# Does Speeding Make Sense?

Most Americans exceed the speed limit almost every time they drive, to the point that we rarely even think about it. The conventional wisdom is that we’re impatient and it saves us time, doesn’t cost us anything, and doesn’t really matter, except maybe for those pesky cops, who are really just trying to line their budgets anyway.

Well, I like to challenge conventional wisdom. I’m not here to moralize and tell you you’re a bad person if you speed, or even that you shouldn’t speed, but I do want to question all these assumptions, investigate how each of us can make our own sensible decision about complicated topics like this, and look at some data to see if the decisions we usually make are actually logical ones.

We haven’t done enough math yet on Control-Alt-Backspace for my taste, so let’s get our pencils out and run some numbers.

## Time savings

The benefit of speeding is that, on a basic, intuitive level, it saves time: we’re traveling the same distance at a faster rate, so we get there faster. But how much faster? When we start to look at the negative consequences, we need some point of comparison to know if they’re worth the positive consequences.

The potential utility of speeding turns out to vary dramatically depending on where and how we’re driving. Therefore, we’ll look at several different scenarios. I will assume that we’re willing to take on only moderate additional risks of causing an accident or getting a ticket, so we will limit our speeding to 10mph above the posted limit. If you go 60 in a 30 mph zone, you’ll certainly save a lot more time, but most of us would agree you’re a maniac and a public health hazard.

This is undoubtedly the most complicated scenario.

A typical speed limit in town is 30 mph. Let’s say we’re willing to do 40 mph (40 in a 30 may be beyond the line of safe and prudent, depending on exactly where we’re driving and how well the speed limit is set, so we’ll have to keep that in mind when we get to a final number). We’ll say we have a ten-mile drive.

Note: You might want to know about shorter drives. It seems reasonable in this scenario to assume that if we save $t$ minutes by speeding for ten miles, we save $\frac{t}{2}$ minutes by speeding for five miles.

A naïve calculation would say that at 30 mph, we could drive 10 miles in 20 minutes, but this would be completely wrong. In actuality, in an urban area we are likely to spend a significant portion of our time stopped, whether that’s at a red light, at a stop sign, in a traffic jam, to let a pedestrian cross, or whatever. We may also be limited to a speed below the limit due to heavy traffic in front of us, and in any event after a stop it will be a few seconds before we’re driving at the maximum speed again, even if we accelerate pretty aggressively. If we tried to account for all of that precisely, we’d likely need a degree in chaos theory, a lot of information about the city we’re driving in, and quite a bit of calculus. But we don’t need to be exact to be helpful; let’s simplify and take some reasonable estimates. I’ll show all of my calculations, so if you don’t like my assumptions, you can recalculate with your own. In my model, we’re either stopped (going 0 mph), going slowly at 15 mph, or proceeding unimpeded at our chosen speed, and we magically jump between speeds as we accelerate.

When our chosen speed is 30 mph, it seems reasonable to estimate we’re in each category about a third of the time. Our average speed when we’re traveling 30 mph is thus:

$$\frac{1}{3} \cdot 0\,\textrm{mph} + \frac{1}{3} \cdot 15\,\textrm{mph} + \frac{1}{3} \cdot 30\,\textrm{mph} = \frac{ 0 + 15 + 30 }{ 3 } = 15\,\textrm{mph}$$

Thus, when traveling at 30 mph, we make the trip in

$$\frac{1 \,\textrm{hr}}{15 \,\textrm{mi}} \cdot 10 \,\textrm{mi} = \frac{2}{3} \,\textrm{hr} = 40 \,\textrm{minutes}$$

Now for 40 mph. It’s hard enough to get up to 30 mph between stops in heavy traffic. Not only will we be able to get up to 40 mph less frequently, but it will take longer to get there; further, since we’re moving faster we will spend less time traveling at that speed before we catch up to the next stop or slowdown. Let’s change the values to still 1/3 of the time stopped, 1/4 of the time going at 40 mph, and the remaining 5/12 of the time going at 15 mph (this feels on the generous side to me). Our actual average speed becomes:

$$\frac{4}{12} \cdot 0\,\textrm{mph} + \frac{5}{12} \cdot 15\,\textrm{mph} + \frac{3}{12} \cdot 40\,\textrm{mph} = \frac{75}{12} + \frac{120}{12} = 16.25\,\textrm{mph}$$

