Thursday, April 17, 2008

Dear CSI

So, obviously my brian hasn't working right lately.

For why, see above.

I can't remember if I mentioned it the first time this episode aired. If I did, consider it annoying enough to be worth mentioning twice.

If a kid is on a go cart, driving about 60 mp/h, and he is behind a truck, also going 60 mp/h, and one of the truck's tires blows out and hits him, it will NOT hit him at a "combined speed of 60 mph."

First of all, the tire won't be going at the full 60 mph. If it was, it would still be traveling along with the truck and would never hit the kid in the first place.

Secondly, when they are traveling in the same direction, you do not add the speeds, you subtract them.

Why? It's simple.

The amount of force isn't based on total speed, it's based on acceleration. (Or, in this case, deceleration). The amount of force is dependent upon the change in speed, not the speed itself. That means that since the truck doesn't change speeds, it only matters in the equation because it can help us guess the speed of the tire, which again, is very much not 60 m/h.*

The go kart, however does change speeds, as does the tire. The tire slows down the go kart while the go cart speeds up the tire. Alternatively, a piece of the go kart could break off, and both the tire and the part would follow the tires path (which is basically standing still) while the rest of the go kart goes on it's merry way. The correct formula for either scenario is:

Force = MA => F = M (change in speed/time)

Which means that in order to get "962 ft-lbs of energy" from the tire hitting the head in the second scenario, assuming the go-kart is going at 60m/h, the head would have had to go from 0 m/h to 60 m/h in about a tenth of a second.

962 ft-lbs = 2 lbs * [ (60 m/h - 0 m/h)/x seconds] => x = 0.1247

Which is so not how quickly the head would come to a full stop.


I have no idea how many ft-lbs it takes to decapitate someone with a blown out truck tire, but I do know that your math sucks and your physics is even worse.



*PS, the speed of the truck is in fact completely irrelevant to the equation unless you want to assume that the tire changes speeds at an even faster rate than within a tenth of a second.

If the tire had only slowed down to 20 m/h (a lot more likely) instead of already being at a dead stop, the equation would look like this:

962 ft-lbs = 2 lbs * [ (60 m/h - 50m/h)/x seconds]

making x = 6 hundredths of a second

If the tire was indeed goingclose to 60, the equation would look like this:

962 ft-lbs = 2 lbs * [ (60 m/h - 55m/h)/x seconds]

making x = 1 hundredth of a second

PPS this would be why I rarely watch you anymore.

PPPS That's not actually true. It would be the sexism and reactionary pov that annoys the hell out of me. But this drives me crazy too. Most especially because while I can forgive some fudging of the math in the service of the story, the story is not at all served by making a really basic physics mistake. It just makes all those pretend smart people look really dumb. And makes me feel dumb for watching.


Weeelll... said...

As I recall, for every action there is an equal and opposite reaction. If the truck wheel is spinning forward at the rate for a truck to be going 60 MPH, when the tire blew out, the rim would provide an action, spinning forward, which would have the reaction of firing the torn off tire backwards. If you think of the tire as moving the road backwards rather than the truck forward, I think it makes a fair amount of sense that you'd still add the speeds.

Mickle said...

this is what I get for trying to think on no sleep :(

(Although, they still said it weirdly)