Ed is an EE, PE, and author in Poughkeepsie, New York. You can contact him at [email protected].
There you are, driving along, minding your own business, when you slowly realize you have absolutely no memory of the last few miles. You've obviously followed the road and handled routine traffic, but you simply don't remember any of it.
You've been running on autopilot, a condition formally known as "Automatic Behavior Syndrome." ABS, not to be confused with "Antilock Brake System," occurs when a slightly fatigued person performs a routine task. In essence, your body keeps on keepin' on while your cognition shuts down: You stop thinking.
That's never happened to you, right?
Unfortunately, ABS isn't the only thing that diverts a driver's attention, nor is it the most common. In-car electronics ranging from cellular phones and entertainment systems to Internet connections affect drivers in ways that we're only now beginning to recognize.
There's more to the issue than the number of pixels on a screen, the shape of buttons on the console, or the speed of the data link. Driving, unlike sitting at your desk, involves some fairly scary physics that often goes unremarked. If your gizmo interacts with a driver, you'd best consider the rest of the road as well.
How Far Is a Second?
Speedometers in U.S. cars display speed in miles per hour and perhaps show kilometers per hour in smaller digits. Those are rather large units, though, so a conversion to feet per second puts the problem in human terms: fps=1.5 mph.
At 40 mph your car covers 60 feet each second and, out on the highway, 70 mph means 100 feet every second.
A second doesn't feel like much, if only because humans lack built-in, elapsed-time clocks. If you measure time by other human activities, seconds can be very short. For example, ordinary folks read text presented on paper at 100-200 words per minute. On the road, expressing reading speed in feet per word may be interesting: fpw=88 mph/wpm.
You'll find highway speeds work out to 50 feet per word. Perhaps you have seen drivers in the other lane engrossed in the morning paper? A 24-word paragraph covers 1200 feet, about 1/4 mile. No wonder their daily commute seems so short!
Reading speed decreases when the text appears on a monitor, drops drastically for small-screen text that's not aligned with your eyes, and falls further if you must first find the text on the screen. A few interesting science fair projects spring immediately to mind, don't they?
Pop Quiz: Experimentally determine how long it takes to read an SMS popup on a wireless PDA. Convert the result to feet and compare with your typical following distance.
Energy at Speed
A key difference between your desk and your car is that your car is generally in motion. That isn't exactly a profound observation, but most discussions of in-car electronics and software seem to ignore it completely.
As a consequence of its motion, your car possesses kinetic energy KE, which is determined by a familiar formula: KE=1/2(mv2)
You'll recall from physics class that the U.S. hasn't quite gotten up to speed with this new-fangled metric stuff, which makes the arithmetic messier. There's a good reason engineering folks favor metric units.
The m represents the mass of the moving object. Mass differs from weight, even though both seem to be measured in pounds. The familiar (to those in the U.S., at least) avoirdupois pound is really the pound-force, the effect of gravity on a pound-mass.
The slug, believe it or not, is the proper unit of mass: divide the weight in pounds by g, the acceleration of gravity, 32.2 ft/s2. Thus, a two-ton car weighs 4000 pounds and has a mass of 4000/32.2=124 slugs.
The v represents the instantaneous speed (a scalar) of the object, not its velocity (a vector). Physics folks use s to represent distance, not speed, probably for reasons that make as much sense as pounds and slugs. You must use feet per second, not miles per hour, to keep the units straight.
Cranking the KE equation reveals that a two-ton car at 70 mph possesses 660,000 foot-pounds of kinetic energy. If you prefer joules, multiply by 1.4.
Energy is one case where nonmetric units provide a definite flavor to the answer: A trio of chunky geeks suspended 1000 feet in the air has 660,000 ft-lb of energy. Potential energy, to be sure, but energy nonetheless.
Friction at Work
At rest, a car's kinetic energy is, by definition, zero. The motor converts the chemical energy of gasoline into mechanical energy that turns the wheels to accelerate the car. Once up to speed, the motor must supply energy to overcome various sources of friction.
Stopping the car requires converting its KE into another form so that, when the KE reaches zero, the car is at rest. Brakes convert KE into heat, producing hot brake pads, disks, and drums. A collision converts KE into crumpled metal and smashed glass. Electric cars convert at least some KE back into chemical energy stored in a battery.
