Fun with RLGs part III: harvest time

The RLG has been running for almost a week -- time to have a look at the data.

First: there was a bug in my script producing the JSON data stream. While the raw theta value from the RLG was correct, the thetaInt and theta values sometimes advanced by an extra ~70000arcsec, thanks to a flaw in my implementation of the 65536-count-wraparound of the raw values. For the evaluation I've corrected this, giving a nice 16-bit sawtooth as shown in the title image.

The first thing on the list is to determine the average rotation rate measured by the RLG during this period with a simple linear fit: 0.00315541°/s. Earth rotates once in a bit less than 24 hours, or with an angular velocity of 0.00417807 °/s.

This is the value one would obtain with an RLG positioned level at one of the geographical poles. At the equator one would measure a rotation rate of zero.

Since I am neither living anywhere close to the Arctic or Antarctic, it makes sense that my measured rate is smaller than the theoretical maximum. Pro-tip: look for an angular function that gives a result of 0 at 0 degrees and 1 at 90 degrees. Sounds like sin(latitude) could do the job here.

So we can in principle calculate my latitude as arcsin(0.00315541 / 0.00417807) The result is ~ 49°03' (actually northern latitude). This is a geocentric latitude. To convert to geographic latitude (which you would normally use), ~11' have to be added at 49°, so we get ~49°14' as a final result.

My actual latitude is in fact 49°21', so there remains a difference of 7' or 7 nautical miles or ~13km when converted to actual distances along the local meridian. There are two possible explanations: the published scale factor of the gyro is not perfectly precise and a fine-calibration is required to improve the results. Maybe. Or: the desk on which the gyro sits is not perfectly level. Very likely and absolutely to be expected...

Now, a gyro cannot be used to fix one's position on the globe, but at least it can be used to significantly narrow down the possible location. Look at it this way: The full earth has a surface of ~510100000 km^2. By adding some sound margin and prior knowledge of the correct hemisphere I trust the RLG data to put me somewhere between 49°N and 49°30'N.

This leaves a swathe with a surface of ~1500000 km^2 in which I can expect to find myself. This is now only about 0.3% of earth's full surface, so in relative numbers quite an improvement! On an absolute scale not really of practical use, but still ;-)

Before moving on to statistical properties of the data (keyword: Allen deviation and angular random walk) in next weekend's post, here is a plot of the measured rotation rate determined from 300s-bins after subtracting the long-term average, and of the absolute angle after subtracting a linear model. In the absolute angle plot I've also shown the internal temperature of the gyro (in degree Fahrenheit) just to check if there is any correlation. This is not the case for the few cold spells aka wide-open-window-mornings, so the internal temperature compensation of the RLG (keyword: active cavity length control) seems to work at least one these scales. Overall pretty low drift, eh?