Every winter, and also the rest of the year, Hay River has a pervasive problem of driving way too slow, in areas of higher speed limits, and way too fast, in areas of lower speed limits. The practice of crawling along the section of Mackenzie Highway where the speed limit is 60 km/h is generally touted as a "safety" measure, and the villagers, being obdurately ignorant of physics and determined not to learn anything different from what they've always done, maintain that this somehow bears a relationship to reality.
Reality, of course, is that what's relevant to driving safety is not driving slowly, but driving to conditions; and second, that the cause of most problems is not speed, but acceleration. And since your correspondent has a degree in physics, I can actually prove it. I just can't write proper notation in HTML, so this will look ugly.
Consider the following.
and when it comes to driving, the relevant force is the friction between your tires and the road, so
If this isn't completely obvious to you, you shouldn't be arguing with me about driving already. Let's drop the s for HTML aesthetic reasons and obviously:
Since μ is the only variable on the right, μ is the constraint on the rate of change of momentum a vehicle can achieve, which is to say that as μ decreases, so does the maximum rate of change of momentum. Which is completely self-evident if you know physics, or if you know how to drive. Speed features nowhere in this equation.
Now since the maximum rate of change of momentum is lower, it takes more times to accelerate. On this note, if you know physics, you're aware that "acceleration" means a change in velocity, which includes speeding up, slowing down, or changing direction. Again, if this is news to you, you shouldn't have been arguing with me in the first place. So as μ decreases, acceleration takes more time. But time is irrelevant in preventing collisions; what matters is distance, and specifically, the ability to stop the vehicle before it can cover the distance to impact.
and
so
and
or
That is to say, you can maintain an almost arbitrary speed safely, as long as you have a long enough distance to any potential catastrophe, and you don't try to apply a force in excess of the static friction force between your tires and the road.
The problem with bad drivers who crawl along in unfavourable weather is thus two-fold. One, by setting some randomly-variable, unpredictable speed, they make it impossible for other drivers to maintain a safe following distance. Obviously following distance has to increase in slippery conditions; by slowing down below the speed limit, you decrease everybody else's following distance. You douche. And two, the crawly drivers are the same ones who hit the brakes spastically whenever they get scared, thus exceeding their static friction force and making ice, which creates yet another hazard for the people who can drive. Again, you douche. If you were paying any attention, you'd notice that loss of control occurs far more frequently in parking lots and at low-speed intersections in town than on the highway. Why? Because of incompetent drivers who stand on the brakes when they want to change their momentum.
Ironically, the RCMP are a good source of hazardous misinformation on this topic, via the propaganda line that "the speed limit is for ideal conditions." There isn't the least truth to that at all. The speed limit depends on the amount of pedestrian traffic that interacts with vehicle traffic on a particular section of road, which is why playground zones have the lowest speed limit and highways have the highest speed limit, regardless of the physical shape of the road. And because both roads and cars are designed by engineers, who know the laws of physics and are most of the time not morons (certainly not as much so as the average driver, anyway), the speed limit is invariably far lower than what a passenger vehicle can physically sustain, even in seriously adverse conditions. The limiting factor is not the road or the weather, but the driver's skill. So when you get into an "accident" (there's no such thing as a car "accident", but let's pretend), it's not the road or the weather, it's you. Unless it was entirely the other driver's fault, which is extremely rare.
Getting back to the local argument for crawling instead of thinking, some luminary on Facebook argued that "if you hit a patch of ice at a steady speed you're gonna spin out regardless" and this would matter more at high speed than low. Obviously this is false. If you were to "hit a patch of ice" without acceleration, you'd just carry on right through with your momentum regardless of whether your tires maintain friction or not. The only way you can spin is if you apply a torque to your car, that is, an acceleration. There is physically no way you can lose control of your momentum except while trying to change it.
Second, very few "patches of ice" are so slick that your tires can't stick to them – as long as you don't try to accelerate beyond the μ of the ice.
