John Fiske Brown Associates, Inc.
ACCIDENT RECONSTRUCTION PRIMER FOR ATTORNEYS
by Jack Debes, Ph.D. and Ken Obenski, P.E.
Underlying Science
Accident Reconstruction (AR) is based on the laws of Newtonian physics. Although many of us may have a tough time remembering these laws from our high school physics class, we live in a world that is governed by these principles so that even if we don’t remember the laws by name, we actually have an intuitive feel for them.
Newton’s First Law states that a body in motion remains in motion unless acted upon by some outside force and a body at rest remains at rest unless acted upon by some outside force. Mathematically, the First Law states that if the sum of all forces on a body is equal to zero, its velocity is constant. In AR this means that if a driver maintains a constant speed while traveling on a level road in a given direction, the vehicle will continue at that speed and direction unless the driver brakes, accelerates, turns, crashes into another object, or the vehicle stops due to fuel consumption or mechanical failure.
Newton’s Second Law states that Force equals Mass times Acceleration (F=ma). In AR, acceleration is a measure of the rate of change of speed of the car. If it speeds up, the acceleration is positive, if it slows down (decelerates) the acceleration is negative. The force required to accelerate the car is equal to the mass of the car times the acceleration. This force, which is called the inertial force, is what you feel when your body is pressed into the seat back when you put the pedal to the metal; likewise it is the force that causes your briefcase to fly forward off of the seat and onto the floor when you slam on the brakes. When two vehicles collide, each vehicle experiences a sudden change in speed called acceleration (or deceleration). This change in speed is known as Delta-V or ΔV. The change of speed divided by the time of the collision is equal to the acceleration (ΔV/Δt=a). And since Force is equal to Mass times Acceleration (F=ma), ΔV is related to the force of the collision by the following relation:
F = m a = m (ΔV/ Δt)
Or solving for the same equation for ΔV, one can write:
ΔV=(F Δt)/m
In auto collisions, the time the vehicles are in contact and transferring momentum (Δt) may vary, but typically it is about 1/10 second. Therefore, ΔV is generally a good measure of the acceleration (a) and ultimately the force (F) of the collision. Since force is what damages vehicles and injures occupants, ΔV is generally a good way to quantify the severity of a collision.
Newton’s Third Law states that every action has an equal and opposite reaction. While this principal may also apply to human behavior, in physics it means that if I lean against the wall with a certain amount of force, the wall pushes back against me with an equal and opposite force. In an auto collision the impacting car is referred to as the bullet vehicle, whereas the impacted car is called the target vehicle. In an auto collision, the force that the bullet car applies to the target car is equally opposed by the target car pushing back on the bullet car.
Application of Principles
Accident Reconstruction is based on the accurate science of Newtonian physics. Unfortunately a scientific answer can be no more precise than the worst input data, and input data is often assumed, guessed, estimated or crudely measured.
One area that is confusing is units of measure. Usually in America speed S is expressed in miles per hour (mph) and velocity V in feet per second (fps), but the terms may be used indiscriminately. In physics V represents a vector, which defines both speed and direction. However, in AR the term V is often used for speed only with no direction specified.
A vehicle can leave tire marks in at least three different ways:
1. Acceleration Skid (“burn-out”)
2. Braking Skid
3. Centrifugal Skid (Yaw Mark)
Burn-outs tend to start out dark and then get lighter as the vehicle gains traction. Generally, speed cannot be determined from burn-out marks. Burn-out skids can be curved or straight, and usually involve only one or two tires (the drive wheels). Braking skids on the other hand start out light and get darker as the skid progresses, since the tire is heating up during the skid and laying down progressively more rubber until the vehicle comes to rest. Braking skids can involve from one to four tires (on a 4 –wheeled vehicle) and they are generally linear. Centrifugal skids occur during turning and are therefore curved.
The most basic technique for estimating vehicle speed is by measuring the length of braking skid marks. The pre-skid speed (mph) is estimated by first multiplying: 30 times the distance the vehicle skidded before stopping without impact times the drag factor; and then taking the square root.
30 is a derived mathematical constant. The distance a vehicle skidded should be straightforward. It is simply the length of the longest skid in most cases. If any other value is used, the reconstructionist should explain why. Drag factor goes by many names, including mu, m, F, C.O.F. (Coefficient Of Friction). It is nearly impossible to know the exact drag factor for a given accident because there are too many variables that determine it. If the same vehicle can be skid tested at the same location this will yield the best available estimate. Tests of other vehicles or other locations may be meaningful or worthless depending on how the test is done. Fortunately, because the answer is based on the square root, small errors in drag factor will be insignificant. The weight of the vehicle is not needed.
