New York Yankee Stadium Problem
Wednesday, April 18, 2018
I came across this New York Yankee Stadium concept first on Robert Kiyosaki’s radio show where he was interviewing a guy, likely a professor and he was talking about compounding interesting and preparing for the worst if exponential growth of disaster situations happened. The idea was that a person is sitting in a football stadium and we just happened to pick the New York Yankee stadium which was the hometown area of the person being interviewed. He gave a scenario where if at 12:00 you had a “magic droplet of water” that doubled in size every minute at what time would your whole stadium be flooded? And to make it more interesting you were chained and handcuffed to the highest seat or place in the stadium. He said what time would you be completely submersed under water. And he said 12:50. And then he said at what time would the stadium still be 93% empty. And he said at 12:45 it would still be relatively empty.
So, I wanted to check the math and am not a mathematician and wanted to check this for myself. So, I did some research. Original URL’s and information can be found below.
I did research first trying to find the volume of New York Yank Stadium and couldn’t find much.
Volume is defined as “the quantification of the three-dimensional space a substance occupies” by http://www.calculator.net/volume-calculator.html. This is often in the case of a cube length by width by height. A stadium is not exactly square. But I found another site that estimated height to be about 115 ft height and an area of 656100 which makes their estimation to be 75,451,500 cubic feet. The numbers are from https://www.reddit.com/r/baseball/comments/2hwmvn/im_trying_to_figure_out_the_average_mlb_stadium/
Then I needed to know how big is a droplet of water. Per WebMD an eyedropper droplet is .05ml. https://blogs.webmd.com/eye-on-vision/2007/09/how-many-drops-are-in-that-eyedrop-bottle.html
That is .05 milliliters. Then I took 1 Cubic Foot and converted it to milliliters using Google which gave
1 Cubic foot = 28316.8ml
Next I multiplied the milliliters by 75451500 to try to get maximum capacity. That was:
2.54855e+12 mL OR 2,136,545,035,200 mL
Next I charted this on an Excel spreadsheet. The first column had rows that numbered each minute like 12:00, 12:01, 12:02, 12:03…
The second column had rows that had droplets of water doubling at every interval. So .05ml, .1ml, .2ml, .4ml.
I added a column just to have it not show scientific notation and one with the commas to 2 decimals but this is optional just for readability.
Then I tried to check the figures. 93% not full means that it is only 7% full. 7% is 149,558,152,464.
My chart shows it reaches this level around a little after 41 minutes (assuming these magic droplets of water don’t evaporate). The guy said it would reach this level around 45 minutes though. And at 46 minutes you would actually drown. So, I am not sure I have the cubic volume or space of the stadium correct in my example. But nonetheless I can see what point he is trying to illustrate. The point was that compounding or doubling makes it so things accelerate very quickly. Also if we were actually compounding or adding on top of the previous, wouldn’t it look more like 1, 3, 6, 12…? Or 1,3,7,15?
ok, so if we’re talking about the FULL stadium, then we can just use outside dimensions of the ballpark. For Globe Life Park, it’s approximately 810 feet square. That gives us an area of 656,100 square feet. Now, just to move the question along, because i cant find any good numbers, if its 100 feet high(using the height of the foul poles at Yankee Stadium being 90 feet, and round numbers being easy to work with) above ground, plus probably 15 feet below ground on average, the total volume is 115*656,100=75451500 cubic feet. (for reference, that’s roughly 2000 Olympic swimming pools). Now then, if you’re looking for the volume of the bowl, you have to do some calculus, and it gets complicated real quick.
75,451,500 cubic feet? = 2.54855e+12 OR 2,136,545,035,200 mL
1 Cubic foot = 28316.8ml
93% of that is 1,986,986,882,736mL which is between 45 and 46 minutes.
Capacity of a thimble?
The capacity of a standard thimble is 50 mL. However, thimbles usedfor measurement can also come in sizes of 25, 35, 125, 175, and 250mL.
A standard eyedropper dispenses 0.05 ml per drop, meaning there are 20 drops in 1 milliliter of medication.
See also Yankee stadium of people:
Consulted Wikipedia and could not get Cubic volume