An Engineer's View



C.R. Tyner and Associates Limited

23 Wildwood Blvd.

Dartmouth, N.S. B2W 2L7

Phone (902) 435 - 5315, Fax: (902) 435 - 7647

Prepared for: The Canadian Institute Conference: Motor Vehicle Personal Injury and Property Claims - Halifax, November 1995










3.3 SEAT BELTS: 15





4.1.1 YAW MARKS 24













I first became interested in motor vehicle accident reconstruction in 1974. I had taken a career change that year and had chosen to move from industry to the public sector. I joined the Nova Scotia Research Foundation as Director of their Engineering Physics Division. In that role I was presented with an array of individual and corporate clients bringing problems that ranged widely. On any day our engineering physics group could be working on diverse problems which might range from apple harvesting to deep sea diving. Typical of most Provincial Research Laboratories clients, problems and projects came through the door from all sectors of the economy.

One sunny day during the summer of 1974, a lawyer arrived with a problem. His problem was to determine the cause of a head-on collision. There were no witnesses and all the vehicle occupants either had been killed in the event or had no recollection of the accident. As I was to later learn this is a fairly usual situation. The only evidence the lawyer had available was a series of photographs showing skid marks and badly crushed vehicles. The problem appeared to me to be amenable to analysis based on the physics of the event. I did not know of anyone that I could refer him to so I undertook the problem myself. I made a site visit, gathered as much data as I could, analysed the accident, wrote a report and thought "well that's that." Six months later, much to my initial dismay, I found myself in court defending my analysis and theory of cause! To make a long story short, I survived and the lawyer won his case! This first "problem" quickly led me into the challenging world of forensic engineering, a world I have remained in close association with since that time.

The following paper will hopefully give an overview of some of the well established and some of the newer aspects of motor vehicle accident reconstruction. I have tried to present this paper in mainly non mathematical terms. Hopefully this will assist the reader to gain a good understanding of the terms and needs of the accident reconstructionist. Good communication and understanding of terms make cases flow much more smoothly and quickly.

One of those newer aspects or tools which can greatly assist in the presentation of accident reconstruction evidence is the use of computer simulation of accident events. The following section discusses this new technique.


Over the past two decades, computers have become integrated into most office environments. They now serve many roles, well beyond their usual first corporate job as an assistant in the accounting department. The desktop personal computer is now a fast and powerful work tool capable of easily handling complex tasks that, only twenty years ago, could only be undertaken by the million dollar mainframe computers of the day. Today's desktop can handle complex graphic images at a speed where real time graphical simulation is possible on relatively inexpensive computers. Three dimensional graphic animation software (3D animation software), which will run on desktop computers, has now become available at relatively reasonable prices (less than $5,000.00). These programs allow the integration of scene drawings, vehicle and other drawings into a three-dimensional environment where these objects may be freely moved to simulate the theory of the reconstruction being presented. Such a tool can be a powerful and effective method of presenting a complex subject.

Many of my colleagues agree with me that presentation of vehicle motions in time and space is difficult in the court room. The difficulty increases when the motion described by the vehicles changes moment by moment through the pre-collision, collision and post-collision phases. When presenting this type of evidence one may often include the use of model vehicles, position versus time drawings, graphs and curves showing changes of velocity and position with time, etc. Frequently these tools are presented with the accompaniment of waving hands and other attempts to show the complexities of time varying movement through space. Three dimensional graphical computer simulations can be an effective means of showing these motions in both real time and slow motion.

The use of this type of evidence must however be used with caution. The recent popular film, "Forrest Gump," was a vivid example of the ability of the camera to lie. Video presentation of accident reconstruction simulations can easily be misleading, can include hidden or overt bias and clearly are subject to challenges of inadmissibility. Therefore, when employing this emerging and potentially highly effective tool, a number of guidelines should be considered. From my experience these should include the following:


To avoid challenge and questions with respect to the accuracy and correctness of the 3D animation software it is very important to first clearly establish the evidence database that you will use. This must include all the known physical facts and all the assumptions you have used to define the motions of the vehicles that will be described in the animation. That being established, then prepare your analysis on paper, such analysis being based on and confined to your stated database. Following the analysis, present your theory as to the cause of the accident on paper. Then prepare your animation. The subsequent animation then becomes simply a graphical presentation of your analysis and theory of cause. Such presentation stands or falls on the strength of your database, analysis and theory. Timing is important. Your simulation must be submitted at the same time as your expert report. It is as important as your report and to be accepted for submission into court, both the simulation and your report must be available for full review by opposing experts and possible discovery examination to insure its eligibility for admission.


Animation software has been designed for many markets, motor vehicle accident reconstruction being a very small portion of that market. Most programs feature stunning graphic and multimedia sound effects. It can be tempting to include some of these features in your simulation. Many users of these software programs are graphic artists who love to demonstrate and use special effects. Avoid these temptations and the use of non relevant effects, their use can, and likely will, result in the inadmissibility of part or all of your evidence. The simulation should be conservative and must not speculate or be sensational. A simulation of accident reconstruction evidence is not entertainment. A simulation however can be a highly effective tool in presenting your analysis of the causal theory of a real and usually tragic event.

The simulation almost always should be visual only. Avoid sound effects such as squealing of brakes, crash sounds, horns blowing and the cries of the victims. These special effects are best left to Hollywood and do not belong in the court room. The addition of sound effects on a simulation becomes highly questionable due to the fact that sound leaves no physical indicia at the scene that can be measured. If sounds were reported, their admission into evidence is best left to those who witnessed them. By including sound in your simulation you may risk the admissibility of your entire theory. This is because the time of incidence of the sound, its duration, nature and intensity are very likely not quantifiable. Therefore, it is best to keep your simulations silent.

Similarly, backgrounds in the simulation should be conservative and representative of the actual scene. If the background does not play a part in your analysis and theories, leave it out rather than lay open an opportunity to have it questioned. If visual obstruction is an issue, then show the obstruction, but do not elaborate it. Obstructions are simply that, adding elaboration distracts the viewer from the real issues of your simulation.


