Targeting Performance

Cars don't always go in straight lines, and sometimes you have to turn the steering wheel. People often think of downforce as being good in the corners but bad on straights, however this isn't really true. Unless you're running with so much downforce that your car breaks apart at high speed, then it's most likely just going to be drag that's the enemy on the straights. Downforce can actually improve straight-line performance for three reasons:

1. You've already increased your grip going through the previous corner. This means a higher apex speed and therefore a higher corner exit speed, and therefore a higher initial velocity at the start of the straight.

2. High torque can mean longitudinal grip is the limiting factor in some low/medium speed corner exits.

3. Similarly, longitudinal grip is usually the limiting factor in braking zones.

In FSAE though, more time is spent turning the steering wheel than going straight, and full throttle for anything more than 2 seconds during autocross is rare. Most of the time spent cornering happens at 35-50 kph, where downforce is unlikely to be more than 15% of the car's weight. 

The question is, what cases should we design and optimise for? Setting up infinite CFD simulations seems impractical so I'd rather have a small selection of scenarios that, when combined, are as encompassing and representative of full-lap performance as possible. 

Validation of lap simulator

We have GPS data of the competition track from our endurance run last year, and while the track layout changes each year, we expect the distribution of tight, medium, and open corners to be similar. Plug this into our custom lap simulation code and we can start to see how cornering affects performance, and vice-versa. Here is a plot of velocity and lateral acceleration:

By isolating the peak accelerations for a number of velocity windows and fitting a curve to these points, the lateral grip-limit can be seen:

This plot looks much nicer, but the density detail has been removed (this will be fixed later).

The first thing to note about this image is the decreasing trend of lateral acceleration as velocity increases. The lap sim doesn't yet consider the effects of tyre slip angles, so this curve is solely due to aerodynamic lift. 

The second thing to note is that I've chosen these specific variables to plot because they are easily obtained in the real world with a basic datalogger. In fact, I can pull the data from the car running on the exact endurance track that was fed into the lap sim to make the previous two plots, and use this as validation data for the lap-sim's ability to predict corner performance distribution:

The real track data clearly takes a similar shape to the simulated data, with a similar distribution of velocities and accelerations. Peak accelerations are matched and even exceeded in a few instances by the real data, butmuch of the data appears shifted left by around 1 ms-1 and lateral acceleration drops off with velocity much faster. The latter is explained by amateur drivers having reduced confidence at higher speeds. Anyway, the plot shows we can predict the densest velocity window within about 10% of reality, and the maximum grip-limited speed with the same level of accuracy (23 ms-1 predicted vs 20.5 ms-1 actual). 

Selecting design cases

The end goal of analysing this data is to determine what corner radii should be selected as CFD scenarios to optimise performance and set validation cases. Having crudely "validated" the lap simulator's lateral acceleration vs velocity estimates, we can look at simulating this year's vehicle. 

There are four candidate cases that seem appropriate to investigate:

• Mean corner radius

• Median corner radius

• Mode corner radius

• Maximum grip-limited corner radius

There is also the skidpan corner radius but this will form its own design case later. 

I'm not so interested in the velocity-lateral acceleration plot now, that was mostly for validation purposes. Here are some more useful plots, which assume a Cl*A of -1.2 and a Cd*A of 0.7 based on goals outlined in the next post:

Mean: 12.8 m

Median: 12.0 m

Mode: 7.2 m

Maximum grip-limited corner radius: 31.6 m

The mode case was ruled out based on being both too similar to the skidpan case, and having a grip-limite velocity far too low for any noticeable or even measurable downforce. The mean and median are similar enough to each other that it would make no practical difference which was selected. 

Practical considerations and adjustments

If these are to be our design optimisation cases, then these will also be the focus of track testing and particularly validation/correlation. For most teams, this would be fine. For us, we are a little more limited. Our only available test track is a karting circuit, which is narrow and thus the corner radii are less determined by cone placement and more by the actual shape of the track. We therefore need to make sure our design cases are reproducible for correlation.

The aerial view reveals that both cornering cases (mean/median radius, and max. grip-limited radius) will have to be compromised in order to make them reproducible at the track. This is fine, as the concept of a "representative" corner being the median radius was not based on any sound mathematical or aerodynamic theory, so there is room to stretch. Ideally the maximum grip-limited corner would remain as close as possible to the estimated value though. The closest option to a sustained 12.0 or 12.8 m radius is the 13.2 m radius corner at the bottom right. It could be tightened to match more closely, but I think there would be more benefit in maximising the arc length achievable at a constant radius, so keeping 13.2 seems best. 

There are three candidates for the maximum radius case at the top, right, and bottom of the track image. The values given for these are all significantly tighter