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Fourier Analysis of in-flight RPM

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Alan Hahn:
Since this is the engineering board, I thought I might show you some work I have been doing.

SOme years ago I had an application that analyzed the sound from a recorded flight and then plotted the rpm you get from the plane in flight.

I managed to lose that application in a software upgrade, but just recently I rewrote the application.

My motivation is to compare how a IC engine compares with an electric motor in a CL plane.

Most of us flying electric use a speed control that has a governor on the motor--so the rpm stays constant during the entire flight. I have been curious to see how the common IC setups handle the power needs during the flight. This first post is my first installment. Just to whet your appetites (this is the engineering forum after all), I will continue to update this post with more info as soon as I can get things measured.

Today I will show you some flight info from Fred Krueger's Magnum 36 powered Tucker Special. Fred has modified the engine (basically blocking the boost port and adding some head gaskets and playing with the venturi size. More or less the engine is running is a rich 2 stroke/lean 4 stroke mode.

This data was taken by placing my Mac laptop near the pilot and recording the sound. This was done (thanks to a suggestion by Brett Buck) to minimize the Doppler effect---which I have directly verified completely dominates the apparent rpm variations when the laptop is located on the circumference of the CL circle. There is still a small Doppler effect from any residual wind, but its magnitude is small as  long as its velocity is ~10 mph vs the 50+mph of the airplane speed. This needs to be compared to the speed of sound, or about 770mph. So a 10mph wind will give an apparent rpm variation of (770+10)770 or about 1.3% (or 130 rpm at 10 krpm).

Briefly (I know, I know), I record the sound. After the fact, I run the sound file back into a fourier analysis--I analyze the sound in 0.1 s slices looking at the frequency components. Fourier analysis tells us that the engine sound can be decomposed into its fundamental harmonics. So for a 2 stroke at 10k rpm, the 1st harmonic is 10k, the second is 20k, the 3rd is 30k......you get the idea.

Now this would be true if the engine was running at a perfect 2 cycle combustion, firing exactly the same every rotation. But if it is partially 4 stroking, or firing non-evenly, you will also generate other harmonics. If it was a perfect 4 stroke, firing every other cycle, and perfectly off in between, then you would see the first harmonic at 5000 rpm, the second at 10k, the third at 15k, ....

The actual engine is somewhere between these two extremes---at least Fred's is running this way.

So one thing I do is to claim the first harmonic is 5000 rpm, the second 10k,... In this extreme, if the engine is running in a pure 4 stroke, I would see the roughly equal numbers of "odd" harmonics (5000, 15000, 25000 or 1, 3, 5....) as "even harmonics (10k, 20k, 30k....). As you will see the actual run is a complicated mix, but I define a measure which is =1 if a pure 2 stroke --only even harmonics) and =0.5 if pure 4 stroke (even and odd).

So after all that here is a graphic of part of Fred's flight. I show the calculated rpm, the "harmonic measure", and the loudness. Since the laptop speaker was fixed, the sound intensity did vary during the flight, and was particularly high during the overheads--when the engine was directly over the microphone.

I'll post the plot of the engine start up to the inside loops in the next post.

Alan Hahn:
Here is the plot of the first 90 seconds of the engine run.

The engine is started at ~30 s on the horizontal axis. Takeoff is at ~57 s. You can see the rpm jumps from 10250 rpm to ~10750 during the level laps. The rpm is the white trace, the green trace is the 2 stroke/4 stroke content. 1.0 is pure 2 stroke , 0.5 is pure 4 stroke. This of course is approximate. Fred's engine is cycling back and forth from 2-4 before takeoff. But you can see the green trace is jumping back and forth  a lot. So take it with a grain of salt. The red trace is the sound level. The laptop has a mike in the top of the screen, and this is facing in one direction, so the oscillation in the red trace between after takeoff at 60 s- is (I think) just the plane flying in front of the mike.

