Explanation – Speed, Difference in Speed and Change in Velocity

It is rare that anyone provides the public with a simple explanation of the difference between “speed of travel along the ground” versus “difference-in-speed” or “change-in-velocity”. These concepts are continually confused yet they are very important in understanding collisions and road safety. Let’s look at some theoretical examples.

Two vehicles travelling in the same direction, side-by-side, along an expressway at 110 km/h may be involved in a collision when Vehicle #1 drifts into the path of Vehicle #2. Since their forward speeds are the same the primary factor that determines the severity of the collision is the speed at which the drifting Vehicle #1 moves toward the side of Vehicle #2. One can visualize this as a minor incident, setting aside what complications may develop after this initial contact.

In a second scenario imagine Vehicle #1 is no longer drifting but is actually travelling behind Vehicle #2 and Vehicle #2 is now travelling only 90 km/h. Vehicle #1 travelling at 110 km/h rear-ends Vehicle #2. Even though Vehicle #2 was travelling slower the severity of the impact was higher to both vehicles because the difference in speed of the two vehicles was higher. The same concept exists at much slower speeds.

Now imagine a city street where Vehicle #2 slows to a speed of 20 km/h and is rear-ended by Vehicle #1 which is travelling 50 km/h. The speeds along the ground are much lower that the examples on the expressway (discussed above). Yet the collision severity is higher in this city street example. Why? Because the difference in speed is higher. In our city street example the difference in speed is 30 km/h (50-20 = 30). In the expressway examples, the difference in speed of our rear-ending example was only 20 km/h and the original example of the drifting vehicle would involve a difference in (lateral) speed of only a couple of km/h.

It is the difference in speed that determines collision severity and what injuries may occur. There are other complications in this discussion which will be left out for now. But one additional explanation will be given.

Speed is a concept that has no “direction” attached to its definition, it only provides a number describing a magnitude. A concept that provides a fuller explanation in collision analysis is the concept of “velocity”. Velocity is the same as speed except that it has a direction attached to it. So a speed along the ground may be 30 km/h, whereas a velocity along the ground may be “30 km/h north”. In the field of road safety research and collision reconstruction velocity is the important concept.

Researchers and reconstructionists often use the following concepts interchangably: Collision severity, Change-in-velocity and Delta-V. They are really talking about the same thing. We often define the severity of a collision by the change-in-velocity caused by an impact. Thus in the city street example, where Vehicle #2 travelling at 20 km/h is rear-ended by Vehicle #1 travelling at 50 km/h, the severity of the impact may be defined by how much velocity was lost during the time of contact. If both vehicles are of the same weight, of infinite stiffness and moving on a frictionless surface they both might sustain a change in velocity of 30 km/h. That is, in a theoretical scenario, Vehicle #2 (the struck vehicle) might  be propelled forward to a speed of 50 km/h whereas the velocity of Vehicle #1 may be dropped to 20 km/h. But such an example will never occur in real-life and something more realistic might involve both vehicles exiting the impact at a velocity change of 15 km/h or less. When we say that a change-in-velocity of 15 km/h has occurred we often exchange this wording to say that a “Delta-V of 15 km/h” has occurred. The Greek letter “Delta” replaces the words “change in” and the “V” replaces the word “Velocity”.

Things get more complicated when we look closer at the time of contact and what forces and accelerations may exist. A Delta-V of 15 km/h may be quite different when the time of contact is very short versus when it is elongated. We often say that in a severe head-on impact  the Delta-V may be completed in just over 100 milli-seconds. 100 milli-seconds is the same as a 10th of a second. But there are many intersection collisions where the Delta-V may be completed in 300 milli-seconds, thus reducing the forces and accelerations at any given time. Yet, in a head-on collision there is much more length of crushable structure that can protect an occupant whereas a vehicle struck in the driver’s door has much less protective structure. So the comparisons and complications can continue with many additional explanations being required.

But keeping the discussion simple, we need focus on this singular difference between ground speed  and difference in speed or Delta-V. There are many times in public discussions when this becomes important. The most common discussion revolves around comments that, if we only reduced the posted speed limit along some section of road then our safety problems would be solved. The obvious fallacy is that changing a posted speed does not mean that the travel speeds will change. Even if the average travel speeds are reduced there is no guarantee that the target speeder’s actions will be changed, it only means that the general, law-abiding, road-user’s speeds will change. The speeder that was the original cause of the problems may continue to ignore the newly reduced speed just like he ignored the original, higher posted speed. But with respect to ground speed, the danger of the severity of a collision is not how fast a vehicle is travelling along the ground but what change-in-velocity is caused during contact. We need to remember from the above examples that a vehicle travelling at 20 or 50 km/h may be involved in a more severe collision than a vehicle travelling at 110 km/h. We need to understand when these concepts apply and when they are being used to confuse an issue.