Amusing Ourselves with Sensors in the Field
My son's math/science club had an opportunity to see a real rocket launch at Vandenberg Air Force Base this week. Unfortunately, the weather was bad enough that our NASA hosts decided not to attend the launch which took away our inside track to the day's activities. We were already half way to Vandenberg (approximately 250miles away) when we found this out. Faced with the prospect of a long trip with the chance of seeing nothing through the fog we decided to change our plans, so we vectored off to Santa Cruz and its famous beach boardwalk for a little Sun SPOT-based physics fun.
You see, Santa Cruz boardwalk includes a bunch of amusement park rides. Our crack team of researchers (the 4th & 5th grade math/science club) decided to use the Sun SPOTs to measure the G forces experienced in some of these amusement park rides. Fortunately, the standard Sun SPOT Telemetry Demo is just perfect for this application. It displays, in real time, the output of all three axes of the accelerometer and a total G force reading. By simply putting a Sun SPOT in someone's pocket while they ride the ride, we can see what G forces their body is being exposed to. We measured 5 different rides:
- Starfish - a spinning ride
- SeaSwing - a large rotating swing ride
- Bumper Cars
- Hurricane - a roller coaster
- Drop Zone - a vertical drop ride
Lets take a look at the project in a little more detail and see what we can learn.
We used the eSPOT 3-axis accelerometer to monitor the motion. The Telemetry Demo application consists of two parts, one that runs on the eSPOT device and one that runs on the host computer. The application that runs in the eSPOT device takes accelerometer readings of all three dimensions and sends them over the base station to the where the data is received and plotted live on a laptop computer and saved for later analysis. (Yes, as you may have guessed, this implies that I was carrying a laptop computer around an amusement park - I wear my geek badge proudly)
The accelerometer on the eDemoBoard is actually 3 separate accelerometers, one for each dimension. The accelerometers are very tiny Micro Electro-Mechanical Systems (MEMS) devices hidden in a computer chip package. You can imagine that an accelerometer is made of two main parts suspended between two mounts. One of the parts connects to both mounts; we'll call it a bridge. The other only connects to one of the mounts, we'll call it the diving board. There is a mass on the end of the diving board so that it will wiggle around with respect to the bridge when the accelerometer is moved.
If you were to grab this device by the two mounts and wiggle it up and down you can imagine that the diving board would bend slightly. When a charge is applied to the bridge and diving board, it creates a sort of capacitor. As that diving board bends ever so slightly, it changes the capacitance between those parts and this can be measured. This allows the accelerometer to report a signal that corresponds to the movement of the device in one dimension. Also, note that the diving board can only bend in on dimension (up and down in the diagram), not side to side. If you imagine three of these packed very tightly together, each oriented 90 degrees from the other, that is a useful model for what goes on inside the accelerometer.
You can also imagine that when a eSPOT device is lying on its back, just sitting stationary, the the Z axis diving board will be bent down slightly by gravity. In fact, it will have 1G (or 9.8 m/sec\^2) of bend to it. Now if you turned it over so that it was lying on it's sun roof, that same Z-axis accelerometer would have its diving board board bending the other direction. Therefore, it would measure -1G (or -9.8 m/sec\^2). Meanwhile, in both of these orientations, the X and Y axis accelerometers would have no gravity working on them so they would have a zero reading.
In fact, it is interesting to note that when the Sun SPOT device is not accelerating (or decelerating), the accelerometers an tell you how the device is tilted. In other words, it can tell you which way is down. That is because the square root of the sum the squares of all the values will add to 1G in a downward direction no matter what way you tilt it. If the X axis accelerometer is measuring a non-zero value and the Y axis accelerometer is measuring a non-zero value, but the Z axis accelerometer measures 0G then Z axis must be parallel to the horizon.
The Telemetry-onSpot samples the three accelerometers every 10 milliseconds and packages the readings into a wireless network packet to be sent to the host application. The Telemetry-onHost application receives these packets and plots them on a moving graph. The green, blue and red lines represent the X, Y and Z axes respectively. It also calculates the the sum of the absolute values of all three readings together. This can be useful in determining the over acceleration applied to the device.
