Stupid Calculations: Monophone

May 14, 2013 | ANIMAL

ANIMAL presents Stupid Calculations, a new series where practical statistics get rendered into utterly useless ones. Look forward to such topics as orange peels, whales, high-priced escorts, elevators, swimming pools, and tears of joy.

Who among you haven’t wondered how many dried tears it would take to fill a salt shaker or how long it would take to sip an Olympic-sized pool through a straw? Doubtless, you’re similarly inclined to have contemplated the size of the screen that could be made if the displays were ripped out of every iPhone ever sold and combined into a single colossus. It’s likely still that you’ve imagined how it might appear looming above the Manhattan skyline. Wonder no more. Armed with pencil and paper, this exercise has been made with you in mind.

The eye-glazing calculations are laid out below for those who appreciate the dirty work but, skipping ahead, the Kubrick-inspired monophone would stretch 5,059 feet into the sky and have a base measuring 2,846 feet across (Central Park is 2,640 feet wide). Its surface area would take in 2.07 billion square inches. That’s 14.39 million square feet or 330.54 acres. The new World Trade Center, by comparison, will have a surface area of 23 glass-clad acres, giving us enough screenage to watch Game of Thrones on all four sides of fourteen WTCs.

But perhaps you’re more into road trips than glass erections. If one was inclined to mass destruction and had $150 billion-ish to spare, glowing iPhones could pave the way of a standard-width highway lane for 227 straight miles. That’s enough for a delightfully crunchy drive from Manhattan’s Union Square to the White House with enough left over for a sightseeing tour around the capital.

Let’s start with the number of iPhones out in the world. Apple’s financials show that 352,292,000 have sold since day one through the most recent quarter. Sparing a potentially huge pain in the ass, every pre-iPhone 5 model conveniently has the same display size. So we automatically know that everything sold before iPhone 5 launched on 9/21/2012 had a 3.5” diagonal screen. That’s 271,073,000 units.There’ve been another 85,219,000 sold since then with a roughly 60/40 split in favor of the 5.

85,219,000 x .60 = 51,131,400 iPhone 5
85,219,000 x .40 = 34,087,600 all other models
So we add 34,087,600 the 271,073,000 for a total of 305,160,600 older models.
And we’ve got the 51,131,400 iPhone 5’s.

Next up, we need to figure out the average size of an iPhone screen. Every iPhone model built before the 5 has had a 3.5” diagonal screen with an 3:2 aspect ratio. That makes it 2.94” x 1.94” for a screen area of 5.65 square inches. iPhone 5 has a 4” diagonal and a 16:9 aspect ratio (same as an HDTV).
That makes it 3.49” x 1.96” for 6.83 square inches area.

305,160,600 older models x 5.65 square inches=1,724,157,390² inches
51,131,400 iPhone 5’s x 6.83 square inches= 349,227,462² inches
TOTAL 2,073,384,852 square inches (14,398,506 sq ft or 330.54 acres or 0.516 square miles)

Super, we’ve got the area. Dimensions are another story and having slipped out of high school algebra only through a teacher’s pity, this took a shameful amount of time to figure. Phone calls had to be made.

What are the dimensions of rectangle with an area of 14.98 million sq ft given a ratio of 16:9?
16x * 9x = 14,398,506 sq ft
x^2 = 99,989.62 (this is the total square footage divided by 144, the product of 16 x 9)
x = 316.211 (the square root of the number above)
16x = 5,059 feet (the product of 16 x 331.271)
9x = 2,846 feet (the product of 9 x 331.271)

Central Park’s almost exactly half a mile across, making the screen just a touch wider. So lay the base of a 16:9 rectangle at the south end of Central Park South and proportionally scale it 7.23% wider than the park’s borders. Then double-check by using the 705-foot height of the General Motors building at the southeast corner of the park: monophone needs to be 7.15 times taller. By happy coincidence, Apple’s 5th Avenue glass cube store is bunkered under the GM Building’s plaza.

Road Trip: A standard highway car lane is 12 feet wide, so it’s 5,280′ x 12′ for 63,360 sq ft per highway mile. So we take the total display area of 14,398,506 sq ft and divide it by 63,360 sq ft for 227.24 miles. We used an as-the-crow-flies highway. The actual trip would be similar, but then that wouldn’t leave enough miles left for sightseeing at the other end.

(Top image: Google Earth. Rendering: Josh Orter)
(Inline image: carlfbagge/Flick. Rendering: Josh Orter)

You can find Josh at www.stupidcalculations.com and on Twitter here: @stupidcalc.