Speed estimates made from vehicles that slide to a stop or strike another object can be useful in determining speed loss. Speed loss is determined by measuring the length of skid marks that are created by the friction on the roadway surface and the tires on the car. Often times, when faced with a hazardous situation, a driver may try and avoid a collision by applying the brakes. If the brakes are applied hard enough to prevent the wheels from turning the vehicle may slide across the surface it is riding on. The friction between the tires and the roadways surface may leave skid marks on the road. A skid mark is a friction mark on a surface by a tire that is sliding without rotation. Skid marks are mostly straight and are usually 300 feet or less. By using certain speed equations and information collected from the scene, a speed estimate can be made to determine the speed loss of the vehicle. When using a speed equation to make a speed estimate, you must remember that the speed determined is the minimum speed traveled to make a vehicle slide a certain distance. The vehicle would have had to be traveling faster than the estimated speed; if it were not it would have slid to a stop without striking the object. This type of speed estimate is very effective. When it is performed properly the speed is usually very close if not exact to the speed loss the vehicle had until the collision. If the vehicle were to slide to a stop, the speed estimate would represent the total speed of the vehicle at the beginning of the skid marks. In the drawing on the next page, the distance of the skid marks are measured. The length of the vehicle listed as “A” has a skid distance of 120.2 feet. By using certain methods, the drag factor or slipperiness of the road can be determined. In this example we will assume it to be .70. If we used the speed equation of S=5.47 times the square root of df, the substitution of the variables is required. When the variables are substituted the equation would read S=5.47 times the square root of 120.2(distance) times .70 (drag factor). After all the math is done the S (Speed) loss is equal to 50 miles per hour. If the same applied to vehicle “B” the speed loss would be 36 miles per hour. Remember, both vehicles had to be traveling faster than the speed estimated or they both would have stopped prior to the collision. There are several ways to make this speed estimate, however the result should be the same. The variation of 100th of a mile is insignificant.
Making speed estimates using yaw marks is another way to document speed. A yaw is defined as a sideways movement of a vehicle in another direction than that in which it was headed; it’s when centrifugal force exceeds traction force. When this happens certain marks are left on the roadway. By taking careful measurements of the marks on the roadway a speed estimate can be determined. If these measurements are performed correctly, the result is highly effective in determining speed. A yaw mark is a scuffmark made while a vehicle is yawing; a tire that is rotating and slipping parallel to its axel of the wheel makes the mark on the road. Once a vehicle reaches its critical speed, or the speed above which a vehicle could not maneuver without all wheels slipping sideways, yaw marks can be left on the surface. When making this type of speed estimates, some critical measurements must be taken. The radius of the curved path taken by the center of mass must be determined. The radius is defined as a line extending from the center of the circle to any point of the circumference. The radius is always one half of the diameter. Next, the chord and middle ordinate must be measured. A chord is the length of a tape measure stretched from one end of the scuffmark to the other. The length of the tape measure is usually 30 to 50 feet, although it can be longer. The middle ordinate is a measurement taken from the midpoint of the chord and perpendicular to it. The measurement is taken from the mid point to the edge of the mark. When the middle ordinate and chord are known, they can be substituted into the radius equation. When making speed estimates using this information, you cannot combine the speed acquired with any other speed. The speed obtained is the average speed the vehicle traveled during the yaw. In limited applications, this method could also be used to check the critical speed of a curve. In other words, a speed can be determined to show how fast an average driver can negotiate a curve without the wheels side slipping and going off the road. If a driver drives above the speed determined, sideslipping could occur.
There are many accidents that involve vehicles becoming air borne leaving the surface they were riding on. This occurrence is called a flip, fall, or vault. A flip happens when a vehicle is moving sideways and the resistance at the tires surface is sufficient to cause the vehicle to raise and become air borne. An example of this would be a vehicle hitting a curb or riding on loose materials such as wet grass or gravel. The vehicles generally travel horizontally for a considerable distance before coming to rest. A fall happens when a vehicle is no longer supported by the surface it is riding on. In a fall situation, the vehicle generally lands lower than the point in which the fall began, although the opposite is also possible the vehicle can experience a fall going uphill, downhill, or on level ground. A vault occurs when a vehicle flips end over end. A vaulting vehicle must be moving forward instead of sideways. Vaults and falls are usually confused. They are similar, but they are two different actions. In order to make speed estimates from vehicles that flip, fall, or vault, some information must be gathered. The vertical and horizontal distance the vehicles center of mass traveled must be determined. The angle of takeoff must also be determined. The point where the vehicle takes off and its first contact with the ground must be found. The point of rest is not as important when making these calculations. Taking the information obtained and applying it to a formula designed for these types of situations yields an accurate minimum speed. There is also a formula if a takeoff angle is unknown, however it usually yields the minimum speed it would take for a vehicle to flip only.