A simulation should be as graphically correct as possible. Vehicle shape and colour should be representative of the real vehicles involved. In particular your simulation must be correct in space and time. Most 3D Animation programs will accept mathematical equations to describe the motions of the objects to be moved. If not, break down the motion into one fifteenth or better one thirtieth second increments. Thirty frames per second is the standard North American video frame rate. The motion data can then be shown as a table describing the velocity, position and rotation of the object on a frame by frame basis. This table is easily prepared using a spread sheet with the cells of the spread sheet containing your rules of motion as defined by your theory and analysis. This table can then be used by the person preparing the simulation. Once the simulation has been prepared, check it carefully to ensure accuracy. Remember if you don't check it someone else will. It's much better for you to find and clear the errors rather than have them pointed out to you by the evidence of an opposing expert!


Motor vehicle accident reconstruction can be an effective tool in determining liability in many accident events. The effectiveness of the use of this type of evidence depends greatly on the quality of the data available for analysis. To quote a now hoary computer adage "garbage in equals garbage out." Much of the data used in accident reconstruction is quite volatile and tends to disappear quite quickly after an accident. The following table illustrates the volatility of such data:

Type of Evidence Comments
Skid marks

(Non ABS)

Endure days to months depending on traffic. Length and fine detail reduces very quickly with time.
Skid marks (ABS) Endure hours to days - if present. Difficult to see. Marks vary with different ABS systems. Some vehicles leave no marks. Others do. Best seen along the travel direction.
Gouge and Scrapes Endure weeks to years depending on traffic. Repaving eliminates completely
Vehicle damage Days to years. Vehicles often sold for scrap before examination. Vehicles often stripped and further damaged in scrap yard
Police photographs Months to years. Files are frequently closed and photographs lost.
Police measurements and scene drawings Sometimes very difficult to obtain depending on jurisdiction.

The quality of accident reconstruction evidence depends greatly on the quality of the physical evidence used by the expert. The earlier you bring an expert in on a case the better the result. Sometimes that opportunity does not occur due to the file not reaching the litigation stage for some time. It is therefore very important for the adjuster or initial investigator to understand the needs of the reconstruction expert and provide appropriate, well-documented physical data. Here are a few guidelines for the acquisition of accident data:


Photographs should be 35 mm colour print film preferable taken with a 50 mm fixed focal length lens. A good quality SLR (single lens reflex) camera is a good choice. If your lens is other than 50 mm note the lens focal length. Avoid zoom lens photography where the focal length will be unknown. In general scene views try and include both permanent foreground and background objects so that the photographers location can be triangulated at some later date. This allows positioning of the objects in the photograph. If you are taking photographs of surface indicia (gouges, scrape marks etc.) make sure you note their location on your sketch of the scene. Relate the photographs to the scene, noting where each photograph was taken.

When photographing vehicles take eight general views of the entire vehicle starting at the front of the vehicle and taking a photograph at forty five degree increments as shown in Figure 1.below:

Ensure that you are far enough back from the vehicle to include all the vehicle and just fill the frame. Once these photos are taken then detailed photographs of damage areas, interiors, tires and seat belts should be taken.


The scene should be measured and photographed as soon as possible after the accident has occurred. All locations of indicia relating to the accident should be recorded with a description and photograph of each mark or object. If possible, determine the final rest positions of the vehicles and any scrape or gouge marks which may locate the point of collision. Any visible skid or yaw marks should be recorded as well as any marks from fluid spills. In measuring skid marks, measure their length and their width as well as the track width at a number of points along the total length of the marks. Measurement of both the mark width and track width is often very important in determining or proving which vehicle made the marks. Also record the road positions of the beginning, middle and end of the marks with respect to a fixed reference such as the pavement edge or centre line.

Use a baseline system of scene measurement. To do this, establish a baseline, usually along a well established line parallel to the road such as the pavement or lane edge. Start your baseline (the 0.0 point) from a fixed reference such as a utility pole, manhole, survey reference mark etc. This reference should be just outside (less than 100 m) of the area you are going to measure. Note down on your drawing the description and, if available, the serial number of your reference. Note the displacement from the reference to your baseline. Measure all indicia and objects along the baseline and at right angles to your baseline as shown in Figure 2 below:

Accompany your drawing with photographs of the marks and objects you measure as well as general scene photographs, noting the locations where the photographs were taken on your drawing. Remember, well documented data usually lasts much longer than the vehicles and the indicia at the scene.


The issue of contributory negligence by non use of seat belts has become a significant factor in motor vehicle accident litigation. Use of seat belts can be a highly effective strategy in reducing the probability of death or serious injury in many accidents. Transport Canada has somewhat quantified the effectiveness of seat belt use through an extensive ongoing Canada wide study. They report the following with respect to risk of death or serious injury:






Seat belt use is highly effective in preventing occupant ejection, a common cause of death, or serious injury in rollover and other accidents. Seat belt use also significantly reduces probability of death or serious injury in head on or rear end collision accidents. Their use in side collision events is also very effective in reducing death and injury probability for occupants on the far side of the point of collision. Vehicles often have quite soft sides and damage intrusion on the near side can negate the effectiveness of the seat belt for the near side occupant if the damage intrudes into the "safe space" for that occupant.

It is important to examine all the seat belts in the vehicles as soon as possible after an accident. Check for functionality of each belt. Check and note if the seat belt was cut in the recovery efforts or possibly failed in the accident. Check for obvious signs of occupant impact with the windshield or the dash board. Look for knee impacts on the lower dash. If you suspect non use of the seat belts call in an expert to undertake a seat belt examination quickly, before the vehicle and its seat belts are lost.


