Wednesday, May 12, 2010

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.

1. Assuming that a 3,000 sq ft patch* will feed one person all year round (I have no idea if that's remotely right: it's tough to find), and that the entire building is converted to vertical farming, it would feed about 0.011% of NYC -- 900 people, give or take.

*After a year of hoeing a 2.5-acre bean field at Walden, Thoreau got tired of so much work and lived his 2nd year on only 1/3 of an acre. With that as your one-man-feeding standard, the whole Empire State Building would feed 190 folks -- or 0.0023% of New York.

2. floor space of the building is 2,768,591 sq ft = 63.5581038 acres

Potatoes yielded from two to four times more calories per acre than grain did, (wiki potato)

Basic daily: round to 2000 (men/women/height/weight/activity make this a large std dev value..)

6000 calories of grain can be produced per acre per day. (http://chemistryandphysics.astate.edu/jpratte/activities/activity8-1.htm)

Assume potatoes as the highest calorie per acre crop. Average it as 3x as many calories than grain, so potatoes can grow 18000 calories per acre-day.

If we've got 63.56 acres, that's 18000*63.56 = 1144080 calories.

At 2000 calories/day-person, 1144080/2000 = 572 people.

New York has a lot of people. Appx 8.4 million people (http://www.nyc.gov/html/dcp/html/census/popcur.shtml)

So 572/8400000 = 6.8e-5, or .0068 % of the population..

Another site (with no references) claims apples produce 23m cal/acre or appx 63k cal/day (and potatoes at 8 million cal/acre or ~22k cal/day). Not sure I trust those numbers.

monsanto claims corn yields of 229 bushels/acre (assuming per year). http://www.monsantoperformance.com/images/sample_yb_b.jpg

1 cup sweet yellow corn (154g, .4 lbs) has 132 cals. So 1 lb of corn would be 330 cals
(1 10 ox package froz corn has 230 cals, so that gives 368 cals lb, lots of variation, pick 350 cals/lb of corn) http://caloriecount.about.com/calories-corn-sweet-yellow-i11179

229 bushels/acre-year * 56lbs/bushel * 350 calories/lb. * 63.55 acres = 285237820 cals/year / 365 days/year = 781473 cals/day / 2000 cals/day-person = 390 people a day, less than potatoes.

3. Here's an even more critical assessment on the limitations of vertical farming:

http://www.alternet.org/food/146686/why_planting_farms_in_skyscrapers_won%27t_solve_our_food_problems

4. Something to note is that most people don't get all their calories from vegetables. If you eat like me, I probably get only 10% of mine out of vegetables. But we could use 50%, so the caloric need would be cut by half to 1000 Cal/day.
(2x)

Then, there is no reason why you can only use the floor that is already there, a lot of vegetables (including potatoes) are not that tall. You could think of putting the floors closer together to fit maybe 10 layers per floor.
(10x)

Since the real state is so expensive one could predict that technologies would be developed to increase the plant density. Lets say fourth-fold increase in productivity.
(4x)

Taking into consideration these factors (4x, 10x, 2x)), we get that the required amount of buildings would go down to 20000/80 =250.

*Maybe it would be fun to calculate how much CO2 a plant like this would remove from the middle of New York City.