The dropouts you occasionally see (~51 s, ~58 s..) are due in part to some technical difficulties in my algorithms when the engine noise is contaminated by other sounds, or sometimes if the rpm is varying rapidly compared to the 0.1s sampling period.

The variation in rpm during the level laps after takeoff is basically due to the unloading of the prop when the plane is moving into the upwind direction and loading in the downwind direction. I see the same with my electric motor. The Doppler effect is too small to explain that large a difference (we were seeing winds at an average of 10mph during that part of the day).

The spikes at 84 and 93 s are due to the wingover.  The inside loops start at ~103s.

Alan Hahn:
I should note that I have recently added an optical rpm sensor to a Skyray. This, along with my data recorder will give a second measurement of the rpm. However the sound gives extra info about the combustion process.

We have discovered it is possible to record the entire flight as a video, and strip out the sound to do the analysis. This coupled with the video picture allows us to see where exactly the plane is in the maneuver, a big help in understanding what is going on.

My intent is to first see what a Fox 35--set up in a "classic" 4-2-4 mode will show during a pattern. Then I plan to put on a LA25 and run in high rpm mode. Finally I want to put on a small 4 stroke to see how it performs. In all cases we will measure both the sound for analysis and take rpm data on my rpm sensor and data recorder (maybe also use my airspeed sensor with the data recorder).

Now if I can just keep that @(#$@^@ Fox running during the entire flight, I can post the results!

I have really been spoiled by electric power.

Alan Hahn:
Here is an expanded region around the wingover to the loops. I tried to tune up the search region for the Fourier peaks, and managed to eliminate the dropouts. This is the same data as before, but a smaller time region, and a more careful selection of the range that the algorithm searches to find the rpm. It is a bit tricky.

This illustrates to some extent, the difficulties of dealing with a real engine run, sound, and the wide frequency region that the engine is running at--especially one that is doing a 4-2-4 dance. Real data is a bitch! n~

Alan Hahn:
Here are a few more details on how this works (these examples are some of the better looking samples).

First I show the raw sound waveform that I get from the microphone. As I mentioned, this is a 0.1s slice of sound. As a note, this particular sample at 8750 rpm would give ~14.5 prop rotations in the 0.1 s. This particular slice comes from 84.45s point, one that you can see in the blowup plot from the previous post.

Second is the Power Spectrum from this particular slice. The white trace is the Spectrum, and the red vertical dotted lines are the peaks my algorithm finds. It is a simple algorithm, it simply looks for the highest peak, and any peak which is at least 5% of this highest value. Note that you see peaks at ~9000 rpm, 14000 rpm, 18000 rpm, 22000 rpm.... The 14000 rpm indicates some evidence of a 4 stroke power pulse. If the engine was 2 stroking, this peak, and the ones at 22000, 30000,.. would be missing. Also note the peaks are all of different intensities, and occasionally missing entirely. Some of the missing ones are probably taken down by the muffler (after all it is doing something) and some "just because"!

In the third graphic I show how I figure out the engine rpm. Since I have to admit the possibility that the engine is 4 stroking, I take the peak rpms (17 were found in this particular example) from the Power spectrum and then divide them by a range of rpm values, starting from 4000 rpm up to about 6000 rpm (actually spaced 10 rpm apart). What you see plotted is the sum of all the squares of the remainder from the division. If I would divide by the actual engine rpm, this sum would be small. So by looking for the lowest value in the plot (~4380 rpm), I claim that is the 4 stroke rpm value, and the "actual" rpm is just twice that. Now I go back and check from the peaks, how many odd harmonics I see and how many even. If the engine was purely 4 stroking, I would see about as many even as odd. If it were 2 stroking, I would see mainly only the even harmonics --in this case 4380 * (2,4,6,8...) rpm.

And as I mentioned earlier, the data are not always as nice as this one--which I would claim is one that the engine is in a 4 stroke.

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