Engineering Math Software


LEGO Batman: Calculating the Limits of the Batcave LEGO Fleet

Ask any group of engineers about their childhood influences and LEGO is probably near the top. The toy is as popular as ever, keeping to its traditional roots while incorporating pop culture. In 2014, the company ventured into new territory with their big screen release, The LEGO Movie. The first spinoff, The LEGO Batman Movie, is now in theaters.


Although LEGO Batman is loved for his irreverent humor and lack of self awareness, he’s much like his comic book counterpart in lifestyle and gadgetry. The LEGO Batcave is chock full of crime-fighting vehicles. All of them are, of course, painted black (or sometimes very very dark grey). However, LEGO Batman’s advantage is the ability to quickly rebuild those vehicles when villains damage them. That is, unless the bricks themselves are destroyed.

How Resilient Are LEGO Bricks?

Several videos on the internet test the strength of LEGO bricks in different ways. The simplistic build and tough plastic show impressive resilience. In one test, a single 2x2 brick only gives out when the force reaches 4,240 Newtons, equivalent to about 950 pounds.

LEGO Batman’s sweet rides rarely incur that kind of force. But could it happen to a lesser known example, like a submarine? Can the Batsub only go so deep before the bricks are crushed? We did some quick Mathcad calculations to find out. 

How to Do the Math

First, we define the brick and its surfaces. Notice we’re making extensive use of units.  

Define the brick dimensions

Brick defined

Then we define the point at which we expect the brick’s structural integrity to fail, which is the previously mentioned 950 pounds. Last, we define the environment with atmospheric pressure and water density. Using 1 atm as a unit instead of the longer 1.013x10^5 Pa makes the math more concise and readable.

Defining forces on brick

Forces defined

Finally, we use symbolics and calculate how deep the sub can go before the pressures equal 950 pounds of force. The answer is just over one mile below the surface.

Depth calculation

Depth calculation using symbolics

Some Caveats

LEGO Batman probably won’t need to send his submarine a mile underwater, though. The vehicle would likely breach and collapse long before the pressure is great enough to crush the individual bricks. And If the Batsub can’t withstand those pressures, an evil lair certainly won’t survive. 

Find More Answers in Mathcad

Want to calculate the g forces on LEGO Batman when he’s doing loops in the Batwing? Try it for yourself with your free download of Mathcad Express. Choose the 30-day full functionality option and you’ll get access to the full version of PTC Mathcad Prime for 30 days.

Download Mathcad free


Posted in: PTC Mathcad