If you've ever tried to push a refrigerator across a tile floor, you've noticed that it took a whole lot more oomph to get it started (static friction) than to keep it moving (dynamic friction). The friction model does not cover the gouges in the floor; that's left as an exercise for the interested reader.
Static friction, which creates the force between two objects that are not sliding, always exceeds the dynamic friction between those same objects after they begin moving. The static and dynamic coefficients of friction, s and k, measures the "slipperiness" of the interface at rest and in motion. Steel skate blades on ice have s=0.05, steel on graphite 0.1, and steel on lead 0.9. Rubber on nearly any solid surface can exceed 1.0, but only when it's exceedingly clean and dry. The dynamic k can be an order of magnitude less than the static s, explaining why that refrigerator smacked into the wall.
Multiplying either m by the force pressing the surfaces together gives the frictional force resisting the sideways shove. An automobile's weight provides the force holding the wheels to the ground, so the frictional force is: Ffric=mg=W.
In metric units, the car's weight W equals its mass m multiplied by g. In nonmetric units, the weight is simply what the car weighs in pounds.
A 4000-pound car thus has, at most, 4000 pounds of frictional braking force available if s=1.0. In the real world, the s where the rubber meets the road ranges from 0.6-0.8, reducing the maximum force to 2400-3200 pounds.
Antilock Brake Systems, the other ABS in this column, maximize the friction force between each tire and the road surface. When a tire begins to skid, s drops to k, the tire stops rotating, and you hear a squeal as it begins painting the road with molten rubber. The ABS system releases the brake on that wheel, waits for the force from k to spin the tire up again, then reapplies the brake with the higher s in effect.
Note that ABS cannot stop the car any faster than will allow. Many people seem to believe that ABS can stop their car on a dime, but you "canna' change the laws o' physics." The effective will always be less than the maximum s you might desperately hope for.
The total energy dissipated by the frictional force is the product of the force and the distance (s, remember?) over which it's applied: FE=sFfric=smg.
If you assume the brakes dissipate all the vehicle's KE as heat, you can find the distance required to accomplish that. Surprisingly, to a good first approximation, the stopping distance depends only on the effective and the square of the vehicle's speed, not on its weight.
Set the KE of motion equal to the energy lost to brake friction:
Then solve for the distance:
In a rare example of synchronicity, an old shagbark hickory dropped a branch across the road near our house a few nights ago, evidently in front of an ABS-equipped truck. The next morning we found a bar-straight pair of dotted dual-wheel skid marks leading up to two streaks of warning flare ashes and a pile of branches by the side of the road.
I measured 110 feet of skid marks, during which the ABS cycled the brakes to produce a 50 percent skid with a 5-foot period. Assuming the truck was doing the usual 45 mph in the 40 mph zone, the effective was 0.64 and the ABS pulsed the brakes at 10 Hz.
The dotted skid marks ended just past the tree, so the truck evidently plowed right through the branches before it stopped completely. Fortunately, the branches weren't all that big and there were no bent metal scraps or shattered glass as evidence of a major impact.
Okay, what does this mean? Because the coefficient of friction doesn't vary all that much, stopping distance goes up as the square of speed. If it takes 100 feet to stop at 40 mph, expect to cover 400 feet at 80 mph.
That's why speed kills.
Driving While Distracted
Another difference between your desk and your car is that vital things happen beyond the windshield. Again, not profound, but when a coworker tosses a Gummi Bear over the partition you need not take immediate action. If you don't notice a black bear on the road ahead, you're likely to discover just how much there is to the afterlife thing.
Drivers must first observe a situation, decide what action to take, and can only then steer or brake as needed. The last is the easiest to evaluate figure 200 milliseconds from intention to action, roughly a quarter of a second.
You can win bar bets with this knowledge. Hold a dollar bill vertically with someone else's fingers poised to pinch the portrait, then play a few rounds of "Catch it or match it."
With their arm on the edge of the bar it's essentially impossible to catch the bill, because U.S. paper money takes 1/8 second to fall half its own length from a standing start. Note that ethyl alcohol both slows reaction time and increases confidence, so if you start with small bills and work upward during the evening, you can finesse the odds very much in your favor.
