Copyright George M. Bonnett, JD 2015 All Rights Reserved
In order to put this in perspective, it is necessary to start from where we have been. When solving collisions back in the dark ages, the procedure for using Conservation of Linear Momentum was the quadrant method. Being new to accident reconstruction back in the late 70's, and having a brand new HP-15C calculator and not knowing any better, I managed to program it to solve Linear Momentum problems using just the two primary formulae for V2 and V1 using the trigonometry functions instead of using the very awkward quadrant method. In fact, it could handle four exit fragments for each of the two vehicles in collision.
In early 1986 several years after the formulae had been given to IAARS, it was on a Radio Shack PC-2 computer with a small 4 color ink-pen printer and was brought to an AI/AR training institution to demonstrate to them a new way of doing Momentum problems. They labeled it "witchcraft" and unceremoniously told us to leave. For well over 5 years several other institutions still taught the Quadrant method, even though the initial institution had finally become a believer. This method still required knowing all four angles and the departure speeds immediately out of collision for both vehicles.
Back around 2009-10, while talking with a friend at the PSP conference in Happy Valley, PA about solving for momentum with less information using just one vehicle, concern was expressed that the departure angles for both vehicles were needed to make this work. But what if we only had the CDR data from one vehicle? There was an experimental version of REC-TEC, but it required input of both the approach and departure angles for the two vehicles, in addition to the weight of the second vehicle. After release a few years ago, another discussion revealed that my friend was now teaching almost exactly the same method.
With this methodology integrated into Crush5, in 2015 it was no longer necessary to input the approach angles as the migration from CDR data to Crush5 enabled solving for them.
All that is left is solving for the 2 departure angles.
New for 2016 is the integration of Restitution (e) into the Crush5 solution and the Vectors (EDM-Momentum) module. Knowing the approach angles gives us a Cone of Departure for the collision. The REC-TEC Vector module permits 2-variable table integration with Restitution (e). It is possible that this, coupled with the implications involving Plane of Impact has brought us ever closer to finding a viable new solution.
Figure 612-IM42 (2016 Release)
The only noticeable change on this screen is the Angles | (e) | Speed (Vc) label on the right side of the screen. This has some exciting implications that will be explored in following screens.
Clicking on the COLM button displays the COLM Angles frame that will self-populate based on the PDOF angles (user override available) of the vehicles. Angles allow the program to compute Speeds V1, V2, V3, and V4. REC-TEC can now compute Restitution (e) based on the angles and speeds. The reconstructionist is able to use his expertise to form truly informed opinions from very limited data.
Figure 612-IM44 displays information on Vehicle 1.
Figure 612-IM45 displays information on Vehicle 2.
Figure 612-IM46 displays the information on Vehicle 1 and Vehicle 2 transferred into 360 LM. The eVelocity (Restitution) is recalculated in 360 LM based on the data transferred from Crush5.
Figure 612-IM47 displays the Plane of Impact basis for (e).
Figure 612-IM48 displays the information from 360 LM transferred into Vectors (EDR - Momentum), along with a vector diagram and the formulae used to arrive at the results in this module.
Figure 612-IM49 displays the Iteration / FDA (Finite Difference Analysis) interface. Employing the user set Range and Interval, Autofill has populated the interface with Minimum, Maximum and Interval information on the associated variables. These can be overridden by the user. Note that Iteration in this module can use two variables. Only Angle 2 has been selected here.
Figure 612-IM50 displays the Iteration screen for Angle 2 based on the information on the Iteration / FDA interface.
Figure 612-IM51 displays the Finite Difference Analysis screen based on the information on the Iteration / FDA interface.
Something New? Yes, a new pink button [> VMO]. Vector Momentum is like Linear Momentum in reverse. It calculates post-impact information. Could this help with solving for our two departure angles? It just might - which is why this option has also been added to the Vectors (EDM-Momentum) module.
Well, not exactly, but we do have more options. This module allows us to use either angles, speeds or a combination of an angle and a speed, and the combination can be on the same vehicle or different vehicles. More options just might let us solve the problem. Use 60 degrees for Angle A3 and 17.6425 for the speed of V4.
