Big skids

While simulating a car in a straight line has only the suspension positions to worry about, simulating cornering introduces two extra complexities: yaw angle and steering angle. Our suspension simulation code spits out the individual tyre slip angles that are expected to maximise lateral acceleration, and from this we can figure out vehicle slip angle at a given point on the car, which taken instantaneously should be the same as the incident airflow yaw angle at that point. Until now though, only suspension position had been validated, so we needed a way to test slip angles. The obvious answer is a yaw probe, but these are expensive and we didn't have time to try and make one before both the aero team and suspension team needed the data. Enter some creativity.

We'd just bought a bunch of light-weight, very soft and flexible "wool" for future tuft testing, and I figured if tuft testing is meant to show local airflow direction on surfaces, why can't we use it to figure out yaw angles? So that's what we did, although I must admit I was somewhat dubious of the merits of this method to start with. The main hurdle was getting both an accurate and precise measurement from inherently transient and imprecise. I targeted accuracy by installing tufts in 3 different locations on the nosecone to allow an average to be taken. One was placed at the front where the surface is flat and flow was expected to be minimally affected by pressure gradients. The other two were places symmetrically around the raised centre of the nose closer to the cockpit opening. Precision was solved by creating angle diagrams and attaching them to the nose underneath the tufts, with a camera mounted to the driver's helmet aimed down at them and the driver operating under strict instructions to keep their head as still as possible. With the team's lack of prior experience with optical flow analysis and no easy way of quickly getting a camera to mount rigidly in a position with sufficient perpendicular view alignment with the tufts to enable this technique, a simple manual interpretation of the footage was employed. 

The track was set up around our two corner test cases, setting the longest possible constant-radius corners at 13.2m and 31.6m (see the first post on "Targeting Performance"). We ran each case first enough times for the driver to feel and get used to the edge of grip in these scenarios, then recorded 10 runs through each corner for averaging. The data was surprisingly consistent, with very little fluctuation in the tufts after the initial shift in angle when entering the corner. From the suspension simulation, we were expecting around 2 degrees of yaw at the centre of gravity for both cases. The averaged results gave us values of 4 degrees for the 13.2m radius, and 3 degrees for the 31.6m radius. Based on driver feedback, we expected the increased yaw to be at least partially due to the difficulty in holding the car directly at peak lateral acceleration, with the transition to oversteer being gradual but quite easy to achieve. We noted this in the wool tufts picking up angles up to 10 degrees in some (rejected) test runs where the car momentarily overcame available rear grip. The uncertainties associated with both the test method and the test equipment meant we didn't consider this data conclusive for validation of the suspension simulation, but it showed that somewhere in the ballpark of 2-4 degrees would be a good estimate for running initial cornering simulations on EV23 for identification/creation of aero validation targets. In the mean time before starting design on EV24, we've got some real yaw probes to make. 

The process of implementing a specific yaw angle into the cylindrical domain in the CFD cornering cases was done using CAD sketches. Under the assumption that the yaw angle was constant for the whole corner (which seemed like a reasonable assumption based on watching the wool tuft recordings during runs when the car was clearly under full control), circles with radius equal to the corner radius were positioned tangential to an angle vector at the car's centre of gravity. The vector between the centre coordinates of this circle and the geometric centre of the corner was the offset applied to the cylindrical domain in CFD for each case. Without needing to run additional suspension simulation cases, estimates of yaw angle at other corner radii could be obtained through interpolation. The CAD sketch setup is shown below in Figure 3 in which the fore and average of the two rear tuft angles are shown as two separate dashed circles for each of the two cases to give a visual representation of uncertainty, as the centre of both circles should theoretically be coincidental. The 30mm offset is simply a translation between vehicle geometric centre and centre of gravity. 

In addition to yaw angle, we were also taking measurements on steering angle. Steering angle data was a lot more noisy and variable, which makes sense given it is a direct input, whereas changes to yaw angle are dampened by the inertia of the car. In general we found that the suspension simulation was underpredicting the relative counter-steer required when driving at or above the optimal slip angle, so we took the track data for the CFD setup and left the suspension team to get on with more research and adjustments for their code. A look at a plot of steering angle vs yaw rate during an autocross event suggests that assuming a single representative steering angle for a given corner to use for CFD simulation (and eventually optimisation) seems appropriate, as the variance is generally constant across the whole range of yaw rates, the relationship is linear, and the time spent in significant counter-steering or under-steering is very minimal (see Figure 4 below). The two colours show two different drivers, with slight differences in driving style evident at the high-yaw cases, but in general the results are very similar.