Automatic Calibration Accuracy
Anyone that has taken the time to watch some of the video from the test flight on 10 April 2022 will notice that I was pretty excited (understatement) when I saw the calibration wizard in action on my iPhone for the first time. Having downed countless pots of coffee whilst looking at LOTS of data, I knew when I saw the summary screen on the phone with set points and curves, we had a good solution. This was borne out in analysis. Figure 1 is plot of coefficient of pressure, IMU and boom derived alpha for Run 1 from 10 April.
As you can see in Figure 1, the three solutions marry nicely across the entire speed band of the airplane from 156 KCAS to stall. Things get a bit wonky post stall due to inertial and roll effects. The alpha vane on the boom cannot react instantaneously, and the IMU-derived alpha is susceptible to error when a wing drops during a stall. The coefficient of pressure derived alpha actually gives the best performance post stall. Overall error for the entire plot is 0.15 degrees compared to the reference gyro (VN-300 IMU) and 0.25 degrees compared to the boom alpha. Assuming no roll present, the IMU derived alpha is a more accurate truth reference than boom alpha. The dynamic correction applied to the boom accounts for upwash, pitch rate and G; but is limited by the accuracy of our TAS measurement the the potentiometers the boom vanes connect to.
Since post-stall behavior for the IMU and boom derived alpha is questionable, Figures 2 and 3 plot coefficient of pressure (i.e., ONSPEED computed) error from the high speed start of the the deceleration run through stall. Overall performance is excellent. Anyone is welcome to download the analysis workbook used to prepare these charts here: https://3c039af6-63d7-4703-82ff-4bf98735a5a3.usrfiles.com/ugd/3c039a_da145d1ee48840c39f41dd4e4b87768a.xlsx . We are always amenable to a cross-check of our homework and welcome any feedback or BS flags.
Although the magnitude of the error relative to truth source varies slightly, both sources align nicely giving us a warm fuzzy that we've got good data to compare the coefficient of pressure solution against. We'll do some more transient response testing as well (high G vertical pulls and high G stalls) to further quantify the quality of the AOA solution at high G onset rates. At the risk of sounding like a broken record, a good AOA system has to be accurate, responsive, damped and ergonomic.
The next step in the flight test program is to validate the goodness of the system calibrated set points. These correspond to L/Dmax (start of the fast tone), ONSPEED fast (start of the solid tone), ONSPEED slow (start of the slow tone) and stall warning. The difference in alpha between ONSPEED fast and ONSPEED slow is the onspeed band. We hope that little or no adjustment is required; but more testing is required to find out. The good news is the quality of the baseline calibration. The pilot always has the option to manual adjust a set point by stabilizing at the desired airspeed/AOA and manually programming a set point using the WiFi interface.
"Static" vs "Dynamic" Calibration Techniques
We have experimented with three primary calibration techniques. The first was GPS "horseshoe" runs to produce average data for each point on the speed band, the second was a series of trim shots across the aircraft speed band and the third was a deceleration from Vmax or Vfe to stall. The first two methods produce what we call a "static" calibration: a table that allows pitch or derived AOA to be plotted against the coefficient of pressure for regression. The later involved plotting 50Hz data (pitch or Derived AOA) from Vmax to stall against coefficient of pressure for regression. Folks that have been following our steep learning curve have noted not only the progression of calibration techniques, but the evolution of our pressure normalization techniques. With the current Dynon probe on the RV-4, we are using our third normalization algorithm--cleverly nicknamed "CP3" for "coefficient of pressure, third try."
The first two techniques produce similar results. Figure 4 shows a portion of an analysis spreadsheet that contains data from some trim shots flown on 6 Feb 22.
The first three columns are self-explanatory. The 4th column is IMU (VN-300 reference gyro) derived alpha. The 5th column is boom alpha corrected for upwash. To obtain an upwash correction, we plot IMU derived alpha (i.e., known angle) against the raw boom angle (i.e., measured angle, no correction). The result is shown in Figure 5. As I discussed in the previous blog, the "goodness of curve fit" for the regression is shown as the R2 value, with 1.0 being ideal.
To obtain corrected boom alpha, we use the regression equation generated in Figure 5 and apply it to the data in column 3. The next column, with the header "CP3 (P45/Pfwd)" is the actual coefficient of pressure. It is measured and processed to eight significant digits. To derive the static calibration curve, we plot IMU-derived AOA against the coefficient of pressure. This is shown in Figure 6.
To calculate AOA, we use the equation generated in Figure 6 and apply it to the measured pressures. This output is in column 7 "Static Curve CP3 Derived Alpha." This angle is compared to our two reference angles (IMU-derived alpha and boom alpha) to determine system error in columns 8 and 9. As you can see, under non-maneuvering conditions, error is quite low: 0.11 degrees relative to the reference gyro and 0.14 degrees relative to the boom alpha. However, things get interesting if we apply the static calibration to dynamic (maneuvering) data. In Figure 7 below, we apply the curve from Figure 6 to a 1G stall. CP-derived, AOA-derived and boom alpha are plotted:
You can see that the CP derived alpha doesn't marry up as nicely with the two truth sources as did the dynamic curve in Figures 1-3 above. Overall error isn't egregious, averaging about 1/2 degree, including the wonky post-stall data; but not as tight as we'd like. We have observed this behavior since our initial transient response testing several years ago. Since we have been designing to an accuracy of 1/4 - 1/2 degree, this has been "close enough" and we've always just scratched our heads and figured that we'd eventually have to sort out "why the difference?"
Before we start speculating, let's revisit the table in Figure 4 above. On the right side of the table are three columns in red font. In those columns, we apply the same methodology we did in Figure 6, but in reverse. We use a dynamically derived calibration curve, and apply it to static data. What immediately pops out is that the magnitude of the error is identical when working the problem in reverse: about 1/2 degree.
So, what's the best calibration technique? That's pretty straight forward: the dynamic calibration. Why? It produces better transient response (maneuvering) performance; and it's easy to fly. But why the difference in accuracy using different calibration techniques? That's tougher to answer. We initially thought there may be some engine power effects during the high alpha, slow speed trim shots that wasn't present during the idle power deceleration. After consulting with Dr. Dave Rogers it appears as the though our dynamic calibration is capturing an inertial effect associated with flow reversal on the top of the airfoil as the airplane slows and the separation point moves forward. The air molecules can't reverse direction instantaneously...picture a tennis ball thrown against a wall. As the ball hits the wall, it compresses before rebounding. Newton's first law.
The Bottom Line
Automatic calibration works and it's as easy to fly as we can make it. More testing is required to validate (or tweak) our automatic set point logic.
Retrofitting the 20 buck Chuck
Phil developed a procedure to retrofit our candidate gyro chip to our existing V3 hardware. This involves sawing off the old chip, and Soldering the new, smaller 6 DOF MEMS platform in place. Lenny has already modified a box for test. First tests will be in the oven and on the bench. If performance is good as the box heats up, we'll strap it into an airplane and fly it. If it works, we'll be able to move on to Phase 2 automatic calibration, making the ONSPEED hardware a completely self-contained AOA solution for any airplane. If it doesn't, we'll keep plugging away.
