Do it yourself physics: Determining the curvature of the Earth, if you have better equipment

Working on this new project, see previous post, made me enthusiastic to do some gravity experimentation myself. I wanted to see if I can measure the curvature of the gravity field of Earth myself. I only needed a gravimeter (fancy word for very precise accelerometer).

Me, being a 'not-paid-much-just-enough' PhD researcher, I can not buy a very precise gravimeter, but I do have a laptop which contains three accelerometers to protect my harddisk in case of a joint meeting of the laptop and the ground. I wanted to see if I could use these for my little experiment (instead of going on an 8 month dedicated submarine voyage with state-of-the-art instruments, hmmmm, what was I thinking).

My laptop is a Macbook Pro (ok, don't start the discussion about which operating system is better. In the end it is all about the person using it) and I found the following code to (pretty easy) access the accelerometer data. The website for reading the accelerometer data gives a nice and clean syntax description on how to use it. You should download the SMSLib package and unzip it somewhere you want it to be on your computer. Then go, using terminal (unix commands), to the directory where you unzipped the package and give your computer the following command:

./smsutil -i0.1 -c100 -atxyz > testcapture.txt

And try to move your computer in some noticeable way (this gives better data and it gives you a sense that it is working). This commands tells your computer to capture every 0.1 seconds (-i) for 100 samples long (-c, this means ten seconds) measurements from the accelerometer and print it (-a) in the following order:

time x-axis y-axis z-axis

This can be varied in all different ways (-atzyx -atz -axyz, and so on). After the computer is finished, you can check your data, by typing:

less testcapture.txt

First column is time after enter, followed by the three read-outs of the accelerometers. If you did move your computer, the read out will have quite some variations. If you did not touch your computer (what I did), you will see that the z-axis will be close to 1 and the other two close to zero (if your screen made a 90 degree angle with the table top, and the table top was level). The numbers will vary a little bit in time, which is the noise of the accelerometers.

Finding out what the noise of the measurement equipment is always the first thing you should do. So I did not touch my computer and turned on the recording of accelerometer data. Then I calculated the magnitude of of the acceleration vector (math!) and plotted it against the variation of the normal Earth.

This was a little bit of a set back. The accelerometers in my computer are noisier (blue curve) than the variation in the normal Earth signal (red curve). Also the acceleration resolution was almost as big as the normal Earth signal variation itself. These sensors just can not do the trick for my experiment. Maybe it is time to buy pendulum equipment like Vening Meinesz and ask the navy if they have a spare submarine...