Which gets us the following time:

$$\frac{1 \,\textrm{hr}}{16.25 \,\textrm{mi}} \cdot 10 \,\textrm{mi} = 0.615385 \,\textrm{hr} = 36.9 \,\textrm{minutes}$$

It looks like we saved about 3 minutes. But

Many cities have so-called green wave areas, which are programmed to yield a number of green lights in a row when driving down a main street, but only if you’re going roughly at the speed limit, which means that speeding can actually slow you down under the wrong circumstances. Even without green waves, our 3 minutes usually ends up being an overestimate of the time we save. That’s because, when traffic lights are in the mix, we only save any time at all if our increased speed carries us through a traffic light we would have had to stop for. If we arrive at a light during the same red phase, it doesn’t matter whether we went 5 miles an hour or 60 since the last light, we still proceed beyond that point at exactly the same time. (If you’ve been driving for any length of time at all, I’m sure you’ve had the experience of having someone pass you aggressively, only for you to smugly pull up right behind them at the next light.)

Verdict: Speeding on surface roads in urban areas, even by 10 mph, almost never yields any useful time savings.

Note: The more suburban you get, the less time you’ll probably spend in heavy traffic and the more time in the full-speed category in my model, and the more time speeding has the potential to save. You still have the problem of traffic light phases, though, so the difference may not be as much as we might hope. Since conditions vary quite a bit based on both the general area and the exact route you’re driving, the only reasonable way to get better than my estimate is to time that route under several different conditions (but if it’s not safe to go 40 on a route, please don’t try it!).

### A small town along the highway

One of my pet peeves is driving on a country road, coming to a small town, and having someone tailgate me as I drive close to the actual posted speed limit. Let’s look at how much time it actually saves to go faster.

We’ll assume the speed on the rural sections is 55 mph and the speed limit drops to 45 mph for 2 miles and to 30 mph for 1 mile at the center (this seems pretty average at least in the areas I normally drive). In our speeding condition, we drive whatever speed we care to on the un-limited section (we won’t actually need this figure), 55 in the 45, and 40 in the 30. (In reality, if you’re speeding through a town you are probably not going at the posted limit out in the middle of nowhere, but in this scenario we’re not even looking at the highway portion.)

To travel 3 miles without speeding, it will take us

$$\frac{1\,\textrm{hr}}{45\,\textrm{mi}} \cdot 2\,\textrm{mi} + \frac{1\,\textrm{hr}}{30\,\textrm{mi}} \cdot 1\,\textrm{mi} = \frac{2}{45} + \frac{1}{30} = 0.078\,\textrm{hr} = 4.7\,\textrm{minutes}$$

To travel the same 3 miles speeding, it will take us

$$\frac{1\,\textrm{hr}}{55\,\textrm{mi}} \cdot 2\,\textrm{mi} + \frac{1\,\textrm{hr}}{40\,\textrm{mi}} \cdot 1\,\textrm{mi} = \frac{2}{55} + \frac{1}{40} = 0.061\,\textrm{hr} = 3.6\,\textrm{minutes}$$

Total time saved: 1.1 minutes per town.

Verdict: This doesn’t save anywhere near as much time as you’d think it would, and it won’t be worth it at all unless you’re going far enough to pass through at least a couple of towns. If you’re trying to cut time off your trip, you’ll probably do better to go faster on the highway (see Intercity travel, later). Speeding in town is much more dangerous than on the open road (that’s why the speed limit is lower there, after all) and is also an uncommonly good way to get a speeding ticket from some dinky little town trying to fill its municipal budget.

### Highway commute

In this scenario, we have a 30-mile drive on a semi-rural limited-access highway. The highway speed limit is 65 mph, and in our speeding scenario we’ll go 75 mph. (Much more and we start to put ourselves at some legal liability in most parts of the country, and I don’t know about you, but I find my car gets harder to control and driving becomes uncomfortable beyond 75.) We’ll assume that we’re able to go at exactly our chosen speed for the entire length of the drive (in reality, we will probably be behind someone driving slower than that speed for a while, but we’ll probably pass them soon enough at faster than that speed, so it’ll come pretty close to even).

