Recently, we took all of the 9th grade physics students at my school to physics day at Six Flags over Georgia. The last time I remember going taking students to an amusement park for a physics day was almost a decade ago, and then I remember us spending large amounts of class time trying to build vertical accelerometers with fishing weights and clear plastic tubing.

When you have smartphones with built in 3-axis accelerometers and GPS, those days are long past. So this year, I set out to try to get my students to use their cellphones to take data and do a deeper analysis of some of the rides.

Before I get too far into reviewing all of the various apps we tried out, I should mention that the first challenge for my students was to figure out exactly how their smartphone is able to measure acceleration, and what it is measuring in the first place.

To do this, I had them download a simple accelerometer app from the list below and then take measurements for different orientations of the phone (face up, face down, standing right side up, etc). The first thing students noticed that was strange is that even when the phone was sitting completely still, which should be an acceleration of zero, the phone would read an acceleration in the vicinity of $10\; \frac{\textrm{m}}{\textrm{s}^2}$, and this acceleration would be labeled x, y or z depending on the orientation of the phone. An even bigger mystery happened when students dropped their phones into a trashcan lined with wadded up paper to cushion the landing. Now the phone would read an acceleration of zero, even though it was falling and clearly accelerating downward. After a few more experiments—seeing that the acceleration could be more than $10\; \frac{\textrm{m}}{\textrm{s}^2}$ while it was in your hand if you were in the act of throwing it, and doing some reading on Wikipedia about g-force, students started to figure out what an accelerometer is really measuring the non-gravitational forces acting on a small mass inside the accelerometer. So when sitting on the table, there is a support force acting on the mass equal to the weight of the object, and it therefore measures an acceleration of $10\; \frac{\textrm{m}}{\textrm{s}^2}$, but if you drop the phone, the small mass experiences no support forces, and measures an acceleration of zero.

This is a pretty difficult concept for students to grasp, but pretty soon, they figured out how you could use this reading to figure out the true acceleration of the phone along with the net force acting on the phone. I only wish I’d had the video below from the Engineer Guy to help students understand this idea even better.

Here are some of the apps we used to take data.

Theolodite & Visual Clinometers

One of the common tasks for students to try to do is to measure the height of various rides around the park. There are a number of apps out there that allow you to measure an angle of elevation to a distant target, and then by making two measurements a known distance apart, it’s possible to use some basic trig to calculate the unknown height. The most functional iOS app I’ve found is Theodolite Pro ($3.99) which has all sorts of wayfinding features—it can even do the height calculation for you, but if all you need is a simple clineomter, seeLevel ($0.99) should do the trick. One thing we quickly learned is that these basic trig calculations are much more difficult when you do them on surfaces that aren’t level or use a baseline that is too small and introduces too much uncertainty into your measurements.

GPS, altimeters, and accelerometers

I didn’t discover my dream app to measure data on roller coasters until after Physics Day, but that’s how it goes. What I would have loved is an app that would log GPS data, altimeter readings and accelerometer readings on the ride, and amazingly, there’s a free iOS app to do that, xSensor.

With xSensor, you should be able to start the app before you get on the ride, put it in your pocket, and take data throughout the ride with your phone safely in your pocket. The one fairly serious flaw of the free app is that you are limited to recording 5kB of data, which gets you about 10 s of recording time at a 4Hz sampling rate. To get rid of this crippling limitation, you have to purchase the $9.99 pro version of the app. Bummer. There are a number of other apps that just measure acceleration or GPS data separately in the various app stores. Here are a couple more that we used. • Accelmeter: This app doesn’t have the ability to continuously record your acceleration. Instead, it draws an arrow on the screen to show the direction opposite the acceleration of the phone. This can be useful for figuring out how the accelerometer works, or for rides that have smaller or more predictible accelerations (like the giant swings) to just allow you to get a visual sense of the acceleration of the ride. • SparkVue-PASCO’s sparkvue app allows you to record the accelerometer readings and email the data file as a CSV for later analysis. This was the primary app we used for recording accelerometer data at the theme park. • MotionX GPS:This$0.99 app allows you to record GPS coordinates and velocities. It seems pretty nice, but I doubt it has a high enough refresh rate to get useful data for a roller coaster, but it might be useful for calculating average velocities, etc along slower rides.

Finally, if you are using an Android phone, I highly recommend Physics Gizmo by Phil Wagner, former physics teacher and now Google Teaching Fellow and all around nice guy (he also keeps a great blog at brokenairplane.com. Physics Gizmo can measure data from the accelerometer, email it as a CSV file, and even use proximity sensor on the phone as a pendulum timer.

Some project ideas

It turns out that the acceleration data produced by most of these apps is pretty difficult to analyze, since in general you don’t know the orientation of the phone in your pocket. Because of this, you have to work with the magnitude of the acceleration, and it becomes much more difficult to determine which way the normal force was acting at any given moment. The data is easiest to analyze on roller coasters that are fairly simple and just consist of up and down motion.

A few of my students were able to make some conclusions about this acceleration data by locating videos of the ride they chose to analyze on YouTube (you can find a video of almost any coaster there) and then correlating the accelerations data with various points along the ride in the video. If I had given students more direction, I think I would have also asked them to film various moments in the ride from the ground—like the bottom of the first hill, the top of a loop, or right before the ride returns to the station, and then students could very easily do some energy analysis to find the amount of dissipated energy along ride, or to compare the normal force that a rider feels at the top of a loop to the toy problems we do in class where we find the minimum speed of a rider going around the loop.

Finally, JT Miller had a great idea to have students make screencasts using Jing to explain their analysis of their rides. This would be super useful since students could show their work in Excel or Tracker, and even show and discuss photos or screenshots from their smartphones in the sccreencast. I plan to do this if I ever take a class to Physics Day again.