What Are All These MacGyver Equations?

Image: CBS/MacGyver from Episode 401

For the first episode of Season 4 (Fire + Ashes + Legacy = Phoenix). It starts off with all the members of the team from the Phoenix foundation doing their own thing. Riley does computer support, and Bozer is making a movie — but MacGyver has picked up a job as some type of adjunct lecturer at a university.

OK, let’s go ahead and talk about this academic position. Could Angus be a professor? Probably not. For most institutions, a professor would be a tenure-track position (able to earn tenure). This includes the academic ranks of Assistant Professor, Associate Professor, and Professor (full professor). In all of these cases, you would a terminal degree in your field of study — so that would be a PhD (Doctor of Philosophy) for a science course. MacGyver doesn’t have a PhD (remember, he dropped out of MIT).

It’s possible to teach a course with a Master’s Degree or even some graduate credits. The common rule is 15 course hours at the graduate level. MacGyver might have these credits. It’s also possible that some universities make exceptions on a temporary basis for exceptional cases (like MacGyver).

Now we can get on to the equations on the board. I’m going to start from left and work my way right.

Water Erosion and a Floating Crate of Money

Oh, you don’t see water erosion on the board? Wrong. It’s there. This is actually an equation from Season 3 Episode 13 (Wilderness + Training + Survival). In that episode, MacGyver is trying to calculate the location of a crate full of money that was swept away in a flash flood. Here is my original sketch for how you might calculate that.

Photo: Rhett Allain

Boom. There you see it. There is the height of the erosion (h), the depth (x) and the fictional “erosion factor”, r. With the erosion factor, you can get an estimate of the speed and duration of the flash flood (along with the depth).

The next step is to look at the floating crate of cash. This will keep moving along with the flood until the bottom of the crate hits the ground. So, for that you need to know the depth that it floats. Finally, putting this all together I can calculate the distance the crate traveled.

I know that’s all a bit complicated — here is a video I created (back in season 3) to explain how this works.

Atwood’s Machine for an Elevator

Next are the equations for an Atwood machine. This is from Season 3 Episode 22 (Mason + Cable + Choices). MacGyver is trying save an elevator from falling (it was set up as a trap) so he connects one elevator to the next one. Here you can see his calculations.

Image: CBS/MacGyver

Really, it’s a classic physics problem — but if you want to get in the details, check this out. Also, here are my original versions of the calculations.

Photo: Rhett Allain

The second half of this calculation shows the cable stretch based on its tensile strength. Oh, you want to see how to get this stuff? Boom, here is the video I made during season 3.

Three Methods in Classical Mechanics

The next board (the half on the right) isn’t from MacGyver — it’s from one of my own blog posts. These are three ways to solve the same problem. It’s just the basic motion of a ball tossed into the air, but there are three approaches.

  • Newtonian Mechanics: With this method, you calculate the net force on an object at set it equal to the second derivative (with respect to time) of the position — yes, that’s the acceleration.
  • Lagrangian Mechanics: In this method, you define a quantity called the Lagrangian (are you surprised) which is equal to the potential energy subtracted from the kinetic energy. From that, you can find the equation of motion (here is a video with all the details). The great thing about Lagrangian mechanics is that it works great for systems with constraint forces.
  • Hamiltonian Mechanics: The Hamiltonian is defined as the Lagrangian subtracted from the product of momentum and velocity. I know that seems counterproductive, but it turns out this method is super useful in quantum mechanics and statistical mechanics.

If you want to see how to solve a basic projectile motion problem with these three different methods, I did that for you.

Here are those problems worked out on one board.

Photo: Rhett Allain. Newtonian, Lagrangian, and Hamiltonian all on one board.

You can only see part of these equations in MacGyver’s lecture room, but they are there. Trust me.

WAIT! There’s MORE!

If you look at the left side of the board, you can see part of the top board (these are those sliding chalk boards — they are pretty cool). This shows part of the calculation for something that actually was cut from Season 2 Episode 6 (Jet Engine + Pickup Truck). The idea was that MacGyver would mount a jet engine to a truck and use it to jump over a gap.

Here are my notes for that.

Photo: Rhett Allain. Calculating the launch speed for a jet truck.

With the gap distance and the angle, I can calculate the launch speed needed to get the truck over the to the other side. Yes, there is a part II. Here it is.

Photo: Rhett Allain

Once you know the launch velocity off the ramp, you can work backwards to find the acceleration of the truck. Do you like that?

But what does it all mean? Why are these equations on the board?

In my mind, here is how it works. MacGyver comes into the room — he’s late, you know because he got caught up in some other stuff. The students are already sitting in there waiting on him. They only have to wait 5 minutes since he doesn’t have a PhD — rumor is that you have to wait 15 minutes for a professor with a PhD

Of course, the class before MacGyver’s was Dr. Tyree’s problem solving session for physics. He was helping students study for their comprehensive final exam. That’s when someone in the class brought up the idea of bank erosion as an estimate of a flash flood. After that, they worked on an Atwood machine problem and then a tensile strength question. Finally, Dr. Tyree was just trying to give “the big picture” in physics by showing three different methods in mechanics (Newtonian, Lagrangian, Hamiltonian). Of course, that went over the students heads and they just wanted to know if that question was going to be on the final exam.

Oh, what about the jet truck jump problem? That was from a class before Dr. Tyree’s session. He didn’t want to erase the board, so he just shoved it up and out of the way.

When MacGyver arrives, he also doesn’t have time to erase the board. It really doesn’t matter, the students weren’t paying attention anyway — so he makes an explosion by dropping potassium in water. That will teach them.

Physics faculty, science blogger of all things geek. Technical Consultant for CBS MacGyver and MythBusters. Former WIRED blogger.

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