And third, there is no such thing as "hitting a patch of ice." Ice on roads forms due to meteorological conditions that are nowhere near localised enough to create "patches" of ice. Either there is ice on the roads, or there isn't. It's not a leopard print. Where there are significant local variations in ice conditions, they're caused by humans, either inept drivers or inept snow plow operators. But where that's the case, it's your responsibility as the driver to anticipate the conditions, by looking far enough ahead and by having a clue how traffic affects ice. If you don't know this, driving slowly won't help you one bit.
Let's now look again at the equation we derived.
Again, as μ decreases, d(min) has to increase. But d(min) is limited by how far you can see. There are essentially four factors here: the amount of light, the opacity of the atmosphere, any obstacles, and where you're looking. If it's dark, you can't see as far, d(min) decreases, you have to slow down. Or, as a lot of cowboys here like to do, but some extra-bright lights on your truck so you can speed in the dark. If the atmosphere is less than clear due to water, smoke, dust or whatever else can float in the air, you can't see as far into it, d(min) decreases, you have to slow down. If the roads bends and you can't see around the corner, d(min) decreases, you have to slow down. You can't control any of these things. You can, however, and you should, control where you look. And this is another problem of bad drivers: they're looking directly in front of the hood, or even closer, instead of up ahead to see what's coming. So they give themselves a very short stopping distance, and therefore they need a large μ or a low speed. Which is exactly why they crawl and hit their brakes hard. But that's not the fault of the road or the weather or the speed limit: it's their fault for not paying attention.
One last option is to increase μ by changing tires. But if you're gonna do that, don't waste your money on "winter" tires, they make next to no difference. Get studded tires. Studded tires have little spikes that dig into the ground, so that the question is no longer so much friction as the shearing force that the ground surface can sustain before it gives way and the studs translate. And that's a pretty considerable amount of force. It's very difficult to skid on ice with studded tires.
So the moral of all this is, in slippery conditions, look way ahead, increase following distance, and change momentum slowly. And get studded tires, not "winter" tires. It's considerably safer than slowing down. Oh yeah, and ignore the RCMP's propaganda. They're not paid to know the laws of physics.
Science: it works, bitches.
Reality, of course, is that what's relevant to driving safety is not driving slowly, but driving to conditions; and second, that the cause of most problems is not speed, but acceleration. And since your correspondent has a degree in physics, I can actually prove it. I just can't write proper notation in HTML, so this will look ugly.
Consider the following.
F = ma
= d(mv) / dt
= dp / dt
and when it comes to driving, the relevant force is the friction between your tires and the road, so
fs = μs ∙ Ƞ
= μs ∙ m ∙ g
If this isn't completely obvious to you, you shouldn't be arguing with me about driving already. Let's drop the s for HTML aesthetic reasons and obviously:
dp / dt ≤ mgμ
Since μ is the only variable on the right, μ is the constraint on the rate of change of momentum a vehicle can achieve, which is to say that as μ decreases, so does the maximum rate of change of momentum. Which is completely self-evident if you know physics, or if you know how to drive. Speed features nowhere in this equation.
Now since the maximum rate of change of momentum is lower, it takes more times to accelerate. On this note, if you know physics, you're aware that "acceleration" means a change in velocity, which includes speeding up, slowing down, or changing direction. Again, if this is news to you, you shouldn't have been arguing with me in the first place. So as μ decreases, acceleration takes more time. But time is irrelevant in preventing collisions; what matters is distance, and specifically, the ability to stop the vehicle before it can cover the distance to impact.
d = vt + at² / 2
and
t = v / a
so
d = 3v² / 2a
and
d(min) = 3v² / 2μg
or
v(max) = √[2μg ∙ d(min) / 3]
That is to say, you can maintain an almost arbitrary speed safely, as long as you have a long enough distance to any potential catastrophe, and you don't try to apply a force in excess of the static friction force between your tires and the road.
