Today's Links Dump came late because I was at the meeting of the APS's Committee on Informing the Public. We apologize for the inconvenience, but I was too busy acquiring this critically important scientific data:
What is that, you ask? It's this:
That's the Superman roller coaster at the Six Flags America park outside of DC, which is where we're meeting this time. Lots of amusement parks do Physics Days as outreach programs, so we did the Physics Day thing ourselves, wearing ugly blue vests holding accelerometers on the major rides. Of course, the vest-mounted accelerometer I was wearing had its battery die, wiping the data I collected, but that's why I have an accelerometer app on my phone, now...
As you can see, the accelerometer really needed to be tared (I'm not sure how to do that), as it recorded 10 m/s/s acceleration when it was standing still, but on the bright side, this does allow you to clearly sort out the initial drop from the rest of the data, so that's cool.
I have x, y, and z-coordinate data, and sample data from someone else's accelerometers, so I'll eventually try to match these up, and do some more analysis. For now, though, I'll settle for a little bit of gloating...
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Nice!
The vast majority of "accelerometers" don't measure acceleration. They measure normal force per unit mass. The difference is subtle.
As a result they read ~10 m/s^2 (or N/kg) when at rest, and 0 in free fall.
Your phone app is also apparently finding the scalar sum of the three axes of acceleration.
One way to interpret these readings is the sensation on your body. Is it the usual force of the chair on your butt? Or more? Or less? The normal force per unit mass measurement is just that.
That's very cool!
Gastineau: I think the difference is too subtle for me, can you clarify?
I thought the equivalence principle was exactly the statement that there's no way for an accelerometer to tell difference between standing "at rest" at the earth's surface and accelerating at 10m/s/s in outer space, because there's really no difference.
I should've been clearer: the data show the total magnitude of the acceleration because I used the vector components to calculate that scalar magnitude. Because the phone was in my pocket, it's not clear to me how the axes were aligned with respect to the car. With a bit of thought, I'm pretty sure I can use these components to rotate things to at least get a vertical value, but I'm not going to put much work in on that now.
Looks like that ride had decent "air" for four or five seconds, but not very smooth. Millennium Force was smooth and right at zero for about five seconds when it was new.
as it recorded 10 m/s/s acceleration when it was standing still
Dude! Einstein Equivalence Principle! It was recording correct data!
(Oh, wait, somebody else already mentioned that.)
Of course, one might take the charitable view that (as a guy used to the precision of optical measurements) Chad takes issue with the *value* the device records for g, rather than his modern physics course.
Next time align it with the seat, and sit on it.
What did you end up using?
With a bit of thought, I'm pretty sure I can use these components to rotate things to at least get a vertical value
What makes this difficult is that the orientation should have varied with time. Low altitude spacecraft normally use magnetic field for attitude determination (the dominant component is the Earth's internal field, with deviations of only 1-2% even in the most extreme cases), so if you happened to also be carrying a vector magnetometer, you are good to go. But you obviously can't do that with an accelerometer on a roller coaster, as you appear to have been pulling either 3g or 4g acceleration (I'm not sure whether the background gravitational force is conventionally subtracted out) at several places along the way.
Rob Knop wrote:
Dude! Einstein Equivalence Principle! It was recording correct data!
Yes, did anyone suggest otherwise? However, we might be interested in recording the deviation from "at-rest" gravitational acceleration, and therefore subtract that constant vector from the measurement. This is exactly analogous to subtracting the weight of an empty container from the measured weight of container plus contents. That is what tare means (http://en.wikipedia.org/wiki/Tare_weight). You have it confused with calibration, which is the act of making sure measurements are correct by comparing with a known standard (http://en.wikipedia.org/wiki/Calibration).
For the iPhone (maybe for Android too, but I don't know) you can capture the gyroscope's angular acceleration values at the same time as the linear acceleration values, and then provided you have some initial "at rest with respect to the ground" conditions you can integrate to get the linear acceleration components in the ground system. With some drift of course.
Gastineau: The vast majority of "accelerometers" don't measure acceleration. They measure normal force per unit mass. The difference is subtle.
