## Tuesday, July 10, 2012

### Cheeto Bike Helmets

Have you ever wondered how bicycle helmets are tested? I've wondered if it was someones job to wear a helmet while a weight was dropped from progressively higher distances onto their head. After each impact they would be asked, "Did that hurt?"

In this experiment we try to answer the question, do Cheetos make an effective bike helmet?

Many kids do an egg drop experiment in school. We figured dropping an egg would be a good helmet test. If the egg in a Cheeto helmet remained unbroken when dropped, we will assume that a head wouldn't get cracked either. We started our experiment by wrapping an egg completely in Cheetos, then wrapping the Cheetos in plastic wrap.

Then we went outside and set up a ladder. We dropped the first Cheeto helmet from 10 feet up the ladder.
We counted down 5, 4, 3, 2, 1, drop.... splat. The egg broke. We did several other drops at different heights to find the maximum distance we could drop the Cheeto helmet without the egg breaking.

8 feet was the highest distance we could drop a helmet without the egg breaking. Using a little math and Torricelli's equation we figured the velocity of an egg dropped from 8 feet.

$v_f^2 = v_i^2 + 2 a \Delta d \,$
"vi" in this case is 0. There is no initial velocity.
"a" is acceleration. The only acceleration is gravity, 32 feet / second squared.
"d" is the distance the helmet fell, 8 feet.
Plugging in the numbers
v = sqrt( 0 + 2 * 32 feet / sec^2 * 8 feet)
v = sqrt( 512 feet ^2 / sec ^2)
v = 22.63 feet / second

If the end velocity is 22.63 feet / second, how far can it go in an hour?

(60 seconds * 60 minutes) * ( 22.63 feet / second) / (5280 feet/mile) = 15.43 mph

Simplified, you can use this formula to calculate the speed in miles per hour of an object dropped from any hight "d", measured in feet: (SQRT( 64 * d) * 3600) / 5280.

Or, here is a chart.

Our experiment shows that a Cheeto helmet can withstand an impact of 15 miles per hour.  So would Cheetos make a suitable bike helmet? You would probably be alright if your head hit the ground slower than 15 miles per hour. Not only could the helmet protect your head, but imagine the fashion statement you could make in the neighborhood with a helmet made out of Cheetos. And it would be a convenient snack!  This was a fun Cheeto experiment that didn't take a lot of time.

For those wondering how bike helmets are actually tested, here is a video we found on YouTube that shows some actual helmet tests. They're not quite as fun, but are more practical. Perhaps we might do some accelerometer tests in the future.