Using the conservation of linear momentum to estimate impact speeds is another useful way to measure speed. It also starts to set the stage for the time/distance equations that follow. The conservation of linear momentum starts with a vehicle inspection to determine impact points and damage. Impact points are crucial in this speed estimate because the way the cars came together and the way they departed needs to be measured. This is more commonly known as the angle of approach and angle of departure. There are a few ways these angles can be measured. The best way, if at all possible, is to put the cars together. When the vehicles are matched back to the point when they originally came together, a scale drawing of the vehicles can be made and the angle can be measured. You can also put them together as close as possible on a diagram to set the angle. Skid marks are also useful and highly accurate in measuring the angle. If the vehicles slide to the collision point, they can be matched and put back on those marks. After the impact, if skid marks are present, the way the marks “change direction” shows the angle of departure. This can also show the point of impact in this example. Photographs can also be used to determine the angle. If there are pictures of both vehicles, they can be used to see where the cars came together. This is certainly not the best way to make the estimate, but it can be done. As the collision phase begins several things start to happen. Damage is done to both vehicles when the force of the impact deforms the materials of the vehicle. As stated in Newton’s Laws of Motion, the force is equal but opposite of one another. The weaker structure will collapse first from the contact and the stronger will follow suit. The damage reflects movement of the vehicles to themselves and not movement related to the road. In the following example, it shows approach and departure angles of two vehicles that skid to impact. The way the vehicles come together and depart makes it possible to determine speed.
Often times when accidents happen, a question arises if the accident could have been avoided. This is when time/distance formulas can be used to answer those type questions. Time/distance formulas use given information to determine answers to questions. There are several equations that can be used to determine the answer to one particular question. Time is measured in seconds and it is useful in measuring how long it would take to travel from one place to the next. Initial velocity and end velocity are described as a rate change of distance with respect to time. The values placed on the units are feet per second. Distance is a linear measurement and is taken from a fixed point. It is a scalar quality having magnitude only, not direction. Distance is always measured in feet. When dealing with time/distance issues we must first determine what we want to know. Often times this means taking one equations information and combining it with another equation to find the answer to the question. For example, if we wanted to know how fast a car was going at the beginning of the skid marks, or the initial velocity (Vi), we would need three pieces of information to complete one of the formulas. If we know the time it took to slide to a stop, the rate of acceleration, and the end velocity we could substitute those values into a formula to answer the question. The equation in this instance would be Vi=Ve-at. If we assumed it took 4 seconds to slide to a stop with an acceleration rate of 24.45 feet per second, and an end velocity of zero the equation would read: Vi=0-24.45(4). In this instance the initial velocity would be 97.8 feet per second. This equates to 66 miles per hour in this example. Other questions such as how much time does it take to cross an intersection, and could the driver have seen the pedestrian in the road can also be answered.
The National Highway Traffic Safety Administration conducts crash test to determine a vehicle’s crash worthiness. This information is not only used to keep us safe, it can also be used to make speed estimates based on the amount of “crush” to certain parts of a vehicle. Engineers have developed a mathematical model that enables us to make the estimates based on known facts. To make the estimates we must determine how much “work” and “energy” the vehicle posses. Work is defined as the amount of force multiplied by the distance in which it acts. The amount of work reflects in a change in the objects velocity, shape and size. It is measured in foot- pounds. Work is a scalar quality meaning it only has magnitude, not direction. When work is done, energy is transferred between two objects. Work and energy are proportional. The more work the vehicle does, the more energy it posses. Energy can also be used to determine speeds. Most engineers use energy instead of the minimum speed equation. The result is usually a difference of 100th of a mile, which is insignificant. When we speak of speed we don’t say a vehicle was traveling 55.65 miles per hour; we simply say 55 miles per hour. Crush measurements are made by measuring the amount of collapse made by a vehicle colliding with another object. That other object can be another car, or some type of fixed object. When we take the known crash test data and combine it with the information gathered from the damaged vehicle, we can put that information into an equation the can be converted into speed. In order to do this, we must start with a scale diagram of the vehicle in question. Next the amount of crush must be taken. Once that information is known it can be added to the appropriate equation to be converted to a speed in miles per hour.