Getting Technical with Forensic Science...       The word forensic is an adjective that means that the work has been prepared in a manner suitable for presentation in court. It has nothing to do with dead bodies.   A forensic engineer applies the principles of science and engineering to investigations which are part of, or potentially a part of, some legal process. A more familiar term is Expert Witness.     These excerpts have  been significantly simplified as many graphics and formulas are not included in this present form.      Motor Vehicle Accident  Reconstruction & Biomechanical Physics Robert C. McElroy, Ph.D.     ABSTRACT     Accident Reconstructionists rely on a wide range of methods to record and analyze motor vehicle accident information. Lets address contemporary methods of obtaining and analyzing collisions with emphasis on G force explanation for biomechanical analysis.     INTRODUCTION:   Traffic accident reconstruction is the effort to determine, from whatever resources are available, how an accident happened. A traffic accident reconstructionist must be familiar with the application of a wide range of mathematics and specialized aspects of vehicle technology. Because of the wide range of knowledge required by the accident reconstructionist, voluntary certification is available through the Accreditation Commission for Traffic Accident Reconstruction. ACTAR certification includes education, work experience, and successful completion of a comprehensive examination.     MATHEMATICS FOUNDATION Mathematics are at the core of traffic accident reconstruction. Many different equations are used to determine different aspects of an accident. Sir Isaac Newton developed three mathematical laws of motion which provide the foundation for traffic accident reconstruction.     In Newton’s first law of motion an important property of matter appears. It is known as inertia, that property of matter by which an object maintains a constant velocity in the absence of an unbalanced external force. When an automobile is suddenly stopped, the passengers obey Newton’s first law and continue in their motion with constant velocity until some external force changes their state of motion. Seat belts in a automobile can provide such an external force which is much preferred to that exerted by the windshield or dashboard. Another statement is the following:   A body at rest remains at rest, and a body in motion remains in motion with constant velocity along the same straight line unless acted upon by some outside force.   Newton’s second law states that if a body is acted upon by an unbalanced force F, its center of mass will accelerate in the direction of the force. The acceleration, a, is proportional to the force, F, and the constant of proportionality, m, is called the mass of the body. Another statement is the following:   The acceleration of a body is directly proportional to the resultant force action upon the body and acceleration is inversely proportional to the mass of the body.     Newton's second law provides the key relationship between force and acceleration since force and acceleration are vectors and vectors have both magnitude and direction. Mass is only a magnitude, so it follows that the magnitude of force equals the magnitude of acceleration times the mass. Unification of these concepts reveals that force direction must be the same as the direction of the acceleration because mass does not have a directional property.     The second law is written F = ma where the unit of force is the Newton. One Newton produces an acceleration of one meter per second, per second, in a mass of one kilogram. One Newton has a value of .2248 lb.     Newton's third law is equally valid in dealing with bodies at rest or in motion, either uniform or accelerated. The wheels of an automobile in motion push backward on the road, but the road pushes forward on the wheels with an equal force during acceleration. Another statement is the following:   Whenever one body exerts a force upon a second body, the second body exerts an equal and opposite force on the first.   ACTION= REACTION   Action (force exerted on the trailer) is equal to Reaction (force exerted on the car by the trailer).   Prediction of what happened during a collision by examination of what remains in the form of residual damage can be used to calculate speed change or Delta Velocity (DV) experienced by the vehicles in the collision. DV is one of the best available measures of accident severity.   DV assumes that collision stopping force on a vehicle is a linear function of residual crush depth. Up to a certain force level, there is no permanent damage and beyond that point, permanent damage increases with increased force. Two stiffness coefficients, A and B, define the force-damage curve. Fundamental to a solution for speed change are appropriate A and B values for a specific vehicle. A and B values are derived from the collision damage sustained from known velocity changes of a vehicle into a barrier. Therefore, A and B values can be used to calculate speed change based on permanent vehicle crush (chart available with full version of publication).   