The thing Jorge and I were attempting was to find a way to compare two tops without having to take into account how hard they are thrown, exactly the problem raised a couple of posts back by johnm. The idea was that if resistive forces in a top go linearly with RPM, then RPM vs. time would be a decaying exponential. If this were so, then the spin time for a given top would have an inherent half-life which could be used as an objective measure of how good the top is. I could say, "My Acrobat has a half-life of 93 seconds. How about your Jon Gates?," and the answer you give based on your measurements would give a direct comparison of our tops even though you spin a top twice as fast as I do. A side benefit of the fitted exponential curve is that it could be easily extrapolated back to time zero to determine the RPM at launch, an interesting number which is not easy to measure directly.

Well, the curves made, in Jorge's case, by taking a video of the the tach while the top is spinning and using the time base on the camera, are beautifully coherent things that sure look like an artist's conception of a decaying exponential, and when you do a semi-log plot, they turn into almost perfect straight lines. Almost. The computed half-lives for a given top are still somewhat sensitive to initial RPM, hardly a surprise given the highly idealized nature of the underlying mathematical model. It may be more of a surprise, however, to see how stable they actually are over a wide range of starting velocities. The case can be made that a measured half-life (pseudo half-life ?) of a top says a lot about how it's going to play. And it is information that we can confidently exchange.

A neat feature of the model is that you only need to measure the RPM at two different times in order to compute both the half-life and the initial RPM. In practice one would use more measurements and perform some kind of best fit, of course, but there is no need to be intimidated by the vast reams of data that Jorge and I produced in our early efforts to come to grips with this thing.

I assume that ta0 will jump in here to correct any errors or false emphasis that I have introduced into this very brief synopsis of a lot of time that we ran down the drain collecting and poking around these data.