My forensic engineering practice extends over the four Atlantic Canadian Provinces. I have found that the policies of various police forces vary considerably with respect to disclosure of police gathered data regarding highway accidents. In some jurisdictions the police have a clear policy to cooperate and provide their data to the parties, their insurers and their representatives, once any possible criminal charges have been put aside. Other jurisdictions make it very difficult to obtain any data without legal action and this takes time and can be quite costly for all involved. In my experience I've found that it is helpful to know the policy in the jurisdiction that your working in. All that is required to obtain policy information is simply to ask. Another important practice in getting as much police cooperation as possible is sympathy and patience. The police have a difficult role to play in motor vehicle accidents and often acquisition of scene and vehicle data is the last thing on their minds. The primary issue they have to deal with at an accident scene is saving lives, rescuing victims, arranging transport for victims to hospital and preventing further accidents from occurring at the site. By the time that's all completed, statements need to be taken, the scene measured and photographed and vehicle data gathered. All this often occurs under difficult weather and dangerous traffic conditions. Be understanding and cooperative in your requests for police information, and despite the variations in policy, you will more than likely get as much cooperation from them as you'll usually need.


This section will examine some of the analytical tools used in accident reconstruction. Accident reconstruction is rarely an exact science so I will also deal with the uncertainties involved in these types of analysis. This paper is titled "Much More Than Skid Marks", and indeed it is; however, skid marks are often key pieces of evidence and must be dealt with. Therefore, the first sub-section will deal with skid and yaw marks.


Determining speed from skid marks forms an important part of accident reconstruction however many factors must be first considered when analysing a set of skid marks such as:

To simply apply the speed from skid mark formulas to any set of skid marks is often incorrect and can be misleading. The normal formula for speed from skid marks is:

S =K*d*+s

Where: S = speed

K = a constant

d = length of skid

= friction or drag coefficient used

s = slope of roadway over the area of the skid

Therefore to determine speed by application of the formula requires that all the factors relating to the skid marks must be known or assumed, i.e. the length of the skid, the friction coefficient and the roadway slope along the skid marks.

The slope of the roadway is easy to determine, but if it is unstated or has not been measured, the result is in question. If the highway is assumed to be level this should be verified and supported by other evidence. Highway slopes are usually low, however, they can range up to 10% and sometimes higher. Secondary and urban road slopes can be even higher.

The skid mark length used in the analysis and the friction coefficient applied are the two factors most often questioned. The length of the skid marks is critical. It is important that they are measured quickly and accurately as they fade rapidly with time and traffic. Were the skid marks all of the same length or did they vary? How they are averaged and treated in the analysis depends very much on their uniformity or lack of uniformity.

The friction coefficient, or drag factor, to be applied is also extremely critical to the results of the analysis. This factor is the one most often wrongly applied. The coefficient used must be consistent with all of the following factors:

- The type of tires making the marks.

- The type of surface.

- The surface condition (wet, dry, icy, snow, etc.).

- The speed of the vehicle.

- The presence of standing water or slush.

All of these factors effect the coefficient to various degrees of significance as the following shows:

TIRES: Performance Radial 105%

Production Radial 100%

Transport tire 85%

Most modern passenger car tires are fairly consistent in dry road braking performance with some slight improvement seen in performance radials under some conditions. Transport or truck tires have significantly poorer friction coefficients on most surfaces due to their harder formulations. Transport tires, however, often offer better braking performance in significant water accumulation conditions or in loose snow and slush. This is due to their much higher inflation pressures than that used by lighter vehicles. Higher tire pressure generally results in greater resistance to hydroplaning.


These factors are the most significant in any speed from skid mark calculations. The values shown in the table below are extracted from Volume two of the Traffic Accident Investigation Manual by Lynn B. Fricke, published by Northwestern University Traffic Institute 1. TABLE OF COEFFICIENTS OF FRICTION FOR VARIOUS ROADWAY SURFACES

Description of Road Surface
Less than 30 MPH

From - To

More than 30 MPH

From - To

Less than 30 MPH

From - To

More than 30 MPH

From - To


New, sharp



.80 - 1.20

.60 - .80

.55 - .75

.70 - 1.0

.60 - .75

.50 - .65

.50 - .80

.45 - .70

.45 - .65

.40 - .75

.45 - .65

.45 - .60


New, Sharp



Excess Tar

.80 - 1.20

.60 - .80

.55 - .75

.50 - .60

.65 - 1.0

.55 - .70

.45 - .65

.35 - .60

.50 - .80

.45 - .70

.45 - .65

.30 - .60

.45 - .75

.40 - .65

.40 - .60

.25 - .55


Packed, Oiled


.55 - .85

.40 - .70

.50 - .80

.40 - .70

.40 - .80

.45 - .75

.40 - .60

.45 - .75



.50 - .70

.50 - .70

.65 - .75

.65 - .75


.55 - .75

.55 - .75

.55 - .75

.55 - .75


.10 - .25

.07 - .20

.05 - .10

.05 - .10



.30 - .55

.10 - .25

.35 - .55

.10 - .20

.30 - .60

.30 - .60

.30 - .60

.30 - .60

It is interesting to note the variance in the values shown in this table and in seeing how these values relate to actual applications. In particular note the significant reduction of values of friction coefficient on some of the surfaces at higher speeds.

The police often will conduct drag sled tests over a skid mark area and make those results available for analysis. The drag sled is simply a weighted section of a passenger car tire that is pulled along by hand force over the area to be measured. The pulling force that causes the sled to continue to slide along the surface is measured using a spring scale. The weight of the sled is known, therefore the friction coefficient of the roadway is simply determined by dividing the pulling force by the weight. The results are usually averaged over a number of pulls done in the same direction as the vehicle making the skid marks. This results in a combined value which includes the slope of the roadway.

Drag test results are very useful data but must be interpreted correctly. The value obtained is likely correct for the low speed sliding friction coefficient of a passenger car tire. It generally could be directly applied in a low speed (less than 30 MPH) situation involving a car or light truck. The drag sled results must however, be factored downward significantly for higher speed events and for use with heavy truck tires.