Vehicle tests sponsored by the National Highway Traffic Safety Administration resulted in a series of computer programs released to the public called CRASH. The last public version CRASH3 was revised and released in 1982. Several computer based accident analysis programs are available for the accident reconstructionist, each ultimately stems from this background.   A collision analysis project is defined as a series of step by step calculations. The investigator will organize the project into separate events which require solutions for specific unknowns. Normally, each event or step will consist of an equation with only one unknown. The art of collision analysis is to determine which event to solve first and then how to proceed with the next calculation to develop a unified collision sequence analysis.   Calculations, as from a popular AI TOOLS computer program, help to address specific information needed in order to piece together the accident reconstruction. When properly used each calculation will help to fill in a missing piece of information.   Equation #1 Speed from Distance & Drag. Calculation of vehicle speed made from skid distance and drag factor. Measured skid distance is 120 feet and deceleration factor for the vehicle & road surface combination is .7 G. The vehicle is calculated to have been going 50 mph when the brakes were applied. (example of equation available in full publication - contact FAI for materials)   MOMENTUM:   Momentum is a restatement of Newton's laws in a form that is useful for the collision analysis or any event which involves very short periods of time. The second law for a single object would be rewritten as F Dt = m DV.     The left side of the equation is the Impulse and the right side is the Change in Momentum. This relationship is still a vector relationship. Force has the same direction as the change in momentum which has the same direction as the change in velocity.     In summary:  Impulse = Change in Momentum     If two vehicles collide, the force or impulse on one of the vehicles is equal and opposite to the force on the other. This is a consequence of Newton's third law. Changes in momentum for both collision vehicles cancel.    There is no gain or no loss of momentum during a collision. Momentum before the collision equals the momentum after the collision and because weight is proportional to mass the final equation can be rewritten as:   AI Tools Linear Momentum module (included  with full version) calculates that the Chevy Lumina came into the collision at 27 mph and that the Dodge had an entry speed of 15 mph. Equation #1 was initially used to determine slide to stop, or departure, speeds for each vehicle.   MEDICAL PERSONNEL   Involved in an accident investigation can provide valuable injury information that assists in cause analysis. Where possible in fatality accidents, autopsies should be performed to determine the cause of death and record information about the injuries. Nonfatal injury information is also useful to the investigator. Location of broken bones is especially useful when graphically represented in a skeleton diagram.  Injury illustration could be done for each occupant to produce a composite occupant diagram for the vehicle. Injuries will indicate the direction of crash loading for the vehicle. Location of bruises and contusions can also be addressed, since these injuries can sometimes indicate use or nonuse of a seat belt or shoulder harness     Head injuries are important clues. If an instrument panel, roof pillar, steering wheel or glass has evidence of a head strike (i.e., blood, skin, hair, dent, teeth), that spot should be documented. With a specific location for the strike and the relationship to the occupant’s body, the investigator can evaluate the angle of head impact, body position, and restraint system function, see below. It is important to remember that an occupants head motion is exactly opposite to the crash loading direction. (graphics and charts contained in full publication)   DECELERATION LOADS   In a biomechanical investigation approach, the most important task is to determine occupant crash loads and probability of serious injury. Other investigative tasks help the biomechanical investigator to understand physical relationships in the accident which lead up to either receiving a serious injury or not. To calculate an average G force crash pulse, a specific equation is used for each axis of occupant traveling this equation G = the average force on the specific occupant and is expressed as a multiple of occupant weight. Because of crash dynamics, peak G figures will typically be twice the average G.   V = velocity change at the major impact, expressed in ft/s g = acceleration of gravity, 32.2 ft/s2 S = deceleration distance, expressed in ft     The biomechanical investigator should look for clues in each axis (i.e., roll, pitch, yaw) for velocity change and stopping or deceleration distance to be able to determine a unique crash loading for each occupant.   