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## Application of Doppler to F2A

The method of Doppler analysis is described elsewhere on this website . In a nutshell, the engine sound radiated from a model in flight carries information which permits the in-flight determination of airspeed and engine RPM. This information is extracted by analysing the sound via the sound card in a computer, using physics first described by Herr Doppler and a computer code written by Richard Horne which yields the frequencies present in the sound.

Click to enlarge

The method has wide application, most notably in F3D pylon racing and Control-line speed events, which are both quite noisy events. However, the method, while robust, does require corrections to be applied to yield quantitative results, especially with respect to the airspeed component.F2A in particular poses a challenge. With the models circulating at one lap every 1.3 seconds (in your dreams!), the Spectrogram code yields results which are somewhat distorted. So why should this be?

The sound frequencies we require for the analysis are those present when the model   is pointing directly at the microphone, and when it is pointing directly away from the microphone. We call these values Fcoming and Fgoing, for want of something better. In the case of F2A, the amount of time this happens is measured in milliseconds, not long enough for the sound sampling period of Spectrogram.

What does this mean? Well in Spectrogram, one is required to make certain settings which permit the program to work. In the case of F2A, these settings are the Sample Rate (Hz) and FFT size (points). They should be set to 11k and 2048 respectively.

Now with these settings, it takes the program about 186 milliseconds to workout the frequencies. In that time the model travels about 14 metres and changes direction quite a lot. This means that the signal we are trying to analyse has changed during the time of sampling. In the case of F2A, this introduces an error of about 20 kph in the Doppler-determined airspeed. That is not really cool at all!  We don't want that!  In contrast , there appears to be almost no error in the RPM result, so we are half-way there!

Now lets do something Supercool. Surely if we know what is causing the problem, then we can do something about it? Yep, sure can. It works this  way. First guess the speed of the model. Then we can readily calculate Fgoing and Fcoming just from the geometry of the model trajectory, which we hope we know, although not always! For each of these, we really need an average value over the 14 or so metres the model covers in the sampling time. If we do this all around the circle, then we can figure out a correction factor which is going to fix things up (we hope!)

Now from here on it gets messy, all that maths and geometry, not much fun, either to read or to write! No need to bother, all you really need is the code. If you log in to my website, both the source code and the .EXE files are there, along with a sample Spectrogram. Now how good is this code? Hard to know. But with a model doing about 280 kph, the new code gave a value of 277 kph. Not bad, that's about as good as you will get from the Doppler method. Of course, you get this lap by lap, which is really good to see how steady is your motor run.

That's it, have fun, folks!