Most mornings on my way to work, at least when school is in session, I pass through a school zone where the flashing lights indicate a speed limit of 20 mph. For those of us who may be in a hurry, reducing our speed to 20 mph from 25 or 30 mph may seem, at best, an inconvenience and possibly even an irritant. How much difference does an extra 10 mph make to safe driving? One would presume that the reason for a slow speed in a school zone is to avoid hitting children that may step/run into the roadway. You may be interested to know that at 20 mph a vehicle travels approximately 30 feet per second [fps]. (A good approximate conversion formula is: speed in mph x 1.5 = speed in fps)
If a child were to run into the roadway, two things need to happen in order to stop short of striking the child. First, it takes the driver some time to perceive and react to the danger and begin braking. Second, once the brakes are applied, it takes some time for the vehicle to come to a stop. During both of those time periods, of course, the vehicle continues traveling forward. Studies have shown that a typical time for a normal driver to perceive, react, and begin to brake when danger first becomes apparent is about 1.5 seconds. Of course, some drivers may be somewhat faster or slower, but that is average.
At 20 mph during perception and reaction time, a vehicle will travel 45 feet (30 feet per second x 1.5 seconds). Once the brakes are applied, it takes approximately 19 feet to come to a stop, for a total distance of 64 feet. In other words, if a child darted out into the road, an average driver would need a distance of 64 feet to perceive, react, and brake to a hard stop just short of striking the child.
One might assume that at 30 mph one would need half again as much distance to perceive, react, and brake to a stop as 30mph is one and one half times as fast as 20 mph. That assumption would be incorrect. While the difference between the time traveled during perception and reaction, 1.5 seconds, is directly (linearly) related to speed. The stopping distance once the brakes are applied is not. At 20 mph, as noted above, once the brakes are applied, it takes approximately 19 feet to stop. However, at 30 mph, the braking distance is not the expected 29 or 30 feet, but actually closer to 43 feet. The total stopping distance at 30 mph (including perception and reaction time) is 110 feet compared to 64 feet at 20 mph.
This phenomenon becomes much more pronounced as speed increases. (The reason for this is not usually intuitive for non-physicists. It arises from the fact that speed lost from braking is proportional to the duration of time spent braking not the distance traveled while braking. Hence, when starting at a higher speed, more distance is traveled during any given braking timeframe. Under normal conditions, dry road, good tires and brakes, etc., the amount of speed lost during one second of maximum braking is about 10 mph (or approximately 15 feet per second) assuming a coefficient of friction of approximately 0.7.
This is true whether one is going 20 mph or 100 mph. Your inner mathematician, if you are fortunate enough to have one, may be noting that acceleration, or in our case deceleration, is technically given in feet per second per second (fps2). However at speeds under 2-300 mph this is a very close approximation). While my parenthetical explanation may be about as clear as mud, the fact is that the distance (as opposed to time) required to brake to a stop increases in a nonlinear manner as speed increases. In fact when speed is doubled braking distance roughly quadruples.
Let’s look at a couple of examples. At 60 mph during the 1.5 second of perception and reaction time, a vehicle travels approximately 135 feet. Once brakes are applied, the vehicle will travel approximately another 172 feet to come to a stop. Recall that at 20 mph during perception, reaction, and braking time, a vehicle travels only 64 feet. At 60 mph the total stopping distance (including perception and reaction time) is not three times that of 20 mph (192 feet), but a much longer distance of approximately 307 feet. At 80 mph, braking distance goes up to 305 feet, almost double the breaking distance at 60 mph. Including distance traveled during perception and reaction time of 180 feet results in a total stopping distance at 80 mph of 485 feet.
Here is a great chart from http://www.csgnetwork.com/stopdistinfo.html putting it all together:
* Note the numbers are a bit different from those used in the examples above as they were calculated using the shorthand mph to fps formula.
The simple way to put it is, the stopping distance for a vehicle does not increase evenly as speed increases but becomes proportionally much greater. Something to think about the next time you see the flashing school zone sign or decide to exceed the speed limit, particularly at higher speeds.