Risky Business

Time for a bit of math (and a break from the usual topics in this space). First, though, let us look at today’s contestants. Our first contestant is a Ford Mustang, weighing in at about 3500 lbs.

Next, we have a Toyota Sequoia coming in at about 5800 lbs.

And finally, for today, we have an International LoneStar (with trailer) at approximately 80,000 lbs.

Now that you’ve seen the contestants, let’s get on to the math.

Before we do, let’s establish a few rules for the the following data: 1) I realize that the numbers I am dealing with are based on a perfect system and that perfect systems do not exist. However, the numbers are best understood when compared with each other. 2) I know that the weights of the above vehicles can vary quite a bit based on equipment, passengers and freight and so forth. Don’t get hung up on the fact that I didn’t get the curb weight just right. 3) The assumption is that the trailer is loaded to maximum weight.

Moving on, then. Energy. Each of the above vehicles has it while traveling down the road. No, not in the fuel tank. Each vehicle has energy based on the mass and the speed at which the mass is moving. The energy of these objects can be expressed by multiplying the mass of each object by the square of the corresponding speed (velocity), or E = M * (V)2.

This energy in motion is transferred if the objects in motion are abruptly stopped. Billiard balls can be used to understand this quite well. One ball runs into another, transfers nearly all of its energy to the second ball and goes no further itself. As noted above, vehicles are not part of a perfect system (too much friction going on with wheels, engine, wind drag, etc) but the billiard balls are much closer to one.

Here then, is the energy of the Mustang at a range of highway speeds:

  • 50 mph = 293,000 ft-lbs
  • 60 mph = 421,000 ft-lbs
  • 70 mph = 573,000 ft-lbs
  • 80 mph = 749,000 ft-lbs
  • 90 mph = 948,000 ft-lbs
  • 100 mph = 1,170,000 ft-lbs

To get the numbers for the Sequoia, we multiple the above by 1.65. To get the numbers for the LoneStar, we multiply by 22.85. Oh, and stopping the LoneStar from 100 mph means we have to do something with 24 million ft-lbs of energy.

Let’s look at the above list for a moment. We notice that increasing the speed from 50 to 100 mph quadruples the amount of energy which is spent if the vehicle should run into something. In a perfect system (where all of the energy was transferred from one object to another without deformation, etc) the Mustang has enough energy at 50mph to move the LoneStar (if that were what was hit) slightly more than 3.5 feet. At 100 mph, we will move the rig slightly more than 15 feet.

Here’s the thing, though. Since we don’t have a perfect system, much of the energy from a sudden unplanned stop (aka crash) is spent as the colliding objects destroy each other.

Driving a vehicle is inherently risky. Driving it at higher speeds increases the risk much more rapidly than you might think. I am not against driving. However, it is important to understand that the time you gain from increased speed is at the expense of increased risk.

Let us look at a highway commute of 30 miles (not at all uncommon these days). The following list gives us the time it takes to drive 30 miles at the various speeds.

  • 50 mph = 36 minutes
  • 60 mph = 30 minutes
  • 70 mph = 25.7 minutes
  • 80 mph = 22.5 minutes
  • 90 mph = 20 minutes
  • 100 mph = 18 minutes

Given this, the time advantage I gain from traveling 80 mph rather than 60 mph is 7.5 minutes (or 20 33% of the 22.5 minutes). Of course, I greatly increase my risk of getting a ticket (assuming the speed limit is less than 80 mph), increase the probability that I’ll be unable to respond fast enough to a deer coming across the road in front of my vehicle and increase (by 73%) the energy expended on me, my vehicle, etc should things come to an unplanned and immediate stop.

Something to consider, no?

2 thoughts on “Risky Business

  1. When I first got my driver’s license, my dad would make me calculate how much time it would take me to get where I was going at the speed limit, and at 10 mph over the speed limit. We lived in Michigan at the time and most of my trips were under 10 miles, so very rarely was the difference more than a few seconds.

    “The single biggest cause of automobile accidents is impatience,” he’d tell me. “Those few seconds aren’t worth dying for.”

    You can imagine how, at 17, I tried hard to make sure I drove when he wasn’t around to have me do the math and then tell me that one more time. You might also imagine how frequently I have done the same with my own children as they have gotten their licenses.

    1. P&R,

      Thanks for sharing. I believe your dad had the right of it. It is good for all of us to consider how much damage some misplaced impatience can cause.

Comments are closed.