August 25, 2016

How Many Ping-Pong Balls Can Fit in a Table Tennis Club?
Today's topic is scary. We're talking something that will leave many readers shaking with fear, sweating like David Sakai, and plucking their eyeballs out as they scream, "No! For God's sake, Stop!" Yes, today we're going to use math. (You have my permission to skip the math part and just read the paragraphs that give conclusions.)

How many ping-pong balls can you fit in your table tennis club? It's a simple matter of working out volume with the sphere packing formula. As we all know (after reading the Wikipedia entry I just linked to), as volume goes up and the size of the balls (sphere) goes down, the packing efficiency approaches the following density, which I'll call the Packing constant (P). (Hopefully, in my formulas below, the subscripts and superscripts will come through properly on your browser.) 

P = π/[3x(2)^½] = ~0.74048

So how can we use this?

• Let N_d = number of balls of width d that will fit in your club.
• Let C = volume in cubic inches of your club.
• Let B = volume of the balls in cubic inches.

Then the number of spheres (N) you can fit inside a given volume approaches the following:

N_d = (C/B)xP = maximum number of spheres you can fit inside your club.

To get C, you simply get the volume in cubic inches of your club. This is easy if it is roughly rectangular shaped. (We're using inches and feet here, since I live in archaic America, which hasn't adopted the metric system.) Multiply your club's dimensions in feet – length x width x height – and then multiply by 1728 (number of cubic inches in a cubic foot) to get cubic inches for your club.

B is the volume of the ball in cubic inches. Since volume of a sphere is 4/3 πr^³, we simply plug in the radius of a ping-pong ball, which is half the 40mm diameter or 20mm, or roughly 0.7874". Plugging this into the volume formula, we get B = ~2.045 cubic inches.

So to get the number of 40mm ping-pong balls that will fit in your club, here's the formula:

N₄₀ = (C/2.045) x 0.74048 = C x 0.3621

So to get the number of ping-pong balls that will fit in your club, you get the volume in cubic feet, multiply by 1728 to convert to cubic inches, and multiply by 0.3621 – and presto, there's your answer!!!

For my club, Maryland Table Tennis Center, the dimensions are about 77' x 126', with 18' ceilings. So MDTTC's volume is 77 x 126 x 18 = 174,636 cubic feet. Multiplying by 1728 we get C = 301,771,008 cubic inches. So for MDTTC, we get:

N₄₀ = C x 0.3621 = 301,771,008 x 0.3621 = 109,271,282

So we can fit a little over one hundred million ping-pong balls in MDTTC!!! Since you can buy training balls from Butterfly at about $80/gross, it would cost us about $60,706,267 to buy enough to fill the club. (Could we get a volume discount? Or get cheaper balls at Walmart?)

Suppose we instead used the old 38mm balls. Then the radius would be 0.7480. Plugging this into the volume formula, we get its volume at ~1.753 cubic inches. Then

N₃₈ = (C/1.753) x 0.74048 = C x .4224

For MDTTC, that's 301,771,008 x .4224 = 127,468,073. Another 18 million balls!

By the way, on Jan. 30, 2014, after a rather weird discussion with a 7-year-old, we calculated we could fit 27 blue whales in MDTTC.

USATT Insider
Here's the new edition, which came out yesterday.

All-America Over-40 Table Tennis Tours 2016 & 2017
Here’s info.

Para Table Tennis Classifications- Explained
Here's the article from Pong Universe.

Nice Rally
Here's the video (36 sec, including slo-mo replay) – no idea who the players are. (EDIT: They are Jun Mizutani (world #5 from Japan) and Tiago Apolonia (world #17 from Portugal), according to Dan Seemiller, who just emailed me.) 

Rallying Robot
Here’s the video (76 sec) of the Omron Table Tennis Robot at Hannover Fair 2016.

Practicing the Around-the-Net Sidespin Looping Receive
Here's the video (21 sec)!

Mini-Trampoline Pong
Here’s the cartoon!

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