TBBT: Crashing Trucks

The first challenge of The Big Brain Theory was a modification of the classic ‘egg drop’ engineering challenge; how do you protect a sensitive payload (such as an egg) from a sudden impact? In our case, our ‘sensitive payload’ was a 160 pound box full of explosives, and you had to keep the box from experiencing too high a G-force in a head-on collision between two pickup trucks. How cool is that? Check out the full episode here:

The answer to this challenge (and indeed, just about any challenge where gentle deceleration is called for) is simple: the farther the payload has to decelerate, the lower the force required to bring it to a full stop. The equation for Work, which is a measure of how much energy you can impart on an object, is simply Force times Distance. The greater the Distance the object travels, the less Force required to stop it. In this case, the G-force on the package needed to be less than 25; that comes out to the force needing to be less than 4,000 pounds at all times. Easy, right? The question then is, how do you successfully guide a 160-pound package, and how do you stop it from moving at 35 miles per hour?

Let’s start with a little context to this episode. You know the shot where you see us all standing in an arc around Kal Penn? That was the first time we had spoken to each other. We had been on total lockdown up until the point when the cameras started rolling. Immediately after being introduced to everyone, two trucks exploded in the background, and away we went! None of us had any idea what to expect from our teammates, the shops, or the show. We arrived at the shops not knowing what tools would be present, what tooling we had on hand, or what raw materials we had access to. In fact, a good chunk of the first day was simply organizing all of our tools and ordering more tooling to fill in large gaps in capabilities. That said, on to the challenge.

This challenge saw me on the Blue team with Joe Caravella, Alison Wong, Tom Johnson, and Joel Ifill. The first thing that happened, as the show points out, is that Joe opened up the design space to a democratic process. As you’ll soon see, I took issue with this – we had 36 hours to build a contraption that could passively apply equal to or less than 4,000 pounds of force to a 160-pound box over a significant distance, working with 4 people we’d never met and in a shop environment we hadn’t used before. We immediately went in 5 different directions, and spent the better part of the first day arguing about ways of stopping the box (though, to be fair, we decided early about what type of rail system, sled system, and rail mounting that we wanted – more on that later). Eventually, I suggested a solution that the team found palatable.

Piston Rails

The suggested solution was stopping the package with a gigantic set of pneumatic cylinders. The idea was that the pistons would compress air in their extension chambers, and use that compressed air to generate a force to slow the package down. They would essentially be used as large gas springs, with an open vent in the back of their chambers to allow air to leak out. In the show’s animation, you’ll also note a second layer of die springs that suspended the package in its trolley to prevent sudden impacts from imparting G-forces. We abandoned this fairly early as being too complex to make work.

To make a very long story short, the pistons as presented probably weren’t going to work without significantly more tuning and analysis. For one thing, gas springs like this have an increasing spring constant (as opposed to a coil spring, which has a fixed spring constant); at the start of their travel, the pistons wouldn’t be creating much pressure, and at the end of their travel, they might be at pressures high enough to rupture the cylinder walls. This type of behavior meant that if we didn’t size the system correctly and pick an appropriately sized air vent, the pistons could easily either not apply enough force to stop the package in the first place, or simply explode. See the chart below for a visualization of increasing versus constant spring values; our pistons definitely fell into the ‘high volume air shock’ regime.

Air Shock Visualization

What happened next is that we essentially spent a ton of time trying to figure out how the system would behave. I can safely say that a) Joe was by far the most qualified of us to do the mathematical analysis, b) there wasn’t enough time in the entire challenge to create a good model no matter who was doing it, and c) characterizing the volumetric flow and resulting pressure out of these pistons, under these conditions, is extremely difficult to do. Air is compressible, its flow is hard to characterize, and it behaves very differently given slight changes in environmental conditions – check out the difference between adiabatic expansion and isothermal expansion if you want to get an idea of what I’m talking about. After a day and night of coming up with the idea and trying to characterize it to no avail, we learned that the cylinders had been held up in shipping and wouldn’t arrive until after the challenge was over anyway! That was the final nail in the coffin, and we moved on.