If there are multiple overlapping skids, it is necessary to inquire how the skid distance was determined. There are many possibilities, but it is almost never valid to add skid lengths together, or to take an average.
Often the vehicle does not stop in one continuous skid. The vehicle behavior must be broken down into separate regimes, then the speeds added together by taking the square root of the sum of the squares.
There are different but perfectly valid ways to rearrange the same mathematics so it need not look exactly as it does here. It is seldom valid to simply add the individual speed estimates together, because the sum is the sum of the energies, and energy is ½ times mass times velocity squared (1/2 mv2). Mass is an unfamiliar term to most people, but it is intuitively similar to weight. Weight is gravity dependent, mass is not. Your weight on the Moon will be less than your weight on Earth. Mass (measured in Slugs) times 32.2 equals weight (in pounds) if you are on Earth. We have not had an AR case on the Moon yet!Another more controversial method for estimating vehicle speed is the critical speed for a curve based on centrifugal skids or yaw marks.
This calculation is often used incorrectly. It can only be valid if the vehicle is in a steady state condition, not out of control. Non-concentric yaw marks imply the vehicle is going out of control. At least three tires must leave marks that are concentric and circular; otherwise the estimate must be adjusted for these non-standard conditions. Valid application of the calculation technique requires that the vehicle travel at a nearly constant speed through the maneuver. This will be evidenced by tire marks called striations that are radial (i.e. perpendicular or nearly perpendicular to the direction of travel indicated by the tire marks). Critical speed cannot be added to speed calculated by other methods (such as speed from braking skids). It stands alone as the speed of the vehicle at the time when the concentric tire marks were made.
One of the most difficult techniques for estimating speed is speed from crush damage. The data are seldom adequate and the formulae alone take up most of a page. The range of possible speeds for an impact with a fixed object varies widely among vehicles. However, assuming the vehicle is stopped by the impact, impact speed (mph) is generally in the range of one to 1 ½ mph times the deepest crush measured in inches plus the speed that the vehicle will tolerate without being damaged.
Impact Speed (mph) ≈ [(1 to 1.5) x Crush (in.)] + No Damage Speed (mph)
In a front or rear impact involving the bumper, bumper ratings can be useful in estimating the no-damage speed. Speed calculated from crush may be expressed as closing speed, barrier equivalent speed, kinetic energy speed, crash speed, delta-V, DV etc. These terms are not interchangeable, although in certain situations some of these values can be equal.
Momentum analysis can often lead to more accurate estimation of the speed when two or more vehicles are involved. The speeds after a collision can be estimated using the methods shown above (i.e. skid distances and speed addition). The pre-collision speeds can be determined from basic Newtonian conservation of momentum. Mass before collision times velocity before collision equals mass after collision times velocity after collision.
M1b•V1b + M2b•V2b = M1a•V1a + M2a•V2a
This can be simple if the collision is in line, or very complicated if there is travel in different directions before or after the collision. It will be complicated if there are more than two objects involved, such as a motorcycle with people that fly off in different directions. This requires knowledge of the mass (or weight) of each involved object, as well as estimates of the drag factor, distance and direction for each post-collision movement plus an estimate of the pre-collision direction of each object. The analysis can be done with massive vector equations that can be very precise but prone to horrible error. Alternatively, graphical techniques can be used which are easier to understand, but less precise.
This document is a brief description of the principles of vehicular Accident Reconstruction (AR). The information described herein should be adequate for attorneys, insurance adjusters, or medical professionals to gain a basic understanding of the concepts and vernacular of the art and science of AR without having to become an expert in the field themselves. Modern technology (e.g., Total Stations, Computer Simulation Software) developed for AR data collection, analysis and presentation can simplify the process of AR and provide impressive graphics. However, the validity of the analysis can only be as accurate as the raw data collected. There is no substitute for high quality photographs and accurate direct inspections of vehicles and accident scenes.
Acknowledgement
The contributions of our colleagues L.L. Wickham, Ph.D., E.S. Shapiro, A.S.E. and Lynda Laws are gratefully acknowledged.