For example, two straight skid marks of two hundred and fifty feet length were found at a site on a level, well travelled, asphalt surfaced highway having a posted speed limit of 100 KPH. These marks were made by heavy truck tires. The accuracy of the skid mark measurement was stated to be better than two percent. A number of hand pulled drag sled tests were conducted at the site under similar weather conditions. The average friction coefficient determined by those tests was 0.75. The actual skid test results, over ten measurements, showed a variance of plus or minus six percent. The speed of the truck was calculated simply by applying the average friction coefficient, derived from the drag sled tests, directly to the formula. The result was a calculated speed of 75 MPH (121 KPH). This calculation resulted in the driver of the truck being charged with exceeding the speed limit.

If the proper factors to account for the differences between a high speed and a low speed skid were applied to the drag sled results, and the differences between truck tire friction values were considered, the correct value to use for the friction coefficient would be reduced by the following factors:

- Speed reduction factor on travelled asphalt (correction for skid at greater than 30 MPH) = 0.89. This is simply the ratio of the averaged values of coefficients above and below 30 MPH

- Heavy truck tire reduction factor = 0.85.

- Total factor to apply to drag sled value = 0.89 * 0.85 = 0.76.

Therefore, the effective friction coefficient that should be applied is: 0.76 * 0.75 = 0.57. Using this value results in a skid entry speed of 65 MPH (105 KPH). To present a single number in this example is not fully representative of this situation, due to the fact that the variance in the measurements was not included. Including variance results in a speed range rather than a single value. In this case, the fair answer including all these factors, would be a calculated speed range of 63 - 68 MPH (101-109 KPH). Such a result would very unlikely attract a speeding violation.


Yaw marks also present their own special problems. In assessing yaw marks, the calculation includes the same coefficient of friction as in those calculations relating to braking marks. Therefore, the same cautions apply. In addition, it must be determined with certainty if braking was or was not applied, and if the vehicle was rotating during the production of the yaw mark. If braking was applied or the vehicle was rotating, the yaw mark calculation very likely goes "out the window." The reason for this is that a tire presents roughly equal sliding force in all directions on the road surface. That force being equal to the weight carried by the tire multiplied by the friction coefficient between the tire and the road surface. This is easily pictured by use of the concept of the friction circle. Figure 3. shows the concept. The outer diameter of the circle represents the limits of sliding friction for the tire forces or drag factors exceeding that limits results in a slide or skid. Forces, or drag factors, less than the limit represented by the circle result in non sliding braking, acceleration or steering forces. The horizontal axis represents forces or drag factors across the tire track while the vertical axis represents forces or drag factors along the tire track.

Figure 4. represents a braking situation where the braking forces are at the limit and the tire would be sliding. This figure represents pure braking with the braking force arrow (dark arrow) lying along the vertical axis in the "BRAKE" direction. The arrow extends to the limits of the circle indicating brake lock up or skidding braking.

Yaw or sideways sliding of the tire, due usually to the application of excessive steering force, results in the tire sliding sideways. This effect is shown graphically on the friction circle in figure 5. By measuring the radius of curvature of the yaw mark, and knowing the slope or superelevation of the roadway, the speed of the vehicle making the yaw mark can be calculated with similar accuracy to that calculated from braking skid marks. This only holds true under conditions of pure yaw or sideways sliding. This is often not the case. In many instances the "Yaw" mark is made while the vehicle is accelerating or more often braking. If this can be shown to be the case, then the simple speed from yaw marks calculations can be shown to be highly erroneous. This situation is shown in figure 6. below:

Figure six shows the result of combined yaw and braking. In this case, both lateral and longitudinal sliding is occurring. The geometrically combined sum of these forces results in a force equal to the maximum sliding limits of the tire. The braking angle "a" is the angle defined between the skid vector and the horizontal axis. In this case "x" represents the yaw forces and "y" the braking force. These two values are related to the total force "z" by the following relationship:

x2 + y2 = z2

If "y" has any significant value, the value of "x" will be less than that of "z". However the calculation that is used to determine the speed to produce the yaw mark is based solely on the drag limits of the tire i.e. it is based on the value for "z". Therefore, if acceleration or braking is occurring during the production of the yaw mark the calculation will result in a higher speed than actually occurred in reality. These calculations can be seriously in error on the high side. The table below illustrates the magnitude of this error versus braking level where the predicted "critical speed" was = 55 MPH. 2.

This table assumes a zero yaw angle, i.e. the vehicle has not rotated and continues to face its direction of travel.

Braking Level "Critical Speed" Actual Speed
0.0 55 MPH 55 MPH
20 % 55 MPH 54 MPH
40 % 55 MPH 50 MPH
60 % 55 MPH 39 MPH

It is clear that if any significant braking or acceleration is present the calculation of critical speed becomes seriously in error. As the yaw angle increases, i.e. the vehicle has rotated about its vertical axis these effects become much more pronounced as shown in the table below:

YAW ANGLE BRAKING LEVEL Critical Speed Actual Speed
20 Degrees 0 % 55 MPH 53 MPH
20 Degrees 20 % 55 MPH 49 MPH
20 Degrees 40 % 55 MPH 42 MPH
20 Degrees 60 % 55 MPH 25 MPH
40 Degrees 0 % 55 MPH 48 MPH
40 Degrees 20 % 55 MPH 41 MPH
40 Degrees 40 % 55 MPH 28 MPH
60 Degrees 0 % 55 MPH 39 MPH
60 Degrees 20 % 55 MPH 27 MPH

This table shows that both braking or acceleration, combined with yaw angle, quickly produces serious errors in the simple speed from yaw relationship. To ensure that such estimates of speed are correct, the calculation must meet the following tests:

1. Does the radius of curvature of the yaw marks change significantly with length? If it does the vehicle was either accelerating or braking. If it increases the vehicle was likely accelerating, if it decreases then the vehicle was likely braking.