At 65 mph, the drive takes us

$$\frac{1\,\textrm{hr}}{65\,\textrm{mi}} \cdot 30\,\textrm{mi} = 0.46\,\textrm{hr} = 27.7\,\textrm{minutes}$$

At 75 mph:

$$\frac{1\,\textrm{hr}}{75\,\textrm{mi}} \cdot 30\,\textrm{mi} = 0.40\,\textrm{hr} = 24\,\textrm{minutes}$$

We saved 3.7 minutes in the speeding scenario. I’m assuming you have a few minutes on surface roads at either end of the highway, totalling maybe 10 minutes one-way, and you drive the route twice a day, so speeding on the highway saves you 7 minutes a day on a 75-minute round-trip commute (split up into two 3.5-minute chunks).

Verdict: If you’re a very impatient person or you’re running late for an important meeting, speeding on your highway commute could make sense. Otherwise, you’re probably better off leaving 4 minutes earlier and having a relaxing drive instead of a harried one passing people and watching for cops. 7 minutes daily isn’t nothing by any means, but it’s not like you can get much of anything useful done in the chunks of 3 minutes you save by speeding, and commuting is one of the biggest sources of stress for most people, so you’ll probably end up happier by making your commute easier than gaining a few extra minutes.

### Intercity travel

We’ll assume again that the speed limit is 65 mph and we’ll speed at 75 mph. The speed difference is exactly the same as in the previous scenario, but this time our time savings will start to add up as we travel a much longer distance. Let’s say we have a 300-mile trip. This is exactly 10 times longer than our previous trip made at the same speed, so we can just multiply our time savings by 10. This time we shave 37 minutes off a 4.5-hour trip.

Verdict: From a pure time perspective, speeding on long road trips adds up to arriving at your destination noticeably faster, so it probably does make sense. (Just don’t get pulled over or have an accident; that will wipe out your time savings for sure!).

### More

If you have your own scenario you’re curious about, try the following handy formula:

$$\textrm{time saved in minutes}\,= 60d\left(\frac{1}{r_p} - \frac{1}{r_s}\right)$$

where $r_p$ is the posted speed limit, $r_s$ is the speed in your speeding condition, and $d$ is the distance you travel. You can use either miles per hour and miles or kilometers per hour and kilometers (just don’t mix miles per hour and kilometers, or you’ll get the wrong answer!)

Warning: If you use something other than the formula above to do your calculations, don’t forget that the relationship between speed and time driving is nonlinear. That is, the faster we start out going, the less time going an additional 10 mph saves us. For example, we save 3.7 minutes by going 75 instead of 65 for 30 miles, but if we were to go 85 instead of 75 (and the highway was empty enough we were actually able to maintain that speed), we would save only 2.8 additional minutes. This may seem a bit odd at first, but if you pick the right example it’s intuitive enough. If you go 20 mph in a 10 mph zone, you’ll self-evidently get there twice as fast, but if you go 75 in a 65, you clearly won’t get there anywhere near twice as fast!

## Gas mileage

People trying to recommend across the board that others not speed often suggest improved gas mileage as a reason to slow down. Let’s see whether that makes sense.

First things first, let’s establish that we end up burning more gas in most speeding scenarios. Most cars are at their most efficient somewhere between 40 and 60 mph, and all cars are at their most efficient with smooth driving. In the city, we have to drive more aggressively and make faster starts and stops to achieve 40 mph for any significant length of time. On the highway, we are driving fast enough that the faster we drive, the worse our gas mileage. (Here’s a straightforward explanation of why.)

Note: If you have a hybrid or electric vehicle with regenerative braking, aggressive driving makes less of a difference to your gas mileage, but it’s still not free – 100% efficient regenerative brakes would violate the Second Law of Thermodynamics, and most systems don’t do better than 70%.

Let’s start by looking at fuel economy on the highway, since it’s easier to calculate.

When we work with fuel economy, we need to remember that miles per gallon is also a nonlinear relationship (see the warning for speed/time driving at the end of the preceding section). That is, if I’m getting 1 mpg and I can improve that to 2 mpg, I will have cut my gas budget in half. But if I’m getting 50 mpg and I improve it to 51 mpg, I’ll have to drive hundreds of miles before I save one dollar. For this reason, it makes more sense to think about the difference in efficiency at different speeds as a ratio. That is, when I go from driving at, say, 65 mph to 75 mph, how much less distance can I drive for each unit of gas my car burns? The answer depends on your car, but Consumer Reports tested a variety of cars in 2009 and came up with figures ranging between 81% and 90%. I averaged their figures for the 7 cars and obtained 85.6%, so we’ll work with that. I’ll also average their figures to assume that your car gets 33 miles to the gallon at 65 mph. (Fuel economy standards have improved since 2009, but this still feels reasonably accurate to me what with the increase in average vehicle size since 2009.)

