This blog has made the terrible decision to ask me to do more regular posts. Well, before trial and error catches up with me, let’s have some fun together…
As young single Caltech graduate students, we have become accustomed to making hearts race with our science. We turn measurements and derivations into heart palpitations. While this has been manifestly obvious for quite some time, we in the Oskar Painter group have recently been interested in quantitatively measuring this effect. Because, as any good Caltech physics graduate student believes, anything (even sex appeal) is uninteresting unless fully quantified in a dataset. We set out to make an accelerometer with enough resolution to sense the irregular and skipped heartbeats of our fawning admirers.
What follows is a multi-part treatise on the optomechanical accelerometers we developed.
Intro to accelerometers…
Firstly, what is an accelerometer? Simply put, accelerometers measure accelerations, which are changes in velocity. Accelerometers absolutely should not be confused with their homonym, excelerometers, which, of course, measure the number of times someone has used Excel® as a program for data analysis (an excelerometer reading $latex > 2$ is a punishable offense at Caltech and grounds for divorce in some northern states). Alternatively, the phrase “The Excelerometers” can acceptably be used to refer to the excellent creators of our optomechanical accelerometer – please greet my colleagues (Alex Krause and Martin Winger) and me as “The Excelerometers” around campus.
How do accelerometers measure accelerations? They measure the displacement of a test mass that is flexibly mounted to a body that experiences accelerations. I think we can learn a lot about how accelerometers work by understanding crash test dummies. For those confused by this reference, no, I don’t think The Crash Test Dummies, a Canadian alt. rock band from the 90’s, can teach us much about physics, although, their career did accelerate after the release of “Mmm Mmm Mmm Mmm” and then quickly decelerated in car-wreck/one-hit-wonder fashion. No, I am referring to the crash test dummies the automobile industry uses to test the forces of impact in car crashes. Please refer to the image provided below. When the car strikes the wall (decelerates), the motion of the crash test dummies (i.e. test masses) lags behind (in the sense that their forward motion doesn’t feel the deceleration as instantly as the car seats’ near-instant speed-drop to zero) and consequently there is a displacement between the back of the dummies’ heads and the seat. The larger the acceleration is, then, the larger this displacement is for a fixed period of time and vice versa. If one could measure this displacement, $latex d$, then one could infer the acceleration (assuming one knows some calibration factors like the stiffness of the seatbelt and the masses of the dummies – for the equations involved in calculating distance traveled due to constant acceleration, see The TV Frontier).
Measuring this displacement is exactly how our accelerometer works. Well, the analogy is not exact. I don’t want you walking away with an image of me jumping around all nimbly-bimbly from seat to seat in a crash test car with a ruler trying to measure the distance between a dummy’s head and the seat behind it. That would be a measurement technique unbefitting a member of the excelerometer team. We use much smaller test masses with relevant sizes on the micro/nano scale and a much more sensitive measurement technique. Such discussions shall be left for part 2 of this treatise.
Tim Blasius (Team Excelerometer) (email@example.com)
More members of Team Excelerometer: Oskar Painter, Alex Krause, Martin Winger and Qiang Lin.