As a result they read ~10 m/s^2 (or N/kg) when at rest, and 0 in free fall.
This is sub-optimal for the educational purpose of things like Physics Day, of course, because reporting an acceleration of 9.8 m/s/s for things at rest feeds right into one of the main points of intro physics confusion, which is plugging 9.8 m/s/s in for acceleration everywhere it occurs, even when an object isn't moving.
Sili: Next time align it with the seat, and sit on it.
I think you overestimate the amount of room in those seats. I could barely wedge myself in with the phone in my front pocket. Sitting on it wasn't going to help anything.
What did you end up using
The free Accelerator Data Recorder, that writes .csv files to the phone. The down side is you have to copy them over to something else if you want to see a graph, but it was the one free app that seemed to provide useful output.
Eric: What makes this difficult is that the orientation should have varied with time. Low altitude spacecraft normally use magnetic field for attitude determination (the dominant component is the Earth's internal field, with deviations of only 1-2% even in the most extreme cases), so if you happened to also be carrying a vector magnetometer, you are good to go. But you obviously can't do that with an accelerometer on a roller coaster,
I can't get an absolute reference, but I can sort out which way things were pointed relative to the car (from knowing that the car was initially horizontal and thus the only "acceleration" should be vertical), which is as much as you would get from the PASCO sensors, I think. (I have data from some PASCO sensors, but got sick of the bullshit needed to install their software, so looking at it will wait until I can put it on one of the teaching lab computers and convert to a real data format.) That's good enough for me.
as you appear to have been pulling either 3g or 4g acceleration (I'm not sure whether the background gravitational force is conventionally subtracted out) at several places along the way
Max acceleration on the Superman coaster is supposed to be just short of 4g. It's pretty intense.
An "accelerometer" A does indeed measure force per unit mass and therefore "physical acceleration", which because of gravity may not correspond to "coordinate acceleration" that shows position w.r.t. time. That is the whole shtick about the equivalence principle, etc: if you are falling then it's as if you were floating in space (itself not clearly definable), if "sitting still" on the Earth then it's as if you were in an accelerating frame in space etc. However, A can be set to measure the *difference signal* in a given g-field and thus be an effective "coordinate accelerometer" to show how something moved, so baseline g could have been removed from this graph.
Segueing into the physics of gravity: For years I wondered, what if a charge was in free fall such as orbit or the SHM up and down a "tunnel through the Earth" - it should radiate EM waves out into space (even if distorted by the g-field, still net energy). But with no *physical acceleration* - how does it "know" how it is moving - where would the radiative reaction force (F_rad = (2/3)kq²(d²v/dt²)/c³) be physically derived from? (BTW it is not a "quantum issue" since I can have a macroscopic body of many n*e charge.) This is sometimes called "Chiao's paradox" of recent vintage (but I have print of my own earlier raising of same issue, not that either of us was utterly first to ask the essential question. Anyone know who was?)
The supposed solution involves curved space-time of the g-field "reflecting" the radiation back to the charge to get the same result as if the charge were accelerating the same way in inertial space. However, this seems shaky to me, esp. what if multiple charges at different positions? Not only usual mutual impedance of antenna effects but how additionally would "reflection" give separately back the right F-rad to each individual charge center, when all their radiation mixes together and comes back in various ways? This looks like another messy issue in gravitational physics.
Another one is the gravitational field energy, which you might have heard cannot be a simple local density like for E and B fields (REM: when mass distributions change to require or do work, the energy lost or generated now has different red shift if projected away from the masses!) That also reminds me, the suspect nature of the glib claim "the energy of all the masses etc. in the universe is balanced by the negative gravitational energy so it can 'come from nothing'." Well, first of all that "nothing" is a physical vacuum or manifold with laws and dimensions, not "nothingness" - a now-misleading name like "atom." Second, it can't be true because it varies with G: imagine making all the masses 10x and G goes to 0.1x, same g-fields and motions but 10x mass to balance out. That also shows the units weren't consistent for that claim, so I don't know how that muddle got started.