We were interested in measuring the amount of acceleration that our subject's body is exposed to as it rides the amusement park rides. It is easy to max out the 6G accelerometer readings by just waving a Sun SPOT back and forth vigorously in your hand. Clearly this would not mean that the subject's entire body was experiencing many Gs worth of force, only their hand. So we determined that it is important to make sure that the device is securely fastened somewhere near subject's center of gravity. We found a front pants pocket to be a fine place put it. Also, it is handy that the Telemetry-onHost application provides some smoothing functions that can reduce some of the noise due to ride vibration.
Now its time to ride some rides.
The starfish is a spinning ride that basically goes around in a circle at high speed. What we expect to see then is the force of gravity pulling down, plus the cetrifugal
force of the ride spinning that makes you feel yourself pulled to the outside. We see a slight oscillation in the data that is either caused by the ride not being level, or slight speed variations in the motor. Generally, however, we see observe we are measuring about 1.3G or ~12.5 m/sec\^2 total acceleration. If we assume that the centripetal
force of the ride is at 90 degrees to the gravitational acceleration, and we know that gravity is contributing 1G worth of acceleration, we can calculate how much acceleration the ride is contributing with the following formula:
By plugging in values we can deduce that the ride is providing an extra ~7.8 m/sec\^2 of acceleration or about 0.8G of lateral acceleration. If we knew the diameter of the ride, we could probably calculate the speed the ride was spinning.
A CSV file of the raw data is available here: starfish.csv.zip
Like the Starfish ride, this ride spins, but it adds an extra twist. The riders are suspended in a swing and the entire ride tilts. Because of the tilt, the rider feels more acceleration on the upswing and less on the downswing as the ride goes round and round. This is borne out in the data that we see below. Once again, its very easy to observe the period of the rotation.
A CSV file of the raw data is available here: seaswing.csv
In the bumper cars we see a lot of shaking around, but generally an average of 1G punctuated by the occasional jarring 2G jolt of a collision. This data is much more noisy and ultimately much more difficult to draw conclusions from.
A CSV file of the raw data is available here: bumper2.csv
The hurricane is a small roller coaster, but it gives us the most acceleration of any of the rides; approximately 4Gs! We can see that the ride lasted only about 40 seconds, but a lot is packed into that short time. If you look closely you can also see a few places early on where the Sun SPOT device changes orientation slightly. These are caused by the subject sitting down and the roller coaster and then heading up the initial hill. Also note that it is really hard to tell a turn from a hill. Because the roller coaster tilts around corners, both tend to push the subject down into their seat. As with many experiments, a gyro would be very helpful here because we could then determine how the subject is tilted in order to understand how to the forces that we are measuring are being applied. For more on this see my Location, Location, Location
A CSV file of the raw data is available here: hurricane.csv.zip
This ride carries the subject up and down a very large tower at high speed. It created some of the prettiest data for us to work with. Because the motion of the ride is restricted to a single dimension, we don't have to worry about any missing data on rotation, so we can really figure out some interesting things about this ride. As you can see, there are three main up and down thrusts followed by three or four successively smaller moves. After a couple of runs (good research requires reproducible results), we found an average of about three Gs of acceleration during the initial lift. Interestingly, our data also shows that the free fall portion of the ride is not actually a free fall. In fact the data seems to suggest that the subject is pulled down with an acceleration of approximately -1G!
A CSV file of the raw data for the two runs are available here: dropzone1.csv dropzone2.csv
Take some of this data and see if you can analyze it further. In particular the DropZone ride is appropriately constrained to provide an interesting area for further exploration. An interesting exercise would be to take this data and calculate how high you think the ride lifts you and how fast you go up and down. Let me know what you come up with.
If there is interest, I can analyze the data in more detail and see what we come up with in a future blog.
Don't let anyone ever tell you that research isn't fun!