Thursday, October 1, 2009

Car vs Pedestrian

Today I am going to talk about a pet peeve of mine, and that is oblivious dumb-ass pedestrians.
Well, to be fair, some of them are not oblivious, just expressing their entitlement to cross the street wherever the hell they want.

I am certain in every college city, drivers are faced with the hordes of students, who after class is over decide that they are going to cross in front of a moving car. They do this in droves, holding up traffic for blocks.

"Hey, the last 20 people just jaywalked across the street, and since the cars are already backed up and stopped then so will I!" They think to themselves.

Well, we all have to deal with that, and it is annoying. But what really gets me are those people who jump out on a crosswalk without even looking!
That's right folks, these people will walk out in front of a large, rapidly moving hunk of metal and not so much as glance upwards from the text they are writing on their cell phone.

In Boulder Colorado, I see this every day on the streets. Some dumb-ass walks out in front of you, and only looks up to give a dirty look and the finger.

The new trend in Boulder are pedestrian walkways.

These walkways either have sensors that detect a pedestrian, and then start flashing a yellow light, or a button that is pressed by the pedestrian to start the lights going.

It seems like perhaps a good idea, but what seems to be happening is that as soon as the pedestrian sees the light flash, they assume that a vehicle will follow state law and yield.
Their mind and sense of self preservation shuts down, then they bomb out onto the cross-walk without hardly sparing a glance upward.

Well, the result of installing these crosswalks are an increase in crosswalk accidents.

Yes, pedestrians have the right of way... but when does having the law on your side mean that you relinquish common sense, or the sense of self preservation? Just because you press a button does not mean a car will stop. Are you willing to put your trust in flashing lights? Or even in the ability of a driver to stop?

Lets consider the physics of an encounter between a moving vehicle and a pedestrian.

To put across why it is a bad idea to step in front of a moving vehicle, regardles if you have the right of way, lets consider some back of the envelope physics.

Persona Dramatis:

1.  A 2007 Toyota Prius.

Weight: 2890 lb (~1300 kg)
Speed: 0 to 100 mph  (0 to ~ 45 m/s)
A butt load of metal, glass, rubber and plastic!


2. An oblivious dumb-ass phone-texting pedestrian

Weight: 220 lb (~100 kg)
Speed: 0 to 15 mph  (0 to ~ 7 m/s)
A butt load of stupidity, soft and fragile tissues, bone, and mostly water.

 Of course I will use metric... after all I am a physicist. ;)

 Lets assume that the Prius is moving at a sedate speed of about 15 mph ( ~7 m/s), and the pedestrian, is standing in the middle of the crosswalk like a dumb-ass.
Now, 15 mph is not very fast for a car, go ahead and try it yourself. Heck, the speed limit in a school zone in Colorado is 20 mph, and if that is safe enough for little kids...

First, lets find the kinetic energy of a 1300 kg Toyota Prius moving at 7 m/s. We do this using:

Turning the crank and I get a kinetic energy of:

K ~ 32000 J

(In case you are wondering, the '~' means 'about')

To put this in perspective, to get this energy our 100 kg oblivious dumb-ass phone-texting pedestrian would have to jump off a ten story building. That is a 100 foot fall!

Don't believe me?
We can calculate this by using the equation for gravitational potential energy.

So, the energy of a slow moving Toyota Prius is the equivalent of a 220 lb person falling 100 feet. Who do you think would win, the car or the dumb-ass?

Now, lets approximate collision between an oblivious dumb-ass phone-texting pedestrian and a 2007 Toyota Prius moving at 15 mph.

Here we use the concept of conservation of linear momentum and conservation of energy to calculate the final velocities of both the car and the pedestrian. We will in this initial run assume a totally elastic collision.

Turning the crank and we get a final velocity of the Prius to be about 6 m/s and the pedestrian is now moving at 13 m/s !

The collision transferred about 8500 J to the pedestrian, which is equivalent to the pedestrian jumping off a 3 story building (30 feet).

Lets assume the oblivious dumb-ass phone-texting pedestrian is launched on an optimum ballistic path as described by the equations:

 Turning the crank and we see the oblivious dumb-ass phone-texting pedestrian is launched a distance of about 56 feet.

Now of course in real life, the collision would be relatively inelastic. You see, energy has to go somewhere.
Some of the energy transferred goes into sound waves (no... not the screaming of the oblivious dumb-ass phone-texting pedestrian), as in the sound of bones breaking, metal bending, flesh tearing.
A good deal of energy goes into breaking bones, tearing flesh, compressing and rupturing tissues and bending metal. Any residual energy then launches the pedestrian into the air, and is reclaimed when the body strikes the ground and bounces several times.

The car, after the collision is still moving at a slightly reduced speed, and therefore has an excellent chance of running over the battered corpse of the oblivious dumb-ass phone-texting pedestrian, thus adding insult to injury.

Now, if you double the speed of the Prius, you quadruple the energy! I will let you do those calculations.
You get the point.

Needless to say, legally the oblivious dumb-ass phone-texting pedestrian may have the right of way. But common sense says that the pedestrian should yield to the car.


  1. Hmm.. most drivers try to decelerate (hit the brakes) upon seeing a (put all your adjectives here ;) pedestrian. How about accounting for that?

  2. The example was considering the velocity of the car at impact with the (put all adjectives here) pedestrian.
    I was neglecting the "jerk" (and no, not the pedestrian) in this example.

    The car's acceleration does not really affect the physics at impact, and would only change the likely hood of the the car running over the "battered corpse of the oblivious dumb-ass phone-texting pedestrian". =)

  3. Ouch. Yeah, people should look both ways before I run them over.