4. The Analysis of Sound — Twin Rotor Chinook Helicopter

The Analysis of Sound – Twin Rotor Chinook Helicopter

Introduction

In this project, I extend the procedures I developed in the first three projects to analyze the sound of a twin rotor Chinook military helicopter passing overhead. The recording is from an unplanned event, made very quickly using the audio recording capability built into a Canon Powershot G10 digital camera. While the recording quality is good, it was made under less than idea circumstances because of the short notice. The fact that the helicopter passed directly overhead at a moderately low altitude above a flat field made it a very desirable situation to record.

The sound of a helicopter is predominantly low frequency dominated by the sound of the rotors. We will examine the time domain waveform to find the impulses due to the rotor blade passage. A very accurate estimate of the blade passing frequency is then calculated by estimating the period, the time interval between impulses. We will calculate the blade passing frequency at several times during the recording, determine the rotor speed at each time, and then use a software curve fitter to fit the Doppler shift function to the data and extract the actual rotor speed, the ground speed, and the altitude of the helicopter.

Acquiring the recording and the acoustic analysis

The situation is described elsewhere. 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 .wav file was then read into Raven Lite.

Interpreting the results

Unlike the sound spectrum of the tractor trailer there is no strong Doppler shift signature in the helicopter spectrum. There is a subtle high frequency component visible but it is not sharply defined and more importantly, it fades into the background early and late in the recording where the shifted frequency asymptotically approaches the maximum and minimum shifted frequencies. Those maximum and minimum values are what we used previously to calculate the ground speed.

An examination of the time waveform shows impulse pairs that we assume are due to the rotor blade passing. The pairs are due to the presence of two rotors on this particular helicopter. The time period between a given feature, the second impulse for instance, on successive impulse pairs is the period,T, of the blade passing frequency. As noted in Project 3, the frequency is just the reciprocal of the period. We could use this frequency directly to measure the Doppler shift or, as I have done, calculate the rotor speed by dividing the blade passing frequency by three, the number of blades on each rotor.

I calculated the frequency for each of three consecutive impulses and took the average value to be the best estimate of the frequency. I did this at eighteen times in the recording. Two examples from roughly 7 seconds in the recording and again at about 20.6 seconds are shown in the table.

Time in record	Period (sec)	BP Freq (Hz)	Rotor Speed
7.1210
7.0420	0.0790	12.66
6.9630	0.0790	12.66
6.8840	0.0790	12.66
	Average	12.66	4.22	Hz
			253.16	rpm
20.7910
20.6910	0.1000	10.00
20.5900	0.1010	9.90
20.4900	0.1000	10.00
	Average	9.97	3.32	Hz
			199.34	rpm

There is one impulse for each blade so the period of one rotation is the time for three impulses to occur. The rotor speed can be calculated by taking the reciprocal of the rotor period or, as I have shown in the Table by finding the blade passing frequency first, then dividing by three to get the rotor speed. You can see that the rotor speed is shifted higher early in the recording when the helicopter is approaching and shifted lower as it pulls away.

The eighteen estimates of the rotor speed, when plotted against the time they appear in the recording show the distinctive S-shaped signature of a Doppler shifted sound. Note that the rotor frequency is actually in the infrasonic region as is the blade passing frequency itself. Note also that the absolute variation in the frequency is quite small, the Doppler shift being a percentage change in the frequency.

We can now extract the information we seek, namely the actual rotor frequency, 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 in Project 3 by curve fitting the function to our data.  I modified the function because the actual time of closest approach was not known:

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 rotor speed f, the ground speed v, the altitude h, and the time in the recording of closest approach.

Coefficient values ± 95% Confidence Interval

f =3.7631 ± 0.0159 Hz = 225.786 ± 0.954 rpm

v =195.71 ± 9.86 ft/sec = 133.438 ± 6.722 mph

h =1426.5 ± 200 ft

t0 =12.368 ± 0.266 seconds

Of these the only value that is known is the rotor speed, f, which is held at 225 rpm when the helicopter is in flight. Even for that value, its precision is not known. The values are all within their respective reasonable operating ranges.