2. Are the yaw marks or striations clean or do they show infilling typical of braking? If they are not clean, braking or acceleration was likely taking place.

3. Do the tracks converge and or cross over? This is a clear indication that the vehicle was rotating.

4. Were the marks examined with a vehicle jig as defined in section 872 of the Traffic Accident Investigation Manual 3. to determine if yaw was present? If no yaw was present and the striations are clean the calculation is likely fairly accurate.


The kinetic energy possessed by a moving vehicle is related to the square of its velocity. Therefore, as speed increases the kinetic energy increases much more rapidly. For example, if a vehicle had a relative kinetic energy of one hundred units at ten kilometres per hour, the same vehicle has a relative kinetic energy of ten thousand units at one hundred kilometres per hour.

In a collision the amount or volume of damage is related to the amount of work done during the collision. The work done in a collision is directly related to the change in kinetic energy involved in the collision. Since kinetic energy and velocity are related in a square law relationship then we can say that the work done in the collision is related to the change of velocity during the collision. This change of velocity is defined as V (delta V). The relationship of V to damage volume requires knowledge of the specific crush stiffness on the particular make and model of vehicle involved. Crush stiffness of most vehicles for front, rear and side impact are now well known. Therefore it is quite possible, in many collisions, to determine speed from the volume and location of impact damage.

The delta V (V) calculated from damage volume is often misunderstood to mean the actual velocity of the vehicle entering the collision. It certainly can mean that when the final rest positions of the vehicles are coincident with the point of impact. However, that situation is relatively uncommon. The usual collision involves partial or incomplete overlaps with vehicles having differing momentum. This results in considerable post collision velocity often accompanied by violent rotation of the vehicles in yaw. In this situation the colliding vehicles come to rest considerably displaced from the point of impact. In this more common situation, V is usually significantly less than the incoming velocity.

To determine the incoming velocity, V must be combined geometrically with the post collision velocity. The post collision velocity Vpc can be determined from analysis of what happened to the vehicle during its post collision slide to rest. This normally consists of an estimate of the post collision drag factor and applying that to the distance travelled post collision. This yields a post collision velocity. The incoming or pre-collision velocity Vi can then be determined from the relationship:

Vi = (V2 + Vpc2)

The incoming or pre-collision velocity is the velocity at impact. Braking often occurs prior to impact and the speed loss during this braking interval must be calculated. The speed loss during pre-collision braking is then simply added to the velocity at impact to determine the speed of the vehicle just prior to pre-collision braking.

There are a number of potential weaknesses in this type of analysis, these are as follows:

- The post collision condition of the vehicle wheels. It is often difficult to determine the condition of each wheel of the now significantly damaged vehicles as they exit from the collision. Were the brakes on or were one or more of the wheels locked by damage? These facts must be known to accurately derive the exit velocity from the collision.

- The effects of dragging portions of the damaged vehicle. Collisions often produce significant downward damage protrusion which drags across the road surface in the final path to rest. How much energy was lost through this action?

- A complex path to final rest. Violent rotation is often a consequence of collision. This rotation often continues to the point of final rest. Making accurate estimates of vehicle speeds under this condition is sometimes difficult.

- The damage area does not involve a significant area of either the front, rear or side of the vehicle. This often happens with collisions involving only a small portion of the total colliding face of the vehicle. Collisions involving small overlaps, utility pole or tree collisions are typical. In this case use of averaged vehicle crush stiffness values may be questionable.

- The condition of the vehicle may not support use of the published crush stiffness values. My forensic engineering practice is in the heart of the Canadian east coast "rust belt", and I often see accident vehicles that are heavily corroded, frequently to the point where the structural integrity has been considerably weakened. A speed determined from damage in these cases should always be questioned. Other methods should be used to derive speed or at least to perform a "reality check" on the results of a speed from damage estimate.

The analysis of speed from damage can be done with proprietary software. A number of programs are available such as "CRASH" and "EDCRASH" 4. I have used EDCRASH for a number of years and find it a useful but occasionally difficult tool to use.

EDCRASH derives speed from both damage and momentum. The program then compares the two methods and if there is close concurrence of the results, the output is likely acceptable. This is not always the case however, as often the damage can not be measured. In this case a momentum analysis may be the most appropriate approach.


Momentum is defined as the product of mass and velocity, i.e. momentum equals mass multiplied by velocity. Momentum is a vector quantity as is velocity, i.e. it has both magnitude and direction. The law of conservation of momentum states that: "In any group of objects that act upon each other, the total momentum before the action equals the total momentum after the action." Therefore if we consider two colliding vehicles, Vehicle 1 and Vehicle 2 having the following properties:
Mass = M1 Mass = M2
Pre Collision Velocity = V1 Pre Collision Velocity = V2
Post Collision Velocity = V1' Post Collision Velocity = V2'

The law of conservation of momentum tells us that:

M1 V1 + M2 V2 = M1 V1' + M2 V2'

Remembering that these are vector quantities and must be treated as such, the incoming speeds of the vehicles may be determined providing that their masses (weights, including contents) are known and the outgoing or post collision velocities can be derived. This equation applies under all collision configurations providing that you remember that velocity is a vector quantity, and therefore since momentum is the product of mass times velocity, momentum also must be treated as a vector quantity.

The most frequent problem in using a momentum analysis relates to the values determined for the post collision velocities V1' and V2'. In simple collinear collisions, such as full head on collisions, where two colliding vehicles come to a complete stop over the point of impact, the determination of post collision velocity is easy, it is simply zero. This "ideal" situation is rarely the case. The usual situation involves deriving the post collision velocities of the vehicles by analysing their post collision paths between the point of impact and their final rest positions. This takes us back to the same analytical situation discussed in section 4.2 above. The same constraints and error possibilities pertain in this analysis as well.

