This is an oft mentioned safety rule that one should employ when driving to ensure an adequate distance is maintained with the vehicle in front of you. When conditions are wet or icy, the rule has been extended to recommend four seconds and up to 10 seconds respectively.

This effectively fixes the traffic volume to a constant arrival rate regardless of the speed of the vehicles. In other words, it presumes to maintain a constant flow of traffic despite the variations in individual drivers and makes the traffic volume absolutely dependent on the number of traffic lanes available.

Since we have a fixed arrival rate of 1 car every 2 seconds (per lane), then we can calculate how many vehicles per hour a road can handle.

Performing the calculation gives us 30 cars per minute or 1800 cars per hour per lane (1) . This defines our saturation point at which the roadway can no longer absorb any additional traffic load. It is important to note that it makes no difference how fast the vehicles are traveling, but only that they travel at a fixed rate and maintain a fixed separation. However, this doesn’t actually tell us anything about the ability to sustain any particular speed, so we need to develop the idea of traffic density.

Since we have this requirement of a fixed arrival rate, the actual speed will affect how many vehicles can be simultaneously sustained on the roadway. In effect, every 5 mph change in speed will add an additional car length to the separation distance. If we use the average of 16 feet for the length of a car, then we will have 11 car length separation when traveling at 60 mph and about 6 car length separation at 30 mph.

If we were to examine a mile long stretch of road and confine it to only one lane, then we saw that the arrival rate was set to allow for 1800 cars per hour. So if we assume that from our one mile “window” we have vehicles that are traveling beyond it and well as before it, we would have a continuous line of vehicles traveling at the defined rate.

However, within the one mile “window” we could determine the actual number of vehicles that could exist within that window at any particular time (known as traffic density) by adding the separation distance and the length of the vehicle itself at a particular speed. At 60 mph, we would have a separation of 176 feet plus the 16 feet of the vehicle itself (2). This would give us a total occupancy size of 192 feet. Over this interval of a mile, we could only have 27.5 vehicles at any given moment without our “window”. At half the speed (30 mph), we would double the number of vehicles that we can have on the road simultaneously (approx 55 cars).

What this illustrates is that as the number of vehicles exceeds the arrival rate, the traffic must slow down to accommodate the larger number of vehicles that must have simultaneous access to the roadway. We will have our “rush hour” scenario.

When we consider that some of the variables that we will encounter are entry onto the roadway being quite specific and the changing of traffic lanes to properly merge into the flow, as well as the attendant lane changes when exiting. This changes the capacity of the roadway dynamically since we cannot maintain a fixed volume with these types of random changes occurring. In addition, individual drivers cannot maintain a fixed speed and separation, so more variation will be introduced into the flow.

What is generally overlooked, is that the ability to enforce such strict separation and speeds is impossible, so to get around these artificial restrictions, drivers will reduce the distance between vehicles and consequently be capable of maintaining higher speeds, which increases the traffic density beyond the recommended two-second rule.

If the separation were one second, instead of two, then twice as many vehicles could be accommodated on the roadway. By increasing the risk, the average driver will find a way to “beat the system”. This is especially true where lane changes can cause dramatic variations in vehicle separation that will be reacted to over a much longer period of time rather than instigating a ripple effect immediately when they occur.

As a result, it is not an unexpected consequence that the more congested traffic becomes, the greater the likelihood that we will be spending it moving at speeds considerably less than we might like. From this we can conclude that abiding by the two second rule and maintaining the rated speed limit are impossible to achieve except under relatively lightly loaded road conditions. Even the simple case of beginning at a red light, presumes that each driver will only begin accelerating after two seconds have elapsed from the previous driver’s starting, a situation that almost never occurs.

A consequence of this rule is that assumptions regarding road capacity based on it, will invariably under-estimate how many vehicles need to be accommodated. When coupled with many states that want to engage in stricter enforcement of the two-second rule, this has the potential to create unparalleled traffic delays. In the following link suggesting improved safety, one approach was to place dots on the roadway, which will simply exacerbate any traffic problems since dots can’t change spacing as speeds vary. Therefore, their placement will be correct for only one speed.

“But the state Department of Transportation pulled the plug on the program after only three days. Confused motorists slowed down to read the signs, causing seven-mile backups during the project’s first weekend, according to state transportation spokeswoman Lisa Murdock.”

I suspect that reading signs is an rather optimistic appraisal of the problem.

(1)  Note that at 10 seconds, this would drop to 6 cars per minute or 360 cars per hour per lane.

(2) At 10 seconds, this separation distance becomes 55 car lengths, resulting in only allowing  6 cars in our mile long "window".