Engineering Mathematics Fun: The Stranger Things We Do With Mathcad
by Mike Gayette | October 21, 2016 | Mathcad Blog
Netflix’s new hit series Stranger Things centers around a group of young friends in 1983, and their unusual small town adventures. Fans love its original story and nostalgic references to dozens of beloved 80’s movies, including The Goonies, Stand By Me, The Empire Strikes Back, and even Poltergeist. Stranger Things is a nearly flawless blend of familiar and fresh.
[Note: Spoiler ahead. If you haven’t watched it, bookmark this post and come back after you’ve binged on all eight episodes. Go ahead, we’ll wait.]
In episode seven, the character named Eleven saves herself and her friends from certain capture. When the kids are nearly trapped by government vehicles (a not-so-subtle hint to the bicycle chase scene in E.T.), Eleven uses her telekinetic power to launch an oncoming van into the air. Its forward momentum carries the van over the group and crashing onto the street behind them.
That moment had us cheering and nearly spilling our popcorn. It also got us thinking. Could Mathcad help us figure out how much force Eleven generated with her mind to catapult a vehicle so violently? To find out, we asked Luke Westbrook, Mathcad Application Engineer and Stranger Things fan. Yes, it can be done, he told us. Here’s his process.
First, the van. Without exact knowledge of the van’s weight and center of gravity, we’re forced to make a few assumptions. The van is most likely a 1983 Chevy. Unable to find the precise curb weight, we know that over a number of years, those vans have weights between 4665 and 5493 lbs. To compensate for added passengers and gear, we’ll use the higher number.
Using screenshots from the scene, we add a red dot where there is a probable center of gravity and for easier tracking through several frames.
Now we figure out the highest point the van attains during its flight. A quick search at IMDB shows that Caleb McLaughlin (the actor who plays Lucas) is 4’ 8”. When riding a bike, your feet should touch the ground without much bend in the knees, so we’ll estimate Lucas on his bike to also be about 4’ 8”. In our frames, the distance from the top of Lucas’s head to the ground is about 154 pixels. Using that, we calculate the distance of a single pixel in the frame and create our own distance unit in Mathcad.
To trace the trajectory of the van, we identify the pixel coordinates of the Center of Gravity of the van at different points in its flight. For the Y-coordinate, subtract the pixel value from 960 (the height of the picture), since the picture editor uses the top left corner of the image as the 0,0 mark. Also, the ground is approximately 888 pixels from the top, so the ground is subtracted from the Y-coordinate, in order to plot the trajectory according to the ground being at zero.
With points in hand, use the genfit function in Mathcad to find the parabolic shape of the trajectory.
Plotting the points and y(x), we see the trajectory of the van.
Note that Quadrant I in the plot above corresponds to the frame of the scene. The trajectory of the van starts at negative x-values because the van’s flight began off screen.
Next, create a solve block to determine the x-coordinate of the maximum of the curve, which then gives the maximum height attained by the center of gravity of the van.
Before the van gets launched, the only mechanical energy is the kinetic energy from its horizontal velocity.
After mapping the van’s travel through the air, we can figure out the amount of energy it takes to make it happen. The only mechanical energy of the van is the kinetic energy from its horizontal velocity. So at the height of the van’s trajectory, the only velocity is still horizontal. The kinetic energy at the height is the same as it was before Eleven changed the van’s course. However, the van also has potential energy, which must be equal to the amount of work Eleven used to launch it. Multiplying the van’s curb weight by its height, we get 118,000 Joules of energy. That’s equivalent to about 28 grams of TNT.
Figuring out exactly how much force Eleven applies to the van is difficult, in part because we don’t know the distance over which she applied the force. Even with visible impact and a cloud of dust, it happens so quickly that Eleven is no longer affecting the van by the time it gets about six inches off the ground. After that, the laws of physics simply do their thing.
Even with some incomplete data, we calculate that Eleven hits the van with about 87 tons of force, sending it over 15 feet into the air. That’s quite a mind trick!
Finding Answers with Mathcad
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