Once post collision velocities are derived, the momentum analysis can be undertaken using various methods for handling vector mathematics. The momentum equation may be solved graphically, or by the use of polar to rectangular conversion, to derive the incoming velocities of the two vehicles. An excellent reference to the solution of momentum equations is contained in Northwestern's Traffic Accident Reconstruction manual. 5.

Computer software is also available to facilitate the analysis of collision through application of a momentum analysis. Trantech Corporation of Redmond, Washington, USA, produce a software package called "AITOOLS LINEAR MOMENTUM" 6. This proprietary program, although sometimes quite "cranky", produces good results and excellent graphic output. The program, despite its occasional crankiness, is easy to use with the usual caution, "garbage in equals garbage out."


The determination of driver perception-reaction time (PRT) is frequently a key issue in accident reconstruction work. Knowledge of this factor is always included in determining total stopping distance. Perception time also plays an important part in the determination of the point where a driver will perceive a hazard when travelling at various speeds, compared to actual physical sight distances. PRT is almost always a critical factor in car-pedestrian accidents.

The human perception - reaction time is not something you can measure at the site of an accident. It is a human factor describing the time it takes a driver to initially detect an object, identify it as a hazard, make a decision and then respond by initiating an action such as braking or steering. There are many excellent studies on this subject some of these are listed in the list of references (7., 8. and 9.). These papers show a wide range of possible values for PRT ranging from the low end, at just less than a second, to the high end of two point five seconds and sometimes considerably greater. The most significant factors that causes this wide variation is the detection and identify components. Typical values frequently used in accident reconstruction usually range from one point five to two point five seconds, however, selection of the "right" value requires careful examination of the circumstances.

Factors which effect PRT are many and include:

- Expected or unexpected hazard

- Presence of fog or haze

- Gradual appearance of a hazard

- A hazard located in a crowded visual scene

- The type of action chosen, steering (faster), braking (slower)

- Poor lighting conditions

- Ingestion of drugs or alcohol

- Fatigue

- Visual contrast between target and background.

Clearly, perception-reaction time is a highly variable and subjective quantity. Can we allocate a likely time for a given situation? The answer is a qualified "yes", and here I quote Paul Olson's paper 7.:

"In light of all the foregoing material, is it possible to make any firm recommendations concern perception-response time in the real world situations with which the readers of this paper may be confronted? The answer is yes, to a degree. Given a reasonably clear stimulus and a fairly straightforward situation, a great deal of data suggest that most drivers (i.e. about 85%) should begin to respond by about 1.5 seconds after first possible visibility of the object or condition of concern."

To this I would add the suggestion that, although I agree with Olson's comments, each situation you address is different. The use of any fixed value such as 1.5 seconds or even 2.5 seconds, as often quoted in determining sight distance in the design of highways, must be tempered and perhaps modified to more closely match the particular situation under analysis.


Visibility plays a big part in many accidents. The sight distance available, when applied to the speed of the vehicle and the perception-reaction time of a driver, often clearly shows that the accident was either simply unavoidable, or that there may have been plenty of time to respond and the driver failed to do so.

If visibility appears to be an issue in any accident, measure and photograph the sight distances as soon after the accident as possible. The Canadian climate is such that foliage and undergrowth density changes considerably with the seasons. It usually makes no sense to measure sight distances in the summer for an accident that occurred in the winter. Delay in measuring the sight distances often lays the results open to needless questioning. These questions may pertain to the possibility that trees had either grown or had been cut, or if the undergrowth seen was the same as at the time of the accident. Again the most important aspect of any data is its accuracy and relevance to the actual accident scenario.


The proper analysis of position vs. time information is a very effective tool in presenting the results of an accident reconstruction. Once vehicle speeds and paths have been determined it is often possible to show a table of vehicle positions with respect to time, both before and after the accident event. The speeds and locations of vehicles prior to an accident will of course become more and more speculative as you move back in time from the accident. Despite the speculative nature of predicting speed and position prior to the accident, if these estimates are consistent with other evidence such as witness statements, they frequently form a useful means of presenting a likely pre-accident picture of what happened.

I find the use of computer spread sheet programs such as LOTUS 123 etc. very useful in quickly and accurately preparing tables of time, speed and position of vehicles in an accident situation. The formulas governing position and speed for each vehicle can be included in the cells of the spreadsheet. By tying those formulas to the cell addresses of stated constants, assumptions and time, a powerful analytical tool develops. This time-position-speed spreadsheet is not only useful for presentation but for "what if" analysis of the reconstruction.

A 'what if" analysis is very useful in testing your theory or hypothesis as to what happened. A "what if" analysis is easily done on the spreadsheet, providing you have tied all your assumptions and stated values into the cell formulas. Once you have done that, all that is needed to undertake a "what if" is to change the cell value, or values, and can you instantly see what happens due to that change. For instance, if you want to see what happens if Vehicle A was travelling more slowly, change the speed assumption for vehicle A, the entire spreadsheet will recalculate showing the new speeds and positions versus time. If you have a lap top, or note book computer, load the spreadsheet into the computer and bring it with you when you discuss your conclusions with your client. Its a great time saver and a very effective way of critiquing your own analysis.

The following is an analysis of a same direction collision between a heavy transport tractor trailer and a car.

