By Brian G. McHenry

©McHenry Software, Inc.

 

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The acronym CRASH stands for the Computer Reconstruction of Automobile Speeds on the Highway. The CRASH computer program is an accident reconstruction program. With CRASH you input the vehicle properties, the impact and rest positions, and the vehicle damage measurements. The program produces approximations of the vehicle speeds at impact the impact speed change or Delta-V (DV).

The Impact Speed Change (DV) is defined as the impulsive change in vehicle speed (i.e., produced by an impact) that occurs along the direction of action of the principal collision force^[1].

The magnitude and direction of the impact speed-change of a vehicle, that occurs during a collision, serve as primary descriptors of impact severity, since they reflect the effect of the ratio of the masses of the two colliding bodies as well as that of the closing speed.  The impact speed-change is expressed in miles per hour and the clock direction from which the principal force was applied is generally stated.

For example, a 20 MPH, 06 o’clock impact speed-change would correspond to a principal force acting from the 06 o’clock direction (i.e., a longitudinal rear-ender) with a sufficient impulse (i.e., time-integral of applied force) to produce a 20 MPH impact speed-change of the subject vehicle.

In a central, collinear collision, the impact speed-change of vehicle #1, DV₁, and the closing velocity, (V₁₀ –V₂₀), are related as follows:

 MPH

Where    V₁₀-V₂₀ = closing velocity, MPH

W₁          = weight of vehicle #1, lbs.,

                              W₂          = weight of vehicle #2, lbs., and

e             =  coefficient of restitution.

The terms barrier-equivalent speed and impact speed-change are sometimes used interchangeably. However, this is appropriate only for that portion of the impact speed-change that precedes restitution.

A further discussion of impact speed-change is presented in Figure 1 from Reference [2].

Figure 1 The significance of Impact Speed Change

In 1952, a pioneer program in highway safety research, the Automobile Crash Injury Research program (ACIR), was created with the objective of determining injury causation among occupants of cars involved in accidents, in order that the injuries might be prevented or mitigated through improved vehicle design. By the mid sixties, 31 states had participated in the program and provided over 50000 cases for study. The main criterion for classifying severity in the ACIR program was through the use of comparison pictures of damaged vehicles.

Also during the 60's the digital computer was coming of age. Mainframe computers, which filled entire floors of buildings and cost hundreds of thousands to millions of dollars had evolved into time-sharing, batch processing machines. These were used in conjunction with 9 track tapes, card punch machines and terminals to provide to scientists, engineers and others number crunching capabilities unlike any utility ever before imagined. The digital computer quickly became an integral part of scientific research and development.

In September 1966, President Lyndon Johnson signed the National Traffic and Motor Vehicle Safety Act and the National Highway Safety Act. These established the authority to develop both the Federal Motor Vehicle Safety Standards (FMVSS) and the National Traffic Safety Agency (currently known as the NHTSA). As part of signing the legislation President Johnson stated that "auto accidents are the biggest cause of death and injury among Americans under 35". In 1965, 50,000 people were killed on the nation’s highways in auto accidents.

The SMAC computer program was initially created as a feasibility study by researchers at Cornell Aeronautical Lab (currently known as Calspan). The researchers at Cornell were interested in demonstrating the feasibility of a mathematical model of automobile collisions which could achieve improved uniformity and accuracy in the interpretation of evidence in automobile accidents. SMAC applications would give more accurate indications of collision severity. This would help to establish priorities, provide monitoring and assist in establishing the regulatory role of the government.

At the time of the creation of SMAC, limitations in the detail and the accuracy of the ACIR study had spawned a number of different exploratory approaches to the ACIR objectives. The SMAC program was evaluated as a possible tool for the investigative teams. SMAC is an "open-form" accident reconstruction program. A requirement of "open-form" programs like SMAC is that the user must initially estimate the impact speeds. The program also generally requires iterations to achieve an acceptable match of the accident evidence. One of the difficulties which arose in setting up SMAC simulations by the investigative teams was that the initial estimate of the speeds were not always obvious. Also, the user had to provide vehicle properties and specifications, many of which were not readily available. Those requirements, combined with the relatively high cost per run for a SMAC simulation run, required that a pre-processor be created which could provide the initial estimate.

The CRASH computer program was initially created to assist SMAC users in determining first estimates of the impact speeds. The original CRASH program utilized both piecewise-linear trajectory solution procedures and a damage analysis procedure to provide an initial estimate. The CRASH program was subsequently adopted by NHTSA as an integral part of the National Accident Sampling Study (NASS) investigations. The rationale for the use of the CRASH program was that for statistical studies, the average error in severity determinations is more important than any individual errors. The CRASH program, with it's question and answer mode, vehicle categorization, single step solutions procedure, and most importantly low cost, redirected the NHTSA interest from SMAC towards the CRASH computer program.

