Saturday, 14 November 2015

Dissecting the Pragmatic Speeder's Rationale

Drivers typically speed for one of two reasons: they derive pleasure from going fast, or they want to arrive at their destination sooner. In this post I analyze how effective speeding is at "making up time".

There's no question that driving faster will shorten your trip time, assuming you don't end up in an accident or stopped by a cop to be handed a speeding ticket because of it. Well, how much time do you actually save?

Let's say you're traveling a distance D down a highway (no stops along the way) where the posted speed limit is Vo. We'll call the duration of the trip at the speed limit to, which would be calculated from Equation 1.

Equation 1: Duration of trip if driven at the posted speed limit

Now you're thinking to yourself that you're not actually going to drive the speed limit, but some other speed V. We'll bring in another quantity, your speed ratio, alpha, which is simply V divided by Vo. If you're speeding, alpha > 1. If you're driving below the speed limit (say due to traffic or weather), alpha < 1.

Equation 2: Ratio of actual speed to posted speed limit

So the actual amount time your trip will take at velocity V is t, calculated from Equation 3 below.

Equation 3: Actual duration of trip

From here we can calculate how deviating from the posted speed limit will affect trip duration, whether you're speeding in an effort to make up time or trying to figure out how much extra time you'll need when you're driving through a snowstorm.

Equation 4: Difference between actual duration and minimum legal duration

So if you want to cut your trip duration by just 10%, you need to drive 11.1% faster than the posted speed limit. A 10% cut in trip duration is only a difference of 6 minutes per hour. In a lot of places you can get away with 15 to 20% over the limit without drawing the attention of police, but even at 20% over you only cut the trip duration by 16.7% (10 minutes per hour). Not really an appreciable amount of time for typical trips. Say you left the house for work late and are trying to make up 10 minutes on a 30 minute commute. In that case you'd need to increase your average speed by 50%! Good way to draw the attention of police, not to mention the several-fold increase to your risk of involvement in a fatal collision. Here's a graph and table to show you how your speed ratio affects your trip duration.

To summarize, speeding a little bit saves you an insignificant amount of time, but in order to make up an appreciable amount of time you need to drive like a maniac. If you consider city driving instead of highway driving, the effect of speeding is even less significant because you spend so much time stopped at red lights. So, while it is technically true that speeding shortens your trip duration, the savings are hardly worth the added risks or costs associated with speeding, such as significantly increased likelihood of involvement in a fatal collision, wasted fuel, speeding fines, and higher insurance premiums.  

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