“Safe” cars

So, from time to time, people will tell me that they like big cars like SUVs because they are safe in car vs. car situations (ignoring the rollover issue and other complications for the moment). My first impression is that this does not exactly jive with my understanding of the word ‘safe’. My second impression is that these would be cool numbers to have examples of. I’ve talked about energy before and how bloody awesome a number it is to know. What’s true in chemistry is true in (Newtonian) physics- these numbers are both knowable and meaningful.

So I went to the IIHS Top Safety Picks and selected a tiny car and an SUV at random by rolling dice in each category
Toyota Highlander -3784 lbs
Honda Fit – 2390 lbs

Then I says ‘what if these two cars had a head-on collision at highway speed’? What else do we need to know? For now, each car needs two numbers- mass and momentum. I’ll also throw in energy, just for fun. The mass is the mass of the car plus the driver, and momentum is the mass of the whole thing x the velocity. For the sake of convention, I will call the direction in which the Fit is moving negative, because velocity always has a direction and the Fit and Highlander are moving in opposite directions.

Highlander with 80 kg (average) adult driver: 1796.4 kg
Energy at 30 meters per second (~ 65 MPH): 1.6168 MJ
Momentum at 30 meters per second: 53892 kg*m/s

Fit with 80 kg (average) adult driver: 1164.1 kg
Energy at – 30 meters per second (~ 65 MPH): 1.0477 MJ
Momentum at – 30 meters per second: – 34923 kg*m/s

So there is this cool thing about momentum- it never really changes. If you add up the momentum of all the pieces you have at the start and do the same at the end, you get the same number. So we have two pieces to start, and we’ll assume one at the end (i.e., the cars stick together after the crash, the safest condition for the passengers)- add the Fit (negative direction) and the Highlander (positive direction) and we have the momentum of the two put together. Since we also know the mass of the wreck, the momentum gives us the velocity.

Combined mass of wreck after head-on 30 m/s collision: 2960.5 kg
Total momentum after collision: 18969 kg*m/s
Velocity after collision 6.4074 m/s (~ 14 MPH)

Note that the wreck moves in the same direction that the Highlander started out going (positive). This new velocity allows us to determine how much change in velocity each car (and its contents) underwent.

Velocity change (Highlander): 23.593 m/s (~ 53 MPH)
Velocity change (Fit): 36.407 m/s (~ 81 MPH)

Remember that energy is nothing more than change in the world, so if we assume that the only thing that happened to the passengers was changing velocity (that is, no debris entered the cabin and hit them or anything like that), we can estimate the total energy they absorbed.

Kinetic energy absorbed by passenger (Highlander): 22.265 kJ (equivalent to the passenger falling ~ 90 ft.)
Kinetic energy absorbed by passenger (Fit): 53.019 kJ (equivalent to falling ~220 ft.)

So how much of a difference is that really?

Difference in kinetic energy absorbed by respective passengers: 30.754 kJ (equivalent to falling an additional ~130 ft. or approximately the kinetic energy of an anti-tank round)

For the sake of comparison I also worked out the numbers for a mirror crash (two cars of the same type) so we can see how much worse off a Fit driver is for being hit by an SUV instead of a car like their own.

Difference in energy absorbed by the Fit passenger in crash with a Highlander vs. crash with another Fit: 17.019 kJ (equivalent to falling an additional ~70 ft. or approximately the kinetic energy of a .50 caliber machine gun round)

All that extra energy was brought to the crash by the Highlander. Safety testing and statistics focus on how well a car protects its own passengers. All that extra mass helps your car to not change velocity, which helps you to not change velocity, which helps you absorb less energy. And that’s fantastic- but that energy goes somewhere.

Now there are loads of features that make cars safer than being shot or falling out of a building- both in small cars and big hulking SUVs. Things like airbags, crumple zones and seat belts all have two things in common- they improve the safety of the passengers and either improve or don’t affect the safety of other people in a crash. Mass, which is the main safety feature unique to SUVs, is unlike all of these in that it is the only ‘safety’ feature which puts other people at greater risk.

None of this is to say that there is no legitimate reason to buy an SUV, or even to entirely exclude the idea that some people should be better protected (I’m a big fan of prioritizing children, for example) than others. But words have meaning and we should be careful about how we use them. So next time you’re tempted to call an SUV ‘safe’, take a moment to ask yourself if there really is some cool thing it has that makes it safer. Failing that, at least ask ‘safer for whom?’

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One Response to “Safe” cars

  1. a coward says:

    I had hoped when I read this that you would point out something else (like that somehow the ‘safer’ larger cars aren’t really safe at all even for the passengers). I’m fairly certain that, when most people say the car is “safe” that they are only referring to themselves. No doubt that some could be reminded of the danger of that thinking, but I feel you went way farther with this argument than needed, to the point where you’d likely lose the root problem.

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