Dichotomy...

Time for adventures in real-life physics! Led by the man who shouldn't have passed Physics II in college and (Brian and Tim should appreciate this) was "taught" Physics I by Jario. Brace yourselves for lots of wrong assertions and frequent formula jockeying! We all know TV lies, especially in commercials. But my new favorite commercial is the Lexus IS where they assert that a vehicle dropped from over 4000 feet can be outrun by a car on the ground. Every time I've seen it, something just doesn't seem right about it. Tonight I busted out my calculator and tried to make myself feel better. I knew that their claim just didn't sound right (according to the fine print, they never attempted it, but in simulations it supposedly works out). Okay, so the falling car has a roughly constant acceleration of 32 ft/s^2 from gravity. My initial calculations told me what I expected, that at impact the car would be travelling about 500 ft/s (340 mph) and the drop would take about 16 seconds. This is ignoring any wind resistance of course. According to Lexus's website, the IS 350 has a top speed of 142 mph (electronically limited). It also can run a quarter mile (1320 feet) in 14.2 seconds, giving it an average acceleration of 13.1 ft/s^2 over that time. Obviously, there's no way that this car is going to travel an additional half mile in less than 2 more seconds. Certainly, wind resistance must play a role here, but even a falling car that's slowed down surely can't fall slower than an accelerating vehicle on the ground. I was ready to call up Lexus and tell them to go to hell. Then I saw the commercial again and it states in fine print that their simulation is for a horizontal drop only. At first this made no sense to me, since clearly things don't drop horizontally, they drop vertically. But when I thought about it some more, I decided they must mean dropping the car wheels down and body parallel to the ground. This would create a lot more wind resistance than nose-first and substantially raise the drag coefficient of the falling car. I had to kind of guess at some parameters (specifically, I used a Cd of 1, though this might be somewhat low), but if you use this new piece of info to calculate terminal velocity of the car, it comes out to somewhere in the neighborhood of 140 mph. So I suppose that when you drop the car that way, and if it doesn't turn over at all, yes, it might be possible to out run it on the ground. I still feel like the falling car will reach its terminal velocity before the driving car reaches its top speed, but I don't have math to back that up. In any case, certainly for this to even be remotely possible the car has to be dropped as non-aerodynamically as possible. Dropped nose-first however, where the Cd is 0.28 (again, from the Lexus website), the car would reach a terminal velocity of 260 mph and hit the ground long before the vehicle travelling parallel to the ground. Even though some crude math proved that least their simulation seemed plausible, the commercial still bugs me every time I see it. Stupid Lexus.

Posted by Rev. Adam on Tuesday, February 13, 2007 at 8:48 PM | Permalink