instantaneously exchanged"
How do you best approximate the reality of 50 to 150 or more milliseconds aka "instants" during a collision interaction as a SINGLE INSTANT with a SINGLE angle/direction?
Simplified momentum program vendors need to prepare OBJECTIVE instructions on these subjective random inputs for placing and directing the "point of momentum exchange"
Their current instructions like "place at point of maximum engagement" and/or "fit the damage areas together like a puzzle" are extremely subjective and random.
To be more honest about it they should add to their instructions "You should randomly and subjectively adjust the point and angle for the 'instantaneous exchange' until you get the answer you want and need!!'
THAT would be more honest!
The validations for these programs use the BEST approximation for the random and subjective momentum exchange POINT and ANGLE/DIRECTION to get the best possible MATCH of the KNOWN results.
They have done 'sensitivity studies' on these programs which interestingly use the SAME 'point and angle' arbitrarily and subjectively determined in their 'validations' and leave THAT out of the sensitivity study...
In other words they don't vary the 'point and angle' for the instantaneous exchange which would demonstrate the major issue which can occur with a BAD point and angle for the 'point of instantaneous exchange'.
The instructions ignore the fact that vehicles have different stiffness and restitution properties and so the residual damage in a crash MAY NOT BE a good indication of the maximum damage and engagement of the vehicles during the crash
Also how do you approximate a SINGLE angle/direction for that SINGLE point/instant to approximate all 50-150 or more milliseconds/instants of changing positions and directions (see this video for an example!)?
Nov 2020 Question on Cone of Departure in Momentum from another forum demonstrating issues of 'instantaneous momentum exchange' particularity when there is a sideslap
Here's a 2007 Fullscale Test and msmac3D Simulation which demonstrate that VEHICLE CRASHES ARE NOT INSTANTANEOUS!
For more of these types of crashes and presentations of measured and simulated accelerations during the 75-150 millisecond crashes (meaning...NOT instantaneous) please see
do the math, that was 25 years ago! and our message has never changed!
In our 1997 paper we included implementation of angular momentum enhancements to the solution procedure of the CRASH trajectory analysis:
"A secondary task required in order to further refine and enhance the trajectory solution procedure of the CRASH3 program was a reactivation and refinement of the angular momentum solution procedure. The original CRASH program included conservation of linear momentum in the trajectory based solution to determine the impact speeds based on the separation velocities. A contract performed on CRASH2 to implement an angular momentum solution achieved mixed results [26]. A major hurdle for any procedure which includes an angular momentum solution is the need to approximate movement of the vehicles during the collision. In the CRASH2 formulation the impact and separation positions and headings were assumed to be identical. The research in [26] revealed that the accuracy of an angular momentum solution procedure for accident reconstruction which includes the assumption of no movement between impact and separation will produce unacceptable error levels (>>20%) in many cases."
Red emphasis and underline added as all the current (2022) programs (pc-crash, virtual crash, etc.) do NOT include any assumption/approximation techniques for movement between impact and separation!
The 1997 paper also included the following comments on the current (as of then 1997) simplified momentum programs like pc-crash, etc.:
"Other analytical accident reconstruction techniques which include provision for an angular momentum solution procedure and/or which are based on conventional momentum analyses, include the somewhat subjective input requirement that either a vehicle-to-vehicle contact "point" [27 ], or a "point of maximum engagement" [28] or an "impact center" [29] be specified. The additional input is required to compensate for the cited solution procedure’s lack of an independent determination of separation positions and orientations.
The requirement that the user specify either an arbitrary impact contact "point" or an arbitrary "point of maximum engagement" detracts from the objectivity of the reconstruction techniques.
Figure 5 and Figure 6 show representative changes in positions and orientations during the contact phase of collisions.
Fig 5 and 6 from CRASH97.png (31.47 KiB) Viewed 980 times
The subjective choice of a “point” can produce a large variation in the predicted results. During “validation,” when the results are known, the user has some guidance in choice of the subjective “point.” In real-world applications, where the answer is not known, the determination and arbitrary specification of a “point” can and will produce a wide range of predicted results. The normal input requirements of accident reconstruction programs of damage dimensions and approximate impact configurations should provide more than adequate information for any accident reconstruction program to independently achieve the function of any contact “point” or “point of maximum engagement” without user intervention. The movement of the vehicles between impact and separation can be initially approximated, for example, by moving the vehicles in their initial directions of motion to positions where the damage regions match. The procedure to determine a separation position should be automated to prevent subjective variations between users in the positions of match and therefore the results.