An extreme example of how the different G loading is experienced by different people decelerating over different distances is found in this illustration. To understand the concept, consider a long uniform airplane fuselage that crashes head-on into a cliff at 200 mph with Persons A, B, and C who decelerate in the crash distances of 5 ft, 20 ft, and 45 ft, respectively. A calculation of the average G-loading experience by Persons A, B, and C would be 266G, 66G, and 29G, respectively. (The average G calculation is included in the full publication)     The average forward load on Persons A, B, and C can be calculated by multiplying each persons weight by each persons average G load. If the weights of Persons A, B, and C were 200 lb, 170 lb, and 100 lb, respectively, the average loading experienced would be 53,395 lbf, 11,346 lbf, and 2,966 lbf respectively. The weight load calculation for passenger C would be:  load = G avg x weight = foot pounds = lbf 29.66 G x 100 lb = 2966 lbf This airplane example assumed seats and restraints that held throughout the crash sequence. For such a severe crash, it is not likely for all of the seats and restraints to remain attached. A seat will fail when its maximum load capability is exceeded. Assume seats with integral shoulder harness and lap belts were designed for 25G static loads in the forward direction. Person C of our airplane example would have a seat where the minimum force before seat separation can be expected of 25 times their weight of 170 lb x 25G or 4,250 lbf.   The load experienced by Person C was 2,966 lbf average or 5,932 lbf peak. Thus, the seat for Person C would separate when its peak load exceeded the design load capability of the seat. The more damaging loads for Person C will occur later, when he or she undergoes major deceleration.   AUTOMOTIVE LOADS A vehicle traveling 35 mph sustained two feet of uniform crush. Substitution into the formula reveals the G forces for this accident. V2 352 Gavg = = = 9.5 Gavg x 2 = 19 Gpeak 2gS 2 x 32.2 x 2   Federal Motor Vehicle Safety Standard, FMVSS 207 Seating Systems.  Under this standard the seat must be capable of withstanding a force "20 times the weight of the seat applied in a forward (S4.2.a) or rearward (S4.2.b) longitudinal direction." Thus if the seat weighs 30 lb then it must not fail at a level below 600 lb when calculated as 20 x 30 lb = 600 lb. It is important to note that occupant weight is not considered. S4.3.2.1 Static force specifies 20 times the weight of the seat back.   VERTICAL CRASH ANALYSIS A more detailed analysis will reveal that the G loading will change throughout the crash sequence. For example, crash loads experienced by an occupant of an extremely high vertical velocity impact are shown on page 10. From point A to B, the crash loads are low (typically 2 to 3 G) as the landing gear deforms. Point B is where the fuselage lower skin contacts the terrain. Loading from point B to C to D to E is extremely high as the aircraft floor comes to rest at point F.   If an occupant is sitting on the floor, the loading experienced would have been points B to C to D to E to F. Note the horizontal line, which is an injury load threshold (within time duration limits) above which severe injury is expected. If the occupant is sitting on a seat, the vertical crash loading experienced will rise from point B to C and then drop to point G. Loads do not exceed point C, as this is the maximum strength of the seat which fails at Point C. The occupant’s load is about zero from point G to H because the occupant is basically free-falling from a seated position until contacting the floor at point H.     However, the aircraft floor is just about to come to rest at point F. Thus, the occupant impacts a nearly stationary floor and the crash loads experienced by the occupant will go from point H to I to J. Unfortunately, occupant load penetration above the injury zone threshold line would indicate that a severe injury would be expected for the example occupant. It is obvious that an average G loading for an entire aircraft is inaccurate and misleading. Understanding the crash loads on an occupant is not possible without good information from the crash survival investigation on injuries, restraints, seat damage, and fuselage damage   The continuation of this publication is NOT available on line: Motor Vehicle Accident Reconstruction & Biomechanical Physics paper is authored by Robert C. McElroy, Ph.D.   In order to retain control of the ownership of this and other materials included in this website, a full version is not available on line. Please contact Mringer@forensicaccident.com for information and the availability of this and other documents located throughout this website with regard to purchase requests   © 1999 copyright, Forensic Accident Investigations, Inc.