It has calculated A4 to be 29.9999 - remember, the program truncates at the requested decimal place (1-4). This gives us a lot of flexibility because it gives us more options. Crush5 (Crash3) gives but one option, it needs the departure angles. Vector Momentum permits six (6) different options. More options give more possibilities for solving the problem, the ultimate goal.
Enter Range and Interval parameters and then use Autofill to populate the interface.
The module only sets the parameters for Minimum, Maximum, and Interval for the Inputs entered into the Main Interface. While the values can be changed by the user even for the unavailable variables, they may not be selected for Iteration.
The radio buttons on the left side of the table allow Selecting a particular Variable (Angle 3 in this instance) as the default value. This value will be transferred to the Main Interface and the Iteration Interface will be reset (AutoFill) automatically. The 63 degree angle will be selected to demonstrate this capability.
The transfer was automatic and the program recalculated the output based on the new value for Angle 3.
This new Iteration data will be used to generate a new table for Speed 4.
Shown above the data for Speed 4 Iteration. Note that the Restitution and PDOF values for all of these changes are an integral part of the tables. This gives a fuller picture of how changing post-impact angles and departure speeds affects the collision.
If reliable data from other sources is available for the pre-impact or the post-impact speeds of one of the vehicles, approach and departure angles for that vehicle can be calculated if the angular difference between the pre and post-impact vehicle is known. Assume we have a V1 of 24.1001 M/H and a V3 of 17.6425 M/H with a angular difference of 60 degrees between pre and post-impact. Check Angle2 checkbox.
In this step we have set the Impact Speed of Vehicle 1.
Here we have set the Post-Impact Speed of Vehicle 1 (V3).
Note: Using correct values for the problem as entered input values kept the proper relationship for the PDOF, DVx, and DVy values. Use of "override" values will cause an imbalance that may be unacceptable.
This paper presents a viable alternative to the CDR only solution when reconstructing accidents. REC-TEC integrating Crush5, 360 Linear Momentum, Vectors (EDR - Momentum), and Vector Momentum Analysis can combine to produce an absolutely stunning array of unique attributes specifically designed to assist in forming your opinions, and reinforcing your informed opinions. If CDR data on pre-impact and/or post-impact speeds is available, Vectors (EDR - Momentum), Vector Momentum Analysis, and Triangle Solver can be used in arriving at a solution.
While the expert is always limited by the data available in forming opinions, sometimes more data is available than first believed, and using all of the data in new and different ways can present a new way of approaching the problem. It has been the objective herein to provide some outside of the usual box approaches to collisions where data was at best limited.
SMAC (2D and 3D) from several companies, "Crash" variants, and several Point-Click-Drag high-resolution animation packages are available, several costing $10,000 or more for a package that is very limited in scope (and installations). Some require minimal training of only a few hours with no emphasis on the physics behind the curtain. All are still limited to the data available to the reconstructionist, although this requirement is all too often waived in an effort to let the computer supply the Suspension of Disbelief for the viewer. Besides some very fancy (and blatantly overly prejudicial) bells and whistles that will certainly impress an uneducated trier of fact, exactly what do these animations (based on simulations that are often based on opinions, or based purely on opinion) really offer? They have been lumped together because most of the time they all accomplish the same thing - a glitzy view of an opinion of one possible solution that could have happened by a (highly-skilled) expert.
Lest someone think this is an overly harsh critique of SMAC, Crash variants, and Point-Click-Drag high-resolution animation, REC-TEC also includes a very efficient SMAC module that is integrated with Crush5 and 360 LM providing a startlingly easy way to set inputs for SMAC simulation>animation. As recommended by many experts, SMAC et al and CDR data are excellent secondary, or tertiary tools, when used to verify the reconstruction. They were never meant to be the primary tool for "doing" the reconstruction..
In a perfect world, a satellite capable of high-resolution and high-speed image capture would provide a video of our collision, which rarely, if ever, happens. REC-TEC is the next best option.
Copyright George M. Bonnett, JD 2015 All Rights Reserved