Other assumptions of the cited techniques [27,28,29] which may detract from the validity of their impact models for objective application to accident reconstruction are:
During the impact no consideration is given for tire-to-ground “external” forces
The impact duration and time for exchange of momentum is assumed to be infinitesimally small.
TIRE-TO-GROUND "EXTERNAL" FORCES: The effects of tire-ground forces must be considered in a motor vehicle collision reconstruction. During the early development of the SMAC program [19, 20] tests were performed to determine the effects of external tire forces on the collision solution procedure. It was concluded that “The conventional assumptions that the effects of vehicle deformations and of tire forces can be neglected in analytical reconstructions of collisions can lead to significant errors. This is particularly true for intersection-type collisions at low to moderate vehicle speeds, in which prolonged or multiple contacts and significant movements of the involved vehicles occur” and that "therefore it is essential in a general procedure for reconstruction calculations that both the collision and tire forces be considered simultaneously."
IMPACT DURATION: The duration of a motor vehicle collision cannot be assumed to be infinitesimally small. Normally the exchange of momentum requires 50 to 125 milliseconds. Significant changes in positions and orientations can occur during the collision which can produce changes in the collision moments acting on the collision partners. Any accident reconstruction solution procedure which contains the assumption of an instantaneous exchange of momentum should be carefully evaluated.
The importance of the inclusion of external forces in collision analysis and use of a finite time increment for the impact duration has also been reiterated more recently by Fonda [30]."
2022 NOTE:
Here we are, 25 years later, and the widely popular programs like pc-crash and now virtual crash and others have updates and enhancements THAT ONLY INCLUDE graphical and convenience functions!
There are no modifications or objective instructions on:
Objectively placing the "point" and 'angle' or instantaneous momentum exchange
Adding consideration and approximation techniques for movement of the vehicles during the collision
see our 1997 paper for further discussion of the importance and requirement for approximating the movement during the collision and additional ideas on much more, which if implemented, might improve the fidelity and objectivity of these simplified momentum 'instantaneous momentum exchange' programs
From the 1997 paper:
"A basic outline of the procedure used to determine the impactspeeds for a combination linear and angular momentum
solution was as follows:
The separation velocities are approximated on the basis of the vehicle travel from impact to rest.
The separation velocities are used with an application of conservation of linear momentum for an initial approximation of the impact velocities.
The separation positions and headings are approximated using the initial approximations of the impact and separation velocities.
With approximation of the separation positions and headings, the following steps are repeated to converge on a solution:
The separation velocities are refined based on the vehicle travel from separation to rest.
The refined separation velocity is used with an application of conservation of both linear and angular momentum for a refined approximation
of the impact velocities."
Obviously for 'validations' they KNOW the answer and can finagle the 'point' and 'angle' accordingly to get the results they want/need/require...
however What are their guidelines for unknown speeds?
Why are there are NO objective scientific steps for determination of the 'point' and 'angle' or momentum exchange such that 10 experienced crash reconstruction folks using pc-crash to reconstruct a crash will get similar and correct results?
And of course in a blind study since, as mentioned, if you know the results you want/need/require...it is easier!
Recall from this and our other threads on simplified momentum programs that with a simple change of 'point' and 'angle' we can produce results which 'prove'? alternate speeds and scenarios!
19. McHenry, R.R., "Development of a Computer Program to Aid the Investigation of Highway Accidents”, Contract FH-11-7526, December 1971, Calspan Report VJ-2979-V-1,NTIS PB# 208537
20. McHenry, R.R.,"A Computer Program for Reconstruction of Highway Accidents", SAE Paper 73-0980, Proceedings of the 17th Stapp Car Conference, November 1973
26. McHenry, R.R., Lynch, J.P., “Revision of the CRASH2 Computer Program”, US DOT HS-805-209, September 1979
27. Limpert, R., Andrews, D.F., "Linear and Rotational Momentum for Computing Impact Speeds in Two-Car Collisions (LARM)" , SAE paper 91-0123
28. Steffan, H., Moser, A.,"The Collision and Trajectory Models of PC-CRASH", SAE Paper 96-0886
29. Ishikawa, H., "Impact Center and Restitution Coefficients for Accident Reconstruction", Japan Automobile Research Institute, SAE Paper 94-0564
30. Fonda, A.G., "Nonconservation of Momentum During Impact", SAE Paper 95-0355