Let’s look at the highway commute above. How much gas do we save by going 65 as opposed to 75 for 30 miles? If we went 65, we would use

$$\frac{1\,\textrm{gal}}{33\,\textrm{mi}} \cdot 30\,\textrm{mi} = 0.91\,\textrm{gal}$$

If we went 75, we would only get 85.6% of our MPG rating or 28 mpg, so

$$\frac{1\,\textrm{gal}}{28\,\textrm{mi}} \cdot 30\,\textrm{mi} = 1.07\,\textrm{gal}$$

Taken round-trip for a daily commute, you save $2(1.07-0.91) = 0.32\,\textrm{gal}$ per day or 1.6 gallons over a 5-day week by slowing down.

Does that make a difference? Well, it’s probably not a lot of money when gas is cheap, like now. That said, if the value of your time in dollars is low and the price of gas is high, it would seem plausible that slowing down could sometimes make sense from a purely financial perspective, so let’s take a closer look. We’ll use numbers from one week of driving.

We’ll define the opportunity cost of slowing down as follows:

$$\textrm{opportunity cost} = \Delta t \cdot \_t$$

where $\Delta t$ is the time lost by slowing down in hours and $\_t$ (pronounced “money sub t”) is the value of your time in dollars per hour. In other words, if we drove fast, saving $\Delta t$ time, then used that time to do some extra work for pay at a rate of $\_t$, we could have made that much money during the time we lost by driving more slowly.

Then we’ll want to know how much money we’re saving on gas when we slow down, which is easy enough: it’s the number of gallons we save times the price of gas per gallon. In order for slowing down to be worthwhile, we want the amount we save by slowing down to exceed the opportunity cost – otherwise that method of saving money is essentially “below our pay grade”.

If we set our savings figure equal to the opportunity cost and solve for $\_t$ we’ll find the break-even point – the $\_t$ at which our savings equal the opportunity cost. So, if we’re saving 1.6 gallons per week and losing 7 minutes per day to achieve that gain, as we calculated above, and using the current price of gas at the station across the street from my apartment:

$$\require{cancel} \frac{1.6\,\cancel{\textrm{gal}}}{\textrm{week}} \cdot \frac{\,\textrm{\2.70}}{\cancel{\textrm{gal}}} = \left( \frac{7\,\cancel{\textrm{minutes}}}{\cancel{\textrm{day}}} \cdot \frac{5\,\cancel{\textrm{days}}}{\textrm{week}} \cdot \frac{1\,\textrm{hour}}{60\,\cancel{\textrm{minutes}}} \right) \_t$$

After we make sure all the units cancel and crunch the numbers and the dust settles, we find that at current gas prices in my area, we would need to value our time at no more than $2.52 per hour to make slowing down our highway commute worthwhile from a financial/time perspective. I’m willing to wager you value your time quite a bit higher than that! What about city driving? The EPA estimates that driving smoothly in the city can yield 10-40% improvements in gas mileage, depending on your car and conditions as always. I won’t recalculate the numbers since they get much more complicated here and involve a lot more assumptions, but it’s safe to say this is a better deal since we established you generally save very little time by slowing down in the city, so your total opportunity cost is minuscule. If you haven’t thought about fuel economy in city driving before, check out the link: if you drive a lot, you might stand to lower your carbon footprint and save$100 or more per year without costing yourself much of anything.

Verdict: With modern cars, current gas prices, and typical driving conditions, slowing down on the highway to save money doesn’t make sense unless you are short enough on cash that you’re struggling to pay for necessities and need every dollar to go as far as it can. Driving more smoothly in the city may be worth it, but it isn’t a time/fuel economy tradeoff so much as a choice between using more fuel and using less fuel and taking the same amount of time.

