How many bricks would it take to build a Lego bridge connecting London to New York?

An extract from What If? Serious scientific answers to absurd hypothetical questions by Randall Munroe, the creator of the wonderful web comic xkcd.

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Q. How many Lego bricks would it take to build a bridge capable of carrying traffic from London to New York? Have that many Lego bricks been manufactured? - Jerry Petersen

A: Let's start with a less ambitious goal. 

Making the connection
There have certainly been enough Lego1 bricks to connect New York and London. In LEGO2 units, New York and London are 700 million studs apart. That means that if you arranged bricks like this...


...it would take 350 million of them to connect the two cities. The bridge wouldn’t be able to hold itself together or carry anything bigger than a LEGO®3 minifig, but it’s a start. 

There have been over 400 billion Lego4 pieces produced over the years. But how many of those are bricks that would help with a bridge, and how many are little helmet visors that get lost in the carpet?

Let’s assume we’re building our bridge out of the most common LeGo5 piece - the 2x4 brick.Using data provided by Dan Boger, Lego6 kit archivist and operator of the Peeron.com Lego data site, I’ve come up with the following rough estimate: one out of every 50 to 100 pieces is a 2x4 rectangular brick. This suggests there are about 5–10 billion 2x4 bricks in existence, which is more than enough for our one-block-wide bridge.

Supporting cars
Of course, if we want to support actual traffic, we’ll need to make the bridge a little wider.

We probably want to make the bridge float. The Atlantic Ocean is deep[citation needed], and we want to avoid building 3-mile-high pylons out of Lego bricks if we can.


Lego bricks don’t make a watertight seal when you connect them together7, and the plastic used to make them is denser than water. That’s easy enough to solve; if we put a layer of sealant over the outer surface, the resulting block is substantially less dense than water.


For every cubic metre of water it displaces, the bridge can carry 400kg. A typical passenger car weighs a little under 2000 kg, so our bridge will need a minimum of 10 cubic metres of Lego supporting each passenger car.

If we make the bridge a metre thick and 5 metres wide, then it should be able to stay afloat without any trouble - although it might ride low in the water - and be sturdy enough to drive on.

Legos8 are quite strong; according to a BBC investigation, you could stack a quarter of a million 2x2 bricks on top of each other before the bottom one collapsed9.

The first problem with this idea is that there aren’t nearly enough Lego blocks in the world to build this kind of bridge. Our second problem is the ocean.

Extreme forces
The North Atlantic is a stormy place. While our bridge would manage to avoid the fastest-moving parts of the Gulf Stream current, it would still be subjected to powerful wind and wave forces.

How strong could we make our bridge?

Thanks to a researcher at the University of Southern Queensland named Tristan Lostroh, we have some data on the tensile strength of certain Lego joints. Their conclusion, like the BBC’s, is that Lego bricks are surprisingly tough. The optimal design would use long, thin plates overlapped with each other:


This design would be pretty strong - the tensile strength would be comparable to concrete - but not nearly strong enough. The wind, waves, and current would push the center of the bridge sideways, creating tremendous tension in the bridge.


The traditional way to deal with this situation would be to anchor the bridge to the ground so it can’t drift too far to one side. If we allow ourselves to use cables in addition to the Lego bricks10, we could conceivably tether this massive contraption to the sea floor11.


But the problems don’t end there. A 5-metre bridge might be able to support a vehicle on a placid pond, but our bridge needs to be large enough to stay above water when waves are breaking over it. Typical wave heights on the open ocean could be several metres, so we need the deck of our bridge to be floating at least, say, 4 metres above the water.

We can make our structure more buoyant by adding air sacs and hollows, but we also need to make it wider - otherwise it will tip over. This means we have to add more anchors, with floats on those anchors to keep them from sinking. The floats create more drag, which puts more stress on the cables and pushes our structure downward, requiring more floats on the structure...


Sea floor
If we want to build our bridge down to the sea floor, we’ll have a few problems. We wouldn’t be able to keep the air sacs open under the pressure, so the structure would have to support its own weight. To handle the pressure from the ocean currents, we’d have to make it wider. In the end, we’d effectively be building a causeway.

As a side effect, our bridge would halt the North Atlantic Ocean circulation. According to climate scientists, this is “probably bad”12.

Furthermore, the bridge would cross the mid-Atlantic ridge. The Atlantic sea floor is spreading outward from a seam down the middle, at a rate - in Lego units - of one stud every 112 days. We would have to build in expansion joints, or drive out to the middle every so often and add a bunch of bricks.

Cost
Lego bricks are made of ABS plastic, which costs about a dollar per kilogram at the time of this writing. Even our simplest bridge design, the one with the kilometre-long steel tethers13, would cost over $5 trillion.

But consider: the total value of the London real estate market is $2.1 trillion, and transatlantic shipping rates are about $30 per ton.

This means that for less than the cost of our bridge, we could buy all the property in London and ship it, piece by piece, to New York. Then we could re-assemble it on a new island in New York Harbor, and connect the two cities with a much simpler Lego bridge.


We might even have enough left over to buy that sweet Millennium Falcon kit.

WHAT IF? Serious Scientific Answers to Absurd Hypothetical Questions by Randall Munroe is published in John Murray hardback, priced £14.99 and is also available as an ebook. Randall Munroe will be in the UK for a WHAT IF? Royal Institution event on Wednesday 5th November.


1 Although enthusiasts will point out it should be written “LEGO.”
2 Actually, the LEGO Group® demands that it be styled “LEGO®.”
3 On the other hand, writers have no legal obligation to include the trademark symbol. The Wikipedia style guide mandates that it be written “Lego”.
4 The Wikipedia style is not without its critics. The talk page argument over this issue featured many pages of heated arguments, including several misguided legal threats. They also debate the italics.
5 OK, nobody styles it this way.
6 Fine
7 Citation: I made a Lego boat once and put it in the water and it sank :(

8 I’m going to get some angry mail about this.
9 Maybe it was a slow news day.
10 And sealant.
11 If we wanted to try to use Lego pieces, we could get kits that include little nylon ropes.
12 They went on to say, “Wait, what did you say you were trying to build?” and “How did you get in here, anyway?”
13 My favourite Friends episode.