Skyscraper Farm

When I was in Chicago a few months back, the Museum of Science and Industry had an exhibit describing one man’s idea to convert skyscrapers into farms that could supply big cities with fresh locally grown produce.  If you converted the Empire State Building into a giant greenhouse, what percentage of New York’s population could you feed on a daily basis?

This clearly depends on what types of plants are being grown.  Some foods are denser in calories than others.  If all you’re growing is celery, you won’t be able to feed as many people as you could by growing potatoes.  A potato plant might produce 10 potatoes each year while taking up 0.25 m² of area.  The Empire State Building has 102 stories and a total floor area of 257,211 m².  From this we can compute the total number of potatoes that would be produced each year by our skyscraper farm,

# of potatoes = (total area) / (area per potato)

= (257,211 m²) / (0.25 m²)

= 1.0×10⁶ potatoes per year.

Given that the population of New York City is about 8 million people, our result already doesn’t look very promising unless New Yorkers have figured out a way to survive one octant of a potato a year.  Assuming New Yorkers have the bodily functions of typical humans, they’ll each consume about 2000 Calories per day.  If each potato has 300 Calories¹, the farm will produce 3.0×10⁸ Calories per year or equivalently 8.2×10⁵ Calories per day.  From this, we can compute the fraction of New York’s population we can feed,

fraction = (Cal. per day produced) / [ (Cal. per day per person consumed) · (# people) ]

= (8.2×10⁵ Cal. per day) / [ (2000 Cal. per day per person) · (8.0×10⁶  people) ]

= 0.0051%

Note, that’s not a fraction: it’s a percent.  It’s 0.0051 percent.  It would take 20,000 Empire State Building-sized skyscraper farms to make enough produce to feed New Yorkers for a year.  That’s a far cry from the estimated 150 30-story building that would be needed according to the article referenced.  Even if by some miracle of genetic engineering, we could get each plant to produce 10 potatoes a day rather than a year, we’d still need 50 Empire State Building-sized skyscraper farms to feed the population of New York. 

This is one of those calculations I desperately wanted to work out.  I love the thought of green energy-efficient buildings producing fresh food for city folk.  I’ve checked my math twice, but can’t find a mistake.  The fact that Zachary and ntm get similar results convinces me that the estimate is at least close.  Even being very generous, I just don’t see how the numbers can work out it. 

[1] That’s assuming large potatoes.