# 5. Air Tractor AT-502B

The Analysis of Sound – Air Tractor AT-502B

Introduction

In this project,  I analyze the sound of an Air Tractor AT-502B agricultural aircraft passing over our house using a method similar to what was used to analyze the sound of the Chinook helicopter.  In this project, a Doppler shift signature is obvious in the spectrogram so the time/frequency pairs are extracted directly from the spectrogram.

This aircraft had made several low altitude passes over our house on its way to and from the airport.  Following one of its outgoing passes, I waited for it to return and was rewarded with a pass directly overhead.  The next day, I drove out to the airport and had an enjoyable conversation with the people there.  They had had a lot of inquiries about that plane, many irate.  They gave me a lot of information about the plane and the operation.  I should have gone out when it was there!  The long and the short of it was that a company called Fisher Ag Services  out of Morrow County was doing aerial seeding.  It just so happened that our house was right on the flight path between the job and airport.

Acquiring the recording and the acoustic analysis

The recording was made using a Canon Powershot G10 digital camera at a sampling rate of 22050 Hz and was saved as a .wav file on the camera’s SD card. The recording was about 36 seconds in length. The .wav file was then read into Raven Lite.

Interpreting the results

The Raven Lite spectrogram showed a beautiful fine lined S-shaped Doppler signature with an approaching frequency of 3328 Hz and a receding frequency of 2394 Hz.  The people at the airport associated this sound with the Pratt & Whitney PT-6A-15AG turboprop engine.  Without knowing the number of blades and the rotor speed that is about all I can say about it.  As long as we have a frequency source on the aircraft we can extract the speed and altitude information.

I zoomed in on the S-shaped signature and manually picked twenty three time/frequency pairs from the display.  These were entered into Igor Pro for the actual curve fitting.

The spectrogram also shows the vocalizations of several insects at the higher frequencies and a crow over in the lower right hand portion of the display.

We can now extract the information we seek, namely the ground speed of the helicopter, its altitude, and the time in the recording when it passes directly overhead, from the analytical function we derived inProject 3 by curve fitting the function to our data.  I used the modified function because the actual time of closest approach was not known:

$f_O=\frac{cf_S}{c+\frac{v_S^2\left( t-t_0\right)}{\sqrt{v_S^2\left( t-t_0\right)^2 +h^2}}}$

I used the curve fitter in a technical software called IGOR Pro but others are available. The results are shown in the figure:

The curve fitter returned estimates along with their 95% confidence intervals for the actual frequency f, the ground speed v, the altitude h, and the time $t_0$ in the recording of closest approach.

Coefficient values ± 95% Confidence Interval

f =2782 ± 6.54
v =187.99 ± 3.21
t0 =22.249 ± 0.104
h =810.92 ± 47.4
f =2782 ± 6.54 Hz
v =187.99 ± 3.21 ft/sec = 128.175 ± 2.19 miles/hour
t0 =22.249 ± 0.104 seconds
h =810.92 ± 47.4 feet

The values are all within their respective reasonable operating ranges.

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