So, I’m on sabbatical this year.
This does not mean, as some erroneously assume, that I just get to not work for awhile. I have a lab; I kind of have to be there…
What this does mean, is that I have the flexibility to set my own schedule, and can blatantly ignore meetings and other college service.
I had thought about going to Six Flags for awhile this summer. I enjoy amusement parks, and I just hadn’t been to one in a few years. I entertained the thought of bringing my summer students, but wasn’t sure it would actually be fun for all of them. (And there is nothing worse than being in a “fun place” and not enjoying it.) So instead, I decided to play hooky from the college convocation, the day after Labor Day. Instead of sitting and sweating in academic regalia for a few hours, I would be sweating in a t-shirt and sports bra. (I promise this is relevant.) A friend of mine, an engineering professor at a nearby school, joined me, as their classes started a couple days later than ours.
I also though I might make this an academic exercise, and log accelerometer data during the rides. We had both ordered the PocketLab Voyager, but alas neither mine nor hers had arrived yet in the mail.
The good news is I had recently discovered the phyphox app on for the iPhone. It can record the sensor data from a whole bunch of the iPhone sensors. For acceleration the data is logged at a rate of 100 Hz, in all three axes.
The park was really empty, which was awesome. We never had to wait in line more than a few minutes. We got a LOT of rides in. This relative emptiness made it a little less awkward for my sensor mounting protocol. The phone display has to be unlocked for phyphox to record data. So I used the sports bra method, which (TMI) I also use for running.
Though this day, I had to be a bit more careful, as I tried to place the phone on cardinal axes. Phone display faced out from the chest (+z). The y-axis was up/down, the x-axis was side-to-side.
Start data collection, put phone in bra, get buckled/locked into the ride, ride goes. So I often have several minutes of data logged corresponding to just sitting still, waiting for the ride to begin.
I’ll go through the data I got for three categories of rides: Kiddie rides, roller coasters, and swing rides.
“The sloping, curving figure-8 track looks just like a whip in the air. But you’ll dart around the track as light and agile as a cat, with long, cruising twists that’ll keep you glued to your chair in slinking suspense.”
Okay, before we get into it, let’s set the parameters. When moving, we change our position in space. (Duh.) How quickly this position changes and the direction we move is characterized by a term called velocity, which basically means speed plus direction. Lastly, we also think about how quickly velocity changes (and in what direction the change is). This is characterized by acceleration.
Human bodies feel acceleration. We don’t really feel position or velocity. This is because acceleration is directly related to the thing we unquestionably feel: force. If you feel a push or pull, you are being accelerated. If you are falling towards the Earth, you are being accelerated towards the Earth at 9.8 m/s^2. We usually call this number “g”. Then if you experience an acceleration more or less than g, you can use g as an intuitive reference. You can just say 2g for an acceleration twice the size of gravity, which would feel like twice the pulling force. (When referring to forces relative to the force of Earth’s gravity, we sometimes say “g force.”)
Accelerations are produced by changes in speed and changes in direction. We experience 1g all the time. Sharp turns can give more than 1g, and are engineered into amusement park rides. Astronauts train under both low g and high g conditions as these can be physiologically jarring for long durations.
(Important footnotes you might read, especially for the advanced reader:  force experienced and  accelerometer comments.)
Back to Catwoman. Here’s a plot of (total) acceleration vs. time for this ride. The spikes correspond to sudden speed and/or direction changes. Lots of moments of >1g. A pretty fun ride!
I have two traces of data here: the red dots (raw data from the sensor) and the blue line (smoothed data). Having no reference for the accelerometer instrumental error, my feeling is that the blue curve is more trustworthy as far as capturing the overall ride experience. The raw data will contain noise from instrument error as well as noise due to random….um…jiggling.
Which may be significant. Remember where the phone is.
“Spinning around each hairpin curve on a precarious platform of this 3D maze, it really feels like you’re just cutting across the air and could fly off into space at any moment. There are more than 17 sudden turns, twists, dips, or drops built into this wild 1,213-foot track, as you make your way from the top to the bottom of the five-story-tall structure.”
This is a pretty similar ride to Catwoman’s Whip but is literally a much jerkier ride. I don’t just mean this colloquially, as I explain in the next bit, though this is the ride that definitely gave me a bruise or two and made my neck hurt! Kiddie ride my foot! (Though I suppose them kids are a little more…elastic than us olds.)
Recall that acceleration is the rate of change of velocity. Jerk is the rate of change of acceleration, and it’s thought (but not well-understood) to have large physiological effects. Think about it this way: you can get used to a force on you, even if it’s large. You’d adapt to a heavy hat on your head or a weight vest. But you can’t get used to a changing force. So in addition to considering the number of “g’s” a ride provides, a ride engineer will also need to consider jerk. Don’t be a jerk. Here’s a cool (academic) paper on the subject.
“Wicked Cyclone is the first coaster of its kind to have a 200-degree stall and two Zero-G Rolls. You also experience more airtime than any other coaster in New England on Wicked Cyclone.”
Super fun coaster on a wooden track. The acceleration plot gives you an idea of how jerky the ride is. Though since this is a more standard coaster, your neck isn’t being whipped like the Gauntlet ride; you’re mostly keeping forward motion. One of the “zero g” rolls I imagine corresponds to the dip around 60 s, where the acceleration is less than 1 g, though not actually zero as that’s too difficult in practice. (I didn’t have a timer or video device on me, so I would have to repeat this to verify.)
“As you load into your chair, note how there’s something missing here – the floor. You’re about to fight crime with your feet just dangling free in the air. And there’s no track visible above you either – so when you take wing off the first 12-story lift and dive into a 110-foot drop, it will feel just like flying.”