From the CRASH3 User’s Guide and technical manual, NHTSA, US Dept of Transportation: 

“The CRASH3 program is a simplified mathematical analysis of automobile accident events. As is the case with any such analytical procedure, certain simplifying assumptions have been made to reduce the complexity and the operating cost of the program.  Any accident event that violates the CRASH3 program’s simplifying assumptions either degrades the accuracy of the solution, or, in the extreme, completely invalidates it. Thus, while CRASH3 users do not need to know the minute details of the analysis procedure, it behooves them to know the major simplifying assumptions so that accidents that violate them may be either avoided or handled with special techniques.”

·        Ballistic Post-Impact Trajectory

CRASH3 assumes that the vehicles spin out to rest with constant rolling resistances, no active steering, and over a single friction surface, although a secondary friction surface may be specified in the trajectory simulation option.

·        Point of Common Velocity During Impact

CRASH3 assumes that at some time instant during the impact, the contact point on both vehicles reaches a common velocity. There are certain situations, notably sideswipes, when this is not the case and a CRASH3 analysis will not be successful.

·        Flat, Single Friction Surface Traversal

CRASH3 is a two-dimensional analysis. The program assumes both vehicles traverse the same friction surface.

·        Quantization of Vehicle Properties

CRASH3 maintains tables of vehicle properties that divide the vehicle population into discrete categories.

·        Uniform Crush Stiffness

CRASH3 assumes uniform individual crush stiffnesses for the side, front and back of a vehicle. The crush stiffnesses have been empirically derived from data generated in crash tests. Obviously the uniformity notion does not account for the fact that a vehicle side is fairly stiff near the axles but less so near the doors. Again, this is a compromise of complexity, convenience and cost.

 

The original CRASH program utilized both piecewise-linear trajectory solution procedures and a damage analysis procedure.

·        CRASH Trajectory Algorithms

·        CRASH Damage Analysis Algorithms

©McHenry Software, Inc.

On the basis of Newton’s 2nd and 3rd laws, the total momentum of an isolated system of masses remains constant. This principal, which is referred to as the Conservation of Momentum, serves as the theoretical basis for reconstruction of impact speeds in vehicle-to-vehicle collisions.

For the moment we will assume that the system is isolated and will ignore the external forces produced by the tires and other possible sources, such as gouging and scraping of vehicle components on the ground, during the collision. The magnitudes of these external forces are normally small when compared with the magnitude of the forces of the collision. However, they can not be totally ignored.

A trajectory analysis is used to determine each vehicle’s velocity and direction subsequent to the collision, thereby providing a definition of the system momentum at separation. This can then be used to define the system momentum at the instant of collision and thereby provide a procedure to determine the vehicle’s impact speeds. This procedure for estimating impact velocities also directly provides estimates of the impact speed-changes (DV) in the form of the vector differences between impact and separation velocities for each vehicle.

Our presentation of trajectory analysis will begin with the simplest form of  vehicle motion, linear motion without yawing:

Linear Motions Without Yawing

For the simplest case of straight-line travel without yawing rotation and with constant drag forces, the corresponding change in velocity can be approximated with analytical relationships for constant deceleration:

                              V=V₀ - at                                                                                         (1)

From integration of (1),

               S = V_o t - 1/2 at²                                                                             (2)

                                                                                                  (3)

Substitution of (3) into (2) yields

                                                                                             (4)

Solution of (4) for V yields

               V² = V_o² - 2aS                                                                                 (5)

where

               V            =             Velocity

               V₀           =             Initial velocity

               a             =             Acceleration

                t             =             Time

               S             =             Distance

In applications of equation (5), a distinction must be made between the prevailing average friction coefficient, m, and the deceleration, a.  If the full 100% friction coefficient is utilized, i.e., wheels locked or pure lateral travel, a =mg ft/sec².

For longitudinal motions with one or more wheels not fully locked and/or sideslip angles less than 90 degrees, , the friction utilization will be less than 100 percent and, thereby, a < mg ft/sec² .

In the case of a vehicle coming completely to rest without further obstacle contacts, V_f = 0, and equation (5) becomes:

               V_o² = 2aS                                                                                         (6)

The decrease of speed with travel distance, for the case of constant deceleration, is depicted in Figure 2.

Figure