Tuesday, August 22, 2006

The Wheels on the Bus...

Have you ever noticed that the wheels in car commercials look like they are spinning in reverse?

I saw a commercial last night for some random, plain, non-eye catching, american car (probably a Ford) and the wheels appeared to be turning backward. Upon review, I think MOST car commercials have at least one moment showing the car driving down a bucolic road, where the wheels appear to be slowly rotating backward.

Is this by design? Do the car commercial people deliberately plan this? Do they implant subliminal messages in these wheels?

This morning I tried to figure out how this phenomenon occurs. What follows is my pathetic mathmatical attempt to solve this mystery:

BACKGROUND: TV cameras film at roughly 60 frames a second. Therefore, if a wheel is rotating at roughly 59 rotations per second, then there will be a strobe-like offset and the wheel will appear to rotate backwards. I got this from a science website.

ASSUMPTION: A five spoke wheel would technically only have to rotate one fifth as much, as you would not be able to distinguish one spoke from the other. Therefore, a wheel would only have to rotate slightly less than 12 rotations per second.

Also for the purposes of this, I am saying a tire is 24 inches in diameter.


Circumference of wheel = pi x 24 inches = 75.4 inches.

for strobing: 59 revolutions/sec x 75.4 inches/rev = 4448.6 inches/sec

Only technically need 1/5 as much travel due to five spoke wheel assumption so----

4448.6 in/sec x 1/5 = 889.7 in/sec

(889.7 in/sec x 3600 sec/hr) divided by 12 in/ft = 266910 ft/hr

266910 ft/hr divided by 5280 ft/mile = 50.5 miles/hr

SO: If a car in a car commercial has 5 spoke wheels and is driving somewhere in the upper 40's to 50 miles an hour, you are gonna get that strobe effect that makes the wheels look like they are moving in reverse.

I bet you that its sort of an accident that it happens, really. It sounds fairly reasonable that if one were to film a moving car, it would be done in the 40 - 50 mph range. Shows good motion of the vehicle, blurs the background, easy for the film crew to keep up, etc.

Its either that, or the commercial crew actually sits down, measures the vehicle tire diameter, looks at the wheel spoke configuration and calculates what speed the car needs to be traveling in order to create the noted effect.

Occam's Razor, baby.


At 10:16 AM, Blogger Knottyboy said...

POP!!!! That was my brain on Occam's Razor with a dash of mathematics. Not pretty is it?

It's also a perfect metaphor of how the american car companies are so living in the 50's still. Big, bigger, biggest gas slurping dinosaurs.
p.s. stop killing those kittens would you? I'm trying...:P

At 11:00 AM, Blogger cb said...

I've already killed a few this morning... at work!

At 11:32 AM, Blogger Six Shooter said...

How about this mathematical equation:

(Science/math)+ nerd * too much time on his hands = this blog post.

At 12:04 PM, Anonymous R said...

Hmmm...Math is science so...we'll just reduce your term to nerd x too much time on his hands = this post.

And I admire him for it. It's pathetic how scientifically illiterate our nation has become.


At 12:33 PM, Blogger Six Shooter said...

I didn't say it was a bad thing.

At 12:47 PM, Blogger cb said...

I was just trying to put some math to something I observed. I have absolutely no clue if my math is right. Ray will have to double check me.

I'm like Barbie when it comes to math "Math is hard. Lets go shopping!"

At 1:44 PM, Blogger Six Shooter said...

Math isn't the only thing that's hard!

I was giving you a "hard" time.

Yeah, that's what I meant.

At 9:23 AM, Anonymous Ray said...

Everyone is so hard --

At 1:19 PM, Anonymous Ray said...

Per request:

Units and values check out. Assumptions seem OK.

Wondering if you could come to the same conclusion with Nyquist rate like ideas? Since you're dealing with things that have discreet frequencies.

At 10:29 AM, Blogger cb said...

Um, isn't Nyquist the stuff you drink when you have a cold and want to sleep better?


Post a Comment

Links to this post:

Create a Link

<< Home