Time - Position analysis
MPH ft/sec
SPEED OF Vehicle A 70 102.7
SPEED OF Vehicle B 40 58.7
Stopping Distance (Vehicle A) 257 feet
Point of impact = time 0
Position reference = POI = 0
DECELERATION 0.25 g = 8.1 ft/sec/sec
Pre Impact Vehicle A Vehicle B
(seconds prior) feet MPH feet MPH (ft)
0 0 40 0 40.0 0.0 IMPACT
0.5 29.3 40 33.4 42.7 4.0
1 58.7 40 66.7 45.5 8.1
1.5 88.0 40 100.1 48.2 12.1
2 117.3 40 133.4 51.0 16.1
2.5 146.7 40 166.8 53.7 20.1
3 176.0 40 200.2 56.5 24.2
3.5 205.3 40 233.5 59.2 28.2
4 234.7 40 266.9 62.0 32.2
4.5 264.0 40 300.2 64.7 36.2
5 293.3 40 333.6 67.4 40.3
5.46 320.3 40 364.3 70.0 44.0 brakes fully on
5.96 349.7 40 415.6 70.0 66.0
6.46 379.0 40 466.9 70.0 88.0 brakes applied
6.96 408.3 40 518.3 70.0 110.0
7.46 437.7 40 569.6 70.0 132.0
7.96 467.0 40 620.9 70.0 154.0 START PRT

Once your analysis is set in this form you can also automatically present the data graphically. The graphs will then change automatically as you do your "what if" analysis. This helps considerably in visualising what is happening to the analysis as you change the inputs. This same technique is also very helpful in determining the sensitivity of your assumptions. For example, this technique can answer the questions relating to "how much does it effect the result if one changes this or that value by (say) ten percent? In summary, I have found the use of a spreadsheet based time vs speed and position analysis a highly effective method of presenting complex data. Furthermore this technique functions as an excellent method to critique and find sensitivities in my own and other expert's analysis.


The safe travel speed on any section of highway depends on many factors relating to the highway geometry such as, sight distances, urban or rural location, and weather factors. These factors often alter the liability situation in many accidents. Was the driver travelling too fast for the constraints of the highway design or for the prevailing weather? Were the correct warning signs in place to caution the driver? Was the highway design, or poor highway maintenance, partially or fully responsible for the accident? These questions can often be answered by the forensic engineer, particularly if the engineer is brought in early.

Determination of critical speed for curves is a fairly common task in accident reconstruction. Critical speed can be determined by physically measuring the curve to ascertain the curve radius and superelevation. Lateral acceleration can also be measured directly by using a car mounted accelerometer. I use an accelerometer quite frequently to measure and record the accelerations experienced in rounding curves at various speeds. The unit, a "g-analyst" is a relatively inexpensive instrument (less than $600.00) that mounts on the floor of my car under the passenger seat. The unit is stated to be accurate to one hundredth of a "g" and records the average accelerations on the two horizontal axis of the vehicle five times per second. Combining the lateral acceleration measurements with curve radius measurements gives both the overall average lateral acceleration in a curve, and the finer detail caused by curve and surface imperfections. Surface and geometry imperfections can be shown to cause accidents.

The accelerometer also acts as an excellent and accurate method of measuring road surface drag factors at any desired speed. If placed in the accident vehicle or an identical vehicle, skid tests using that vehicle become very credible evidence to the precise performance of that vehicle in braking.


I am frequently asked why injuries occur in minor collisions when no vehicle damage was observed. Urban collisions often involve low speed bumper collisions at speeds less than twenty kilometres per hour. These collisions frequently result in minimal or no property damage and yet people get injured. Soft tissue injury, whiplash, nerve damage and occasionally major injury can and does occur. One of the reasons for this can be seen by looking closely at the accelerations involved in low speed collisions and their relationship to the kinetic energy in the collision.

Modern vehicle bumpers are built to withstand collisions of at least five miles per hour without permanent damage. The "five mile per hour bumpers" absorb the impact energy in springs and then restore that energy to the colliding vehicle or vehicles during the rebound. The acceleration, and consequential forces, applied to the occupants involved in a typical collision is proportional to the rate of change of velocity with time (V/t). In a low speed bumper collision, assuming a rear end impact on a stopped vehicle of (say) ten kilometres per hour, the struck vehicle will be projected forwards at a speed of ten kilometres. Assuming the two vehicles have equal mass, the striking vehicle will be stopped by the collision. Therefore both vehicles experience a V of ten kilometres per hour. All the momentum of the striking vehicle is transferred to the struck vehicle. All the energy of the impact is stored in the bumper shocks of both vehicles during impact and restored during the rebound of the bumper shocks. The typical deformation of the bumper shocks is about three to six inches, i.e. all this velocity change occurs over a distance of about six inches. The struck vehicle is accelerated to ten kilometers per hour in six inches and the striking vehicle is brought to a stop from ten kilometers per in the same distance.

The acceleration experienced can be calculated by the relationship:

V2 = V02 + 2ax

Where V = the final velocity

V0 = the initial velocity

a = the acceleration

x = the distance over which the acceleration occurs

In this case V = 10 KPH = 9.1 feet per second

V0 = 0

X = 6 inches = 0.5 feet

Solving for the acceleration "a" yields a value of 331 feet/second/second or 10.3 g. This is a significant acceleration. To compare this value with highway collisions which involve massive crush and vehicle damage, the acceleration experience in a highway collision is only three to five times higher (30 to 50 g).

Acceleration experienced in a collision increases roughly linearly with speed, while damage increases as the square of the speed beyond the limits of an elastic collision, i.e. above about ten KPH. In low speed elastic bumper collisions the acceleration is higher than might be first expected due to the elastic rebound of the "five mile per hour bumper". This is usually not the case in side collisions where crush can occur at very low speeds. Side collisions should be considered as essentially inelastic at all speeds.

Low speed impacts, particularly rear end collisions, are often events that produce little or no property damage but often can cause quite serious occupant injury. The absence of property damage does not always mean that the collision was a minimal event for the occupants.


Use of computer assisted analysis and simulation can create a problem in presenting the results of the analysis for litigation purposes. These programs can be very useful in speeding up the analysis, in handling complex and tedious calculations, and in graphically presenting the data, however, these programs need to utilized in the appropriate way to be acceptable in court.