The tasks of observing and deciding require the driver's attention, precisely what cellular telephones and other in-car electronics demand for their use. Unfortunately, human attention is not multithreaded: You can pay attention to only one thing at a time and must switch your attention from one task to the next with some effort.
Yes, you can enjoy background music while working, but you cannot simultaneously listen to the lyrics while doing whatever else you're supposed to be doing. Try it! There's a vital difference between hearing and listening, similar to that between seeing and noticing, which depends on your undivided attention.
Back in the days when Morse code transferred information to ships at sea, experienced operators could simultaneously transcribe Morse with one ear, carry on an unrelated conversation with the other, and smoke the inevitable cigarette. Surprisingly, Morse transcription can be a reflex.
Some tasks, such as dialing a phone, require only a brief slice of attention. Others, such as holding a conversation, require nearly continuous attention to maintain your mental model of the other person. It's not what you're doing with your hands, it's what's going on inside your head.
A phenomenon called "attentional blindness" (or, sometimes, inattentional) occurs when a person sees an event without noticing it, because their attention is elsewhere. When this occurs while driving, it can result in baffling collisions: "How could he not see that bus?" seems typical.
If you've ever tuned a car radio while waiting at a traffic signal, you've noticed that your attention remained fixed on the radio until it settled on a station, even if you used on-the-wheel controls and looked directly at the red light. The radio's tuning delay adds directly to the duration of your attentional blindness, so that when you notice the signal again, you wonder how long it's been green and the horns have been blowing.
When you are absorbed in an activity, external stimuli literally fade into the background as you cease looking around and stop paying attention (see how that works?) to anything other than the task at hand. You stop seeing and hearing anything unusual, which is attentional blindness at work.
Distractions have always been a part of driving. What's new and different is that they're getting longer because the new tasks require so much more attention. Many tasks demand extended, quite abstract, reasoning: reading text, selecting an option, then tapping a button in response. You simply cannot notice another event until the task reaches a point of closure: The PDA displays a message, you read the SMS text, the phone begins an outgoing call, and so forth.
Hands-free phones and voice recognition technologies seem to be of little help because the tasks inherently capture your attention. Even if you're not grappling one-handed with a phone, your mind is still far away from the steering wheel.
Time to Reconsider
Switching attention from one task to another requires hundreds of milliseconds, plus hundreds more for evaluation, plus another 200 or so of reaction time. Estimating the total as one second probably isn't all that far off, as it's certainly not less than half a second.
Add to that the duration of attentional blindness and you've got the beginnings of real trouble. Remember, the skid marks don't start until you hit the brakes, at which point you start wishing for a higher coefficient of friction.
We must not expect users to concentrate on in-car electronics for more than a second, 100 feet, at a time and even that may be too long. Generally, we decide the speed of an embedded CPU, the screen update rate of a display panel, or the number and location of buttons as a trade-off between cost, function, and human factors. For in-car electronics, the choice may be a matter of life and death.
Before you release a new gizmo, do some timing on common tasks and convert the result into feet. You may be terrified at the results.
Better that, than dead.
The National Highway Traffic Safety Administration's summary of its Driver Distraction symposium at http://www-nrd.nhtsa.dot.gov/departments/nrd-13/ DriverDistraction.html includes a chillingly dry experiment about reading a few digits while driving at http://www-nrd.nhtsa.dot.gov/departments/nrd-13/driver-distraction/PDF/9.PDF.
More on the physics of friction, tires, and stopping at http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/frictire.html. This is a popular Physics 101 topic and you'll find lots of calculators and examples across the Web, not all of which give the correct answer.
A relentless description of (in)attentional blindness at http://www.visualexpert.com/Resources/inattentionalblindness.html.
For anecdotal evidence and links to serious studies, look no further than http://cartalk.cars.com/About/Drive-Now/.
Observe the effect of reaction time on driving congestion with a Java applet at http://www.orbicon.demon.co.uk/traffic/traffic.html.
Zen and the Art of Motorcycle Maintenance (ISBN 0553277472), by Robert Pirsig, may get tedious in spots, but you'll never drop a wrench on the floor. Try reading it again.