A new yaw probe

This post covers the design and testing of a new yaw probe design carried out by a first-year aero team member. The intention was to investigate a small vertical symmetric aerofoil design that utilises differential static pressures in an attempt to improve the somewhat poor precision of the current probe that relies solely on dynamic pressure components (briefly discussed in It's off to track we go).

The first tests were run in Java Foil as a batch run of 2D NACA profiles of varying thickness to find the best trade-off between maximising static pressure difference for a given change in angle of attack, while avoiding separation near or upstream of the ideal pressure tap location. Separation will be reduced on a 3D profile though, so with this in mind, the target for the 2D profiles was to find a case where the separation point coincided with the ideal pressure tap location at 10 degrees incidence (towards the upper bounds of the yaw angles we expect to see under aggressive but controlled driving) and at Re=50000. The best candidate ended up being 0014 (Figure 1). 

The 0014 profile was then run through CFD as a finite 3D profile with the pressure taps at 50% vertical span. I decided to use Ansys Fluent instead of our usual Star-CCM+ as it's a bit more user-friendly for beginners and it's quicker for setting up simple simulations like this one. Velocity was set to 10m/s (the slowest speed that we would be interested in looking at yaw angles) and chord length was 100mm, giving the Re of 50000 as mentioned above. The aim of these simulations was to get a more accurate estimate for pressure differentials at different angles to see if the concept was worth continuing with. The results here were pretty linear, and suggested 12-13 Pascals increase in differential pressure for each degree increment, tested up to 13 degrees (Figure 2). With the 10 Pa uncertainty (+/- 5 Pa) previously calculated for the pressure sensors, this gives a simulated 0.8 degree precision at 10m/s. This is nearly at the original goal of 0.5 degree precision, and is significantly better than the 2 degree precision measured on the existing yaw probe, so the go-ahead was given for manufacture (Figures 3, 4, 5). Given how far forward the pressure ports are, we probably could have cut the aerofoil chord length in half and just had a bluff trailing edge without affecting the readings. I decided not to though, as the full length gives better mounting options for the pitot-static tube on top, and we would have wanted at least a longer base anyway to improve mounting strength to the nose of the car. 

The finished yaw probe (Figure 6) was calibrated in the wind tunnel at yaw angles from 0-10 degrees in 1-degree increments, and velocities of 5, 10, 13, 16, and 19 m/s. The results showed similar trends across all airspeeds which was nice, but revealed some non-linear behaviour; particularly, an increased sensitivity in the range of 3-6 degrees. All tests were run on a single differential pressure sensor, with serial outputs read through a laptop and converted to Pa using the previously calibrated conversion for that particular sensor. Raw results in 3D form are shown in Figure 7. Unfortunately there was no obvious 3D surface formula that appeared to suit the shape of the results, so for the time being we are relying on interpolation of the raw results which doesn't iron out any issues from, for example, a slightly mis-aligned installation angle for one or more of the tests. We also found later that true 0-degree yaw was achieved closer to the wind tunnel's 1.5-degree mark, suggesting the mount plate was rotated slightly. Consequentially, we effectively only tested up to 8.5 degrees, so future calibration testing may be required if we see the car regularly exceeding this at track (we haven't had enough testing with the current yaw probe to know this with much certainty, especially given its low precision). 

Figure 7: Surface plot of the corrected raw wind tunnel test results from multiple view angles (higher yaw angles were omitted at 19 m/s due to a lack of confidence in the integrity of the mounting method)

Out of interest, I compared the experimental results (corrected for the 1.5 degree offset) to the 3D CFD results, as shown in Figure 8. The agreement was reasonable considering the slightly imperfect resin-coated surface finish on the manufactured part, and the lack of consideration of y+ values and any sort of mesh independence tests in the CFD model. 

The last step was to figure out where the best spot to mount it on the nose of the car is. By combining the expected average slip angle of the car at its wheelbase centre from VD simulations with the cross-flow from rotation through the most critical corner radii (9-14 m), the expected airflow yaw angle at any longitudinal point on the car could be measured using similar methods to those shown in Big skids. The increased sensitivity of the yaw probe between 3-5 degrees (corrected) dictated its location, such that it was placed where the expected cross-flow was primarily between these angles in the driving scenarios of interest. Small corner radii mean that most of the time, the cross flow due to rotation of the car outweighs the slip angle, so it will see airflow coming from the direction of steer if positioned anywhere on the nose. The chosen position was subject to change once actual track data from the probe at various longitudinal locations was obtained, but this was be the initial position that was used in the meantime. 

Because of the combination of effects from the car's rotation and lateral slip (and the limited precision compared to methods such as lasers or GPS/IMU), it will be difficult to get accurate slip angle measurements from the yaw probe (i.e., differentiate the two effects). The best we can try and achieve is taking the rate of change of heading and using this combined with velocity to estimate the instantaneous effective corner radius and thus the expected cross-flow from rotation. It can't be proved if this method will work or not, but I'm hoping we'll at least be able to tell if the resulting slip angles look believable or not, and go from there to try and improve the estimate.