This was a fun one I did more than once! You can see the initial drop is intense and there are plenty of high-g moments. There supposedly is a zero-G roll. Maybe around 95 seconds?
“Welcome to the world of the hypercoaster. This style of roller coaster is so intense they had to come up with a whole new category for it. Hypercoasters are the modern breed of oversized roller coaster that are pumped up to more than 200 feet tall. SUPERMAN The Ride easily clears that distinction, with a height of 208 feet and a mind-blowing 221 foot drop.”
This was the only ride we had to wait in line for. Sadly, there were some track issues so we waited for about 20 minutes, got fed up, and decided to come back later. I got some sweet shots of the creepy test dummies that live under the track though.
After our return, we still had to wait, as it’s the most popular coaster. But only a few minutes. Well worth it! A scary first drop, lots of g’s, and cheesy music the whole time.
Speaking of the first drop, here’s a zoom in on the acceleration. Free fall would be 1.0. But you start at zero at the top so need a finite time to get to 1. It sure feels like free fall though, especially for the second half of the drop! You’re looking straight down too, which adds to the feeling.
“Fly through the air, on this seated, swinging, twisting and tilting carousel that sends you sailing through the clouds.”
This is a swing ride, where you go around in a circle. The primary acceleration comes from the centripetal force caused by rotation. The acceleration can be calculated from acceleration = v^2/R, where v is the speed of the swing and R is the distance from the rotational center. This gives a pretty good acceleration of about 1 g, as you can see from the graph below.
However, depending on how you start the ride, you might also be swinging back and forth, left and right, or some combination, on top of the main circular motion. (Also this ride had some twisting of the swing, too.) The exact kind of swinging is caused by subtle things like how your feet dragged on the ground as you left the ride. This creates the wobbles in the graph. Were there no swinging, we’d expect the graph to be pretty flat.
You can see this effect a little more by looking at the individual acceleration traces. I’m plotting z (red) and x (blue) here. Remember I’m in a moving frame, and the z-axis corresponds to forward/backward. Thus the acceleration in z is roughly zero, but with large fluctuations because I was swinging (I even touched one of my neighboring swings with some regularity). The x-axis is where the main acceleration is, but it’s wiggly too, as I’m shifting in x.
This next plot is just kind of fun, I don’t know what to do with it really. I’ve plotted x, y, and z accelerations “parametrically.” I’ve plotted x vs y, y vs z, and x vs z. I did not filter out the data before the ride began here so there is a big clump at (0,0).
“The New England SkyScreamer and Texas SkyScreamer differ from the standard models, although the actual ride experience is intended to be the same. The gondola of the two rides hold 12 two-seat chairs instead of 16. When the gondola reaches full height, the chairs rotate in a larger circle—124 feet (38 m)—but at a slower speed—35 miles per hour (56 km/h).” – from Wikipedia
This was basically a MUCH higher version of Crime Wave (about 400 ft!). Such awesome views!
We didn’t experience much more acceleration than Crime Wave. Even though its bigger and faster, those effects kind of wash each other out (a = v^2/R). Actually using the numbers above we can calculate expected acceleration! Using these numbers we get about 1.3g. Pretty close to “actual” value seen on graph.
We also have wobble as before. The thing is, no matter the fashion of wobble (left-right or back-forth), every pendulum has natural frequency. We can easily see from the graphs that the period of oscillation is about 8 seconds. Using the formula for period of a pendulum T = 2*pi sqrt(L/g), we can deduce the length of the swing is about 16 meters, about 50 feet. Looking at the still image below this is plausible.
If you take the speed and radius numbers from above, you’ll notice the time for one rotation is also about 8 seconds. My guess is they tune the length of the pendulum so that the period of swinging is close to the period of rotation, so you won’t notice the swinging too much. I didn’t notice any, especially compared to Crime Wave. (Visually, you’ll get about the same view every time around. If the times weren’t matched you’d get a much messier visual stream.) If you noticed the swinging at 400 feet, that would be alarming, though not actually any more dangerous.
And once more, I made the parametric plot of accelerations. No major analysis here, aside from this seems to be a jazzier plot 🙂
Other Rides / Rides We Didn’t Get To
There were a few rides we got to, but my phone wasn’t set up to log data (or I had inadvertently locked the screen while doing the bra maneuver). The Joker was a fun ride, we also did Mind Eraser, and a few others I’m forgetting. After a long and intense day, I didn’t have quite the stamina to take on Goliath. I’m sure it would have been fine, but I decided to save it for next time.
Next time? Well, they were running a special on next season passes, and both of us took them up on it. Also our PocketLabs just came in the mail. 🙂
 I am not getting into details about the rider’s actual experience of the force. I am simply showing the absolute acceleration of the phone, with axes as specified. The actual force experienced by the rider is a whole other calculation in itself, as you need to incorporate the normal force of the seat / restraint, etc. And will also need to take into account non-inertial frames and pseudoforces. Not going there in this post.
 The actual accelerometer technically measures gravity as well, meaning that for someone sitting still, the raw reading will read as 9.8 m/s^2 in whatever direction is vertical. This is because of how accelerometers actually work, as they actually are measuring force and you can’t remove gravity as a force. I am technically using the “virtual accelerometer” which subtracts this effect, and figures out the orientation of the phone/gravity using the gyroscope sensors (I believe). With the virtual accelerometer, no motion –> acceleration reading is zero. As far as I can tell the virtual accelerometer data is trustworthy; it appropriately compensates for orientation. I’ve done a number of controlled motions to test this. The other thing is that especially with the swing rides, there may be some other effects due to misalignment of the sensor. More here.