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 
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.
Murmurs from the Earth... 
225 RRPM is the speed at 100% for the chinook. Would it be possible to determine the speed of the blade itself? Very interesting work.
Adam,
If you are looking for the tip speed of the blade you can find that by mulitplying the swept circumference of the blades (2*pi*l where l is the length of a blade in feet) by the rotational speed (225 rpm). That will give you the tip speed in feet per min.
I got thinking about why the sound of a helicopter exhibits beats. My first guess is that there are two main frequencies the helicopter produces (motor and blade?) and their unequal frequencies produce beats. You say “impulse pairs… are due to the rotor blade passing”. What do you mean by that? That you assume the time between peaks to be the time it takes the blade to make one full revolution?
Thank you for commenting Denis. Typically the term beats refers to the rise and fall in amplitude caused by two tones that are close to the same frequency but not exactly. They are close enough that the ear can’t hear the individual sounds but only the combination which rises and falls in amplitude as the two sounds add and subtract from each other due to phase interference. I suspect what you might be hearing is the interference due to reflections off the ground or possibly a building in a city. I am no expert on helicopter noise but I am pretty sure that the frequency difference between the motor and rotor rotation would be too great to exhibit a beat frequency.
As to your other questions, each time a rotor blade passes an observer it generates a pressure pulse that a microphone can measure. On this helicopter there are three blades on the rotor so there are three pulses for every complete rotation of the rotor. The time between peaks would be the time it takes for one third of a full revolution. Also on this particular helicopter there are two rotors separated by some distance along the fuselage but also out of phase by some amount in their rotation but operating at exactly the same speed. Because the blade passage pulse from the rear blade has to travel a little further than the one from the front blade and they are somewhat out of phase in their rotation, two distinct pulses show up on the wave form.
Thanks for the reply. You are right about beats, of course; I should have refreshed my college physics before theorizing :).
Regarding the peaks, since the blade rotates continuously I would expect it to create a pressure front that would spiral towards the listener and not produce any peaks.
Also, I found a relevant discussion here: http://boards.straightdope.com/sdmb/showthread.php?t=452889
I guess the only answer I have is that the data and analysis I did speaks for itself. I made a recording of a Chinook helicopter flying almost directly overhead. When I examined the waveform, I saw the peaks I show on the page above and they are consistent, through the analysis of the Doppler shift I describe, with the 100% rotor speed of 225 RPM that is used in flight, as verified by someone who actually flies them.
Seeing the peaks is really quite easy if you have a notebook computer. Download the Raven Lite software described in the Analysis of Sound overview (click ‘Analysis of Sound’, a weirdness of WordPress is that the menu header is also a menu item), find some helicopter traffic and record it right in Raven Lite. You will have to keep expanding the time axis of the waveform until the peaks separate from each other.
Thanks again for the comments.