The expert's analysis of any event will very likely be challenged and subject to intense review by others. In my experience, in using these programs, it is best to present your analysis on paper employing a "classic" physics approach as well. By showing your calculated results together with the computer output, you eliminate a lot of concern about the accuracy and appropriateness of the computer software. In addition, programs such as "EDCRASH" 4 produce as output, reports indicating warnings and errors. Failure to include those reports with the EDCRASH results immediately places the entire analysis under question. This may lead to questions being raised as to why the report was not included, and if there are possibly fatal errors in the analysis that are not being disclosed. A clean warning report will reduce these concerns considerably.

The same cautions apply to use the of computer simulation of an accident. Computer simulation of accident events can be very effective in illustrating the theory of cause of the accident. However, the simulation stands or falls on the quality of the data and analysis from which it was built. The best approach is to present a solid foundation of evidence and analysis and then use the computer simulation to demonstrate the results. Providing that the foundation of your theory is accepted, this approach will leave little opportunity for serious challenge of the use of the simulation.


Computer simulation of reconstruction evidence has been discussed throughout this paper. This section is included to recognize the software manufacturers and the suppliers who have been most forthcoming in providing video recordings of both real and contrived simulations of accidents. These are:


The Video clips presented at the conference have been supplied by the following:

1. Reconstruction of Cronin v Republic Airlines:

Pixel Motion Images inc.

1577 Granville Street

Halifax NS B3J 1W9

This reconstruction was prepared by Steven Elliot in 1994. Steven now works with Pixel motion. The animation was prepared on a Silicon Graphics workstation and was used in an actual case that was subsequently settled out of court.

2. 3D Studio simulations courtesy:

Graphics Unlimited

260 Wyse Road

Dartmouth NS

Simulations from:

Copyright 1993, Autodesk Inc.

Copyright 1994, Autodesk Inc.

Copyright 1994 Autodesk 1994

Portions of the music copyright 1994, Interactive Audio

Copyright 1995 Autodesk Inc.


This paper, as promised by its title, has dealt with much more than skid marks. Skid marks, yaw marks, vehicle damage, highway factors, the physics of motion, visibility, weather, the properties of vehicles, tires, seat belts, and a number of human factors collectively must be considered in solving the accident reconstruction problem. These problems rarely can be dealt with by the engineer alone.

The role of a forensic engineer is primarily problem solving. The data we frequently first address is often flawed or insufficient to resolve most problems at first sight. The process to solve the reconstruction problem is often a lengthy, and occasionally, a convoluted one that usually requires a team solution. Team members can include counsel, the forensic engineer, insurance adjusters, the police, surveyors, vehicle mechanics, metallurgists, meteorologists, aerial photographers, illustrators, drafters and graphic artists. Counsel, aided by the forensic engineer, usually leads the team.

I hope I have given you greater insight and reflection into the role played by the engineer in accident reconstruction. The forensic engineer must contend with a broad spectrum of engineering applications and other factors in defining the problem, gathering and analysing information, presenting theories and testing them before coming to any firm opinion. To do this, he or she must function as an investigator, analyst, teacher, consultant and finally as an author and presenter. The engineer, working closely with counsel and the team members, can effectively bring together all the needed factors to produce a well founded solution to the problem of vehicle accident reconstruction.


1. Title: Volume 2 of the Traffic Accident Investigation Manual

Author: Lynn B. Fricke

Publisher: Northwestern University Traffic Institute

2. Title: Highway Speed vs. Sideslip (Critical Speed in a curve)

Author: Lindley Manning, P.E.

Publisher U.S. National Academy of Forensic Engineers

3. Title: Steering Overcorrection in Traffic Accident Reconstruction. Topic 872 of the Traffic Accident Investigation manual (see 1. above)

Author: Gary W. Cooper and Lynn B. Fricke

4. Title: EDCRASH Vehicle Analysis Package

Vendor: Engineering Dynamics Corp. 530 First Street, Lake Oswego, Oregon 97034 (this address may have changed)

5. Title: Momentum Applications in Traffic Accident Reconstruction. Topic 868 of the Traffic Accident Investigation manual (see 1. above)

Author: Lynn B. Fricke


Author: ARSoftware

Vendor: Trantech, 2703 152nd Avenue NE, Redmond, WA 98052-5515, Phone: (206) 861-4666

7. Title: Driver Perception Response Time

Author: Paul L. Olson, The University of Michigan, Transportation Research Institute

Publisher: SAE paper # 890731

SAE, 400 Commonwealth Drive, Warrendale, PA 15096-0001

8. Title: Perception and Reaction in Traffic Accidents. Topic 864 of the Traffic Accident Reconstruction Manual (see reference 1 above)

Author: J. Stannard Baker

9. Title: Perception/Reaction Time Values for Accident Reconstruction

Authors: M.J. Sens, P.H. Cheng and J.F. Wiechel

Publisher SAE paper # 890732

SAE, 400 Commonwealth Drive, Warrendale, PA 15096-0001

Biographical Sketch

CLIFFORD R. TYNER, P.Eng. is president of C.R. Tyner and Associates Limited. Mr. Tyner graduated in Electrical Engineering in 1962 from Denbighshire Technical College in the U.K. He has worked in Canada and the U.K. in government, university and industry prior to joining the Nova Scotia Research Foundation in 1974. After serving for twenty-one years with the Foundation, Mr. Tyner retired as Vice President in April 1995 and formed C.R. Tyner and Associates. Much of the work of the new company focuses on forensic engineering, particularly in the area of motor vehicle accident reconstruction, a field Mr. Tyner has worked in for more than twenty years. Mr. Tyner's work ranges over all four of the Atlantic provinces. In that practice he has performed over four hundred reconstructions and appeared in court in all four provinces a total of twenty-six times. He is an instructor in accident reconstruction for the Continuing Education Division of the Technical University of Nova Scotia.

C.R. TYNER AND ASSOCIATES LIMITED, is an engineering consulting company offering forensic engineering and product design consulting services throughout Atlantic Canada. Principal areas of expertise include motor vehicle accident reconstruction, vehicle - pedestrian accidents and electro-mechanical product design.




Phone: (902) 435-5315

Fax: (902) 435-7647