Plan B was to replace the pistons with a brake and spring system that tied to our existing rails (note: the show only discussed the brake system). We designed a floating brake system that could pivot to follow the rails, was lined with standard brake material, and had four independent shoes (two per brake) that were each sprung by heavy-duty die springs. These engaged with the C-channel on the outside of our rail structure as the sled slid down. In addition, we designed for a significant latex spring system to add a little extra stopping power; for those that are curious, we actually tuned the spring system to be critically damped with the brakes.

Brake RailsAs far as the rail, sled, and rail mounting system were concerned, we had a fairly good idea of what we wanted from relatively early on. The most robust rails we could think of were two heavy-gauge L-brackets turned inwards, with a trolley mounted on rollers between them. The advantage of the system was that it was extremely rigid, and it completely prevented the trolley from moving from side to side, up and down, or twisting. The downside, of course, was that it was complex and took a long time to build.

Mounting the rails proved to be its own engineering challenge. We were worried that if we simply welded the rails to the frame of the truck, they would twist and distort in the crash, and somehow prevent the trolley from moving. As a result, we took care in designing the rails to mount as a statically determinate beam; the front of the rails were on pivots that were welded to the truck bed, and the rear section of rails were attached via pegs in slots. The net result was that the truck could crumple, bend, or twist, and the rails still had enough freedom of movement to stay straight. The picture below illustrates the setup; the left-hand attachment is a pivot, and the right-hand attachment is both a pivot and a side-to-side slider.

Simple Beam

Now, all that said, we didn’t finish on time. A little past the halfway mark of the build, I noticed that we just weren’t getting things done. We were still going off in many different directions – Joel was welding frames together, Tom was teaching Alison how to use a number of the tools in the shop (which, while noble, sank a lot of time unnecessarily), and Joe tended to be running around between a number of different tasks and states of mind. Metal was being cut in inefficient order that left Tom and Joel unable to keep working at various points, and it became pretty clear that at the rate we were moving the project wasn’t going to get done. I got pretty frustrated, snapped, and took over the build by handing out jobs and specifically ordering all work. After I told everyone to shut up and get to work, the teaching stopped, cuts were ordered so that Joel and Tom could stay productive with their tasks, and we started moving pretty quickly through the build.

When the buzzer sounded, we had an attached rail system with a functional trolley and one working brake; we still needed to weld on one completed brake assembly, tighten the brake springs appropriately, attach a lid to the box with four sections of all-thread, and attach a single nut to 5 or 6 spring assemblies. As Tom Johnson put it, the system very likely would’ve worked had we had another 10 more minutes of assembly time. Oh well!

When game day came, however, both trucks exploded. Having seen Red Team’s truck, we were initially surprised – it seemed fairly robust, all things considered. When we looked closer, however, there were a couple of really critical design errors which seemed to doom it. The show mentioned the brakes being “too tight” as the ultimate downfall of the Red Team – that was a simplified and, I believe, slightly inaccurate assessment of the cause.Red Team Bent Truck

The first and potentially largest error was that of material selection. When we designed our brakes, we used easily-sourced brake liner and bolted it to steel. The Red Team decided to create their own brake pads from scratch using aluminum blocks, under the theory that a softer metal will wear against a harder metal and serve as a functional slide. In theory, this tends to work out (especially with brass and bronze acting as the softer material), but the caveat is that they chose aluminum for their brake pads; aluminum, unfortunately, has very low surface energy and as a result readily undergoes galling when slid across any other material. Galling increases frictional forces very, very quickly, and could easily account for the sudden stop their package experienced after starting to move.

The second error was that of rail mounting. For whatever reason, the Red Team decided to weld the front supports of their rails to the crumple zone of the pickup truck. In addition, they welded the rails directly to their supports, which meant that when the supports moved in the collision, the rails likely underwent buckling because there was no way for them to pivot out of the way – this would have warped the rails and potentially either squeezed the trolley or caused the rails to change cross-section (and therefore dramatically change the friction in the system). You can see this bending in the screenshot above, and you can see that the package stopped right at the bend in the rails.

All in all, however, this was a great first challenge. It built on a type of challenge we were all familiar with, it called for us to build relatively straightforward and simple systems, and it left us more than enough rope to hang ourselves in the end. If we had to do it again, I think the simplest, most effective system would likely be one where we have rails designed and mounted similarly to the rails we had on the Blue team, with a simpler trolley (perhaps with sliding contact instead of rollers), connected to a common, off-the-shelf disc brake spooling out cable to decelerate the package.