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As an exercise designed to communicate the scale of plastic waste in the oceans, which was estimated at 268,940 tons in 2014, I'm trying to describe how many life-size buildings one could construct with your basic 2x4 lego pieces of the same weight. A believe a 2x4 piece is 31.8mm long, 15.8mm wide, and 9.6 mm tall, not including the studs, and 2.32g.

Naturally, I don't aspire to simulate skyscrapers that anyone could actually live in, but I'm trying to come up with a defensible estimate for the number of bricks in, say, a Lego Empire State Building (1,250' tall, not including the spire).

One idea is to imagine building a solid structure that is completely enclosed. Another is to make a hollow one with double-layered floors and a solid base.

Forgive me for the open-ended question, but is anyone familiar with the mechanics of how one builds a extremely large structure with Lego pieces that, while not necessarily structuring sound for human consumption, and least holds together?

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Great question. Others may have better answers for a more "realistic" design, but the math for a solid structure is actually pretty quick. Take the Empire State Building for example:

Height: 381m
Base: 129m x 57m
Volume: 381m × 129m × 57m = 2 801 493m³

And a basic 2x4 brick:

Volume: 31.8mm × 15.8mm × 9.6mm = 4.823424e-6 m³

The number of bricks needed to simply fill the volume is total volume over brick volume, so:

Number of bricks: 2 801 493 / 4.823424e-6 = 580 810 022 092 bricks
Weight: 580 810 022 092 bricks * 2.32g = 1 347 479 metric tons

Basically, you're looking at 580 billion bricks weighing in at ~1.3 million metric tons for a solid structure the size of the Empire State Building.

This puts you at about a fifth of an Empire State Building's worth of bricks dumped in the ocean in 2014.

  • Thank you! I haven't quite decided if the Lego ESB should be solid. It dramatically changes the result, of course, but is also more difficult if one considers the depth of the walls and so forth. – Chris Wilson Apr 6 '18 at 5:36
  • So 58 billion bricks at $0.10 USD on average, you could buy that many bricks for $5.8 billon USD! – Mark Stewart Apr 6 '18 at 18:58
  • I think there's an order of magnitude wrong in this calc -- I'm getting 580 billion blocks. Fortunately, the annual amount of plastic dumped in the ocean is actually 8 MILLION tons, so we're still good :) – Chris Wilson Apr 11 '18 at 15:00
  • Thanks! It looks like I missed entering the last "3" on the ESB volume the first time. I've fixed this error and updated my answer. – jncraton Apr 11 '18 at 15:55
  • Yeah, a quick back of the envelop estimate for building a double layer shell, along with 102 double thick floors only comes to about 4,000,000,000 bricks. However, you'd use less if you modelled windows and doors, more for interior walls and stair cases ;) – Zhaph - Ben Duguid Apr 11 '18 at 16:36

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