Note: It’s worth pointing out that there are many good reasons besides raw economics you might want to improve your gas mileage. You might be concerned about the environmental impact of driving and burning fossil fuels (and you should be). Some people, including me, also find it mildly entertaining to watch the fuel economy figures on their cars and drive to optimize them, and appreciate saving a few bucks into the bargain. Some people speed and weave through traffic because it keeps them entertained; if that’s you, give this one a shot instead – it’s a lot less stressful, dangerous and annoying to other drivers!

## Other externalities

I would be remiss if I ended this article without discussing the negative consequences of speeding beyond spending a bit more money on gas.

Most obviously, speeding is illegal, if generally accepted, and could get you a ticket or even a felony (at least if you go faster than we discussed in this article). And if you get a ticket, your car insurance rates will often go up, which often ends up costing you more than the ticket itself, since it takes a few years to leave your record at most insurance companies. Since I have no actual figures whatsoever to quantify the damage per unit of time, let’s try a Fermi estimate.

• Maybe in fines plus increased insurance costs, a typical speeding ticket costs about $1,000. • The average American probably gets 2 speeding tickets in her lifetime? • And she drives 5 days a week, 50 weeks a year for 30 minutes a day? • And she drives at this average rate for 50 years? • And her odds of getting a speeding ticket are equal for every minute driven, no matter what kind of driving? (Obviously not true, but we’ll let it average out.) Multiplying it out, that’s 125 hours a year spent driving, 6250 total lifetime hours driving, and a total lifetime speeding-ticket cost of$2,000, for a per-hour speeding-ticket cost of $3.13 attributable to consistently speeding compared to always driving the posted limit. I’m surprised that came out to more than the gas savings, but it’s worth pointing out a rule of thumb says we can reasonably expect even good Fermi estimates to be off by up to an order of magnitude in either direction, so we would be smart not to assume my estimate is any more accurate than somewhere between$0.31/hour and $31.30/hour, which is still a pretty wild range! This said, I’d be really amazed if it was more than$10/hour unless you’re an incredibly bad driver, and many Americans drive more than 30 minutes a day, 5 days a week, which would decrease the hourly figure further.

So the cost of speeding tickets probably isn’t going to exceed the opportunity cost of going slower in absolute terms. The main concern is risk and unpredictability. If you usually drive 10 mph over the limit, you might never get a speeding ticket (a high school friend of mine had a 40-year-old mother who was an absolutely crazy driver and had never gotten a ticket of any kind), or you might get slapped with three in one year. If you rarely drive over the speed limit at all, you’re unlikely to ever get a speeding ticket, though you could still get unlucky. If you’re like me and you work at an insurance company, or you don’t have the cash available to pay these costs suddenly, you might have a pretty low tolerance for this risk and prefer to play it on the safe side most of the time.

### Safety

It’s a matter of fierce debate whether speeding actually increases accident risk or whether the bigger concern is how much your speed differs from surrounding traffic, at least in places where speed limits are perceived as too low. What’s not up for debate is that speeding substantially increases accident severity when you do have an accident. This is a matter of simple physics: the amount of energy you have to absorb in a collision is proportional to the square of your speed, so traveling at 80 mph isn’t twice as bad as 40 mph, it’s four times as bad (and a crash at 40 mph is already bad news). Stopping distance is also proportional to the square of your speed, so if you start braking with the same amount of warning at twice the speed, you won’t get your speed nearly as low before you crash.

This relationship means a pedestrian struck at 25-30 mph will usually survive; a pedestrian struck at 40 mph will usually die. For people in cars, the fatality risks start becoming serious at higher speeds, but they still begin to rise rapidly beyond 30 mph or so. Basically, the slower you go, the less likely you are to hurt yourself or someone else.

By the time you’re going 65 or so, you’re almost certain to die if you hit an immovable object, even in a modern vehicle with all the safety systems functioning, so you might argue it doesn’t matter much on the highway. This isn’t quite true though, because going slower still means you can slow down faster and potentially get your vehicle below a survivable speed before you crash, and most accidents on divided highways are with objects that absorb at least some of the impact.

Check out this study for some interesting information and scary graphs, or just start googling for information about speed and injury risk. Ultimately, the best justification for not speeding is likely that driving is a lot more dangerous than we think it is, and slowing down really does reduce the risk.

Is it worth the risk? I think there are too many factors to give a simple answer that applies to everyone in every situation, but hopefully you learned enough from the article to be able to make better decisions in each situation.

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