The problem with bad drivers who crawl along in unfavourable weather is thus two-fold. One, by setting some randomly-variable, unpredictable speed, they make it impossible for other drivers to maintain a safe following distance. Obviously following distance has to increase in slippery conditions; by slowing down below the speed limit, you decrease everybody else's following distance. You douche. And two, the crawly drivers are the same ones who hit the brakes spastically whenever they get scared, thus exceeding their static friction force and making ice, which creates yet another hazard for the people who can drive. Again, you douche. If you were paying any attention, you'd notice that loss of control occurs far more frequently in parking lots and at low-speed intersections in town than on the highway. Why? Because of incompetent drivers who stand on the brakes when they want to change their momentum.
Ironically, the RCMP are a good source of hazardous misinformation on this topic, via the propaganda line that "the speed limit is for ideal conditions." There isn't the least truth to that at all. The speed limit depends on the amount of pedestrian traffic that interacts with vehicle traffic on a particular section of road, which is why playground zones have the lowest speed limit and highways have the highest speed limit, regardless of the physical shape of the road. And because both roads and cars are designed by engineers, who know the laws of physics and are most of the time not morons (certainly not as much so as the average driver, anyway), the speed limit is invariably far lower than what a passenger vehicle can physically sustain, even in seriously adverse conditions. The limiting factor is not the road or the weather, but the driver's skill. So when you get into an "accident" (there's no such thing as a car "accident", but let's pretend), it's not the road or the weather, it's you. Unless it was entirely the other driver's fault, which is extremely rare.
Getting back to the local argument for crawling instead of thinking, some luminary on Facebook argued that "if you hit a patch of ice at a steady speed you're gonna spin out regardless" and this would matter more at high speed than low. Obviously this is false. If you were to "hit a patch of ice" without acceleration, you'd just carry on right through with your momentum regardless of whether your tires maintain friction or not. The only way you can spin is if you apply a torque to your car, that is, an acceleration. There is physically no way you can lose control of your momentum except while trying to change it.
Second, very few "patches of ice" are so slick that your tires can't stick to them – as long as you don't try to accelerate beyond the μ of the ice.
And third, there is no such thing as "hitting a patch of ice." Ice on roads forms due to meteorological conditions that are nowhere near localised enough to create "patches" of ice. Either there is ice on the roads, or there isn't. It's not a leopard print. Where there are significant local variations in ice conditions, they're caused by humans, either inept drivers or inept snow plow operators. But where that's the case, it's your responsibility as the driver to anticipate the conditions, by looking far enough ahead and by having a clue how traffic affects ice. If you don't know this, driving slowly won't help you one bit.
Let's now look again at the equation we derived.
v(max) = √[2μg ∙ d(min) / 3]
Again, as μ decreases, d(min) has to increase. But d(min) is limited by how far you can see. There are essentially four factors here: the amount of light, the opacity of the atmosphere, any obstacles, and where you're looking. If it's dark, you can't see as far, d(min) decreases, you have to slow down. Or, as a lot of cowboys here like to do, but some extra-bright lights on your truck so you can speed in the dark. If the atmosphere is less than clear due to water, smoke, dust or whatever else can float in the air, you can't see as far into it, d(min) decreases, you have to slow down. If the roads bends and you can't see around the corner, d(min) decreases, you have to slow down. You can't control any of these things. You can, however, and you should, control where you look. And this is another problem of bad drivers: they're looking directly in front of the hood, or even closer, instead of up ahead to see what's coming. So they give themselves a very short stopping distance, and therefore they need a large μ or a low speed. Which is exactly why they crawl and hit their brakes hard. But that's not the fault of the road or the weather or the speed limit: it's their fault for not paying attention.
One last option is to increase μ by changing tires. But if you're gonna do that, don't waste your money on "winter" tires, they make next to no difference. Get studded tires. Studded tires have little spikes that dig into the ground, so that the question is no longer so much friction as the shearing force that the ground surface can sustain before it gives way and the studs translate. And that's a pretty considerable amount of force. It's very difficult to skid on ice with studded tires.
So the moral of all this is, in slippery conditions, look way ahead, increase following distance, and change momentum slowly. And get studded tires, not "winter" tires. It's considerably safer than slowing down. Oh yeah, and ignore the RCMP's propaganda. They're not paid to know the laws of physics.
Science: it works, bitches.
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