Monday, July 2, 2007

How To...


...Fill an office bathroom with Ping Pong balls!

First, measure the volume of the bathroom (width x length x height) and subtract out any volume for cabinets etc., unless you will be filling them as well. 1 ping pong ball has an exact volume of 33.51 cubic centimeters (or 2.04 cubic inches), based on the formula for spherical volume of V=(pi x diameter cubed) / 6. Next, assume an effective sphere density of 0.74048 based on the Hales' proof of the Kepler conjecture. Therefore, assuming the effective size of the bathroom is 10' x 12' x 8' tall (or 120" x 144" x 96"=1,658,880 cubic inches) we divide the bathroom volume by the ping pong ball volume to arrive at 813,176 ideal ping pong balls. Factoring in for the sphere packing density, we will need 602,140 Ping Pong balls.

Next, the cheapest price for Ping Pong balls was found at Rebecca's Online Catalog, where they can be purchased for $10.15 per gross (144) for more than 20 gross. However, they are non-standard and 1.5 inches in diameter. A quick re-calculation will show that we now need 695,114 of these slightly smaller Ping Pong balls. At the best price of $10.15 per gross, we will need 4,828 gross (for a remainder of 118 extra Ping Pong balls). This will cost $49,004.20 (not including any taxes and shipping). Per Rebecca's Catalog, the shipping weight of one gross is 3.48 pounds. Our order comes to 16,801.44 pounds. Assuming that they will ship in individual boxes of 144 (i.e.-4,828 3 1/2 pound boxes), an approximate UPS charge for ground freight would be $19,939.64 (based on shipping from Euless, TX to Gresham, OR=UPS zone 7 to 2, at $4.13 for a 3.48 pound box). Therefore, our total Ping Pong ball cost will be $68,943.84.

Now we need to figure out how to put the Ping Pong balls into the bathroom. Assuming the goal is maximum quantity of Ping Pong balls filling the finite volume of the bathroom, then the balls will obviously need to be packed loose (as opposed to staying in the boxes) to get as close as possible to the theoretical maximum density of 0.74048. To actually fill the bathroom, you will need an electric leaf blower, about 10 feet of drainage pipe, and around 3 feet of 1-1/2" Schedule 40PVC pipe. You will also need a 6 inch wide board that is about 6 inches shorter than the door, a 6 inch by 6 inch piece of mesh (window screen or similar), a funnel, some duct tape, and probably a helper.

Now for the fun. We'll assume (because it's a lot easier), that the door opens into the bathroom. Wedge the board into the door opening, leaving a 6 inch gap up at the top. Duct tape the screen onto the end of the drain pipe, and cut out an opening for the pipe. Tape the screen/pipe assembly to the top of the board. Cut a small hole in the side of the drain pipe just big enough for the PVC pipe to fit into (flush-DO NOT protrude PVC pipe into drain pipe). Next tape the funnel onto the end of the PVC pipe, and the leaf blower onto the end of the drain pipe. Turn on the leaf blower. If everything is sealed tight, you should have flow through the PVC pipe and into the drain pipe, thanks to the Venturi Effect. Now, just dump the 695,114 Ping Pong balls (not all at once) into the funnel and watch as they blast into the bathroom! Eventually, the bathroom will be full and you will be able to disassemble your contraption and close the door. Great laughs for the first person who really has to use the bathroom! Since there was about a 6 inch (blocked) opening in the door, there should be enough 'slack' to slightly push the door ajar and allow the Ping Pong balls to slowly cascade out the narrow opening. While the shipping weight of our balls is almost 8 1/2 tons, the closest value I could find online was 1 gram for a ping pong ball (which sounds about right). Therefore, the room will be full of 1,532.5 pounds of Ping Pong balls. Yay!

4 comments:

Lefty said...

Oh my GOD!! No wonder they never called me back after the interview!! Tlad to see you are back in action..this job search sucks, and your blogging is much more fun!!

Anonymous said...

Go back to work, slacker!
Cary

Thomas Paine said...

Ha ha, lefty! Nice login name. Also, all times are PST, so Cary's reading blogs at 1 in the morning Mississippississippippippippi time. Come on!

Lefty said...

I thought you would like that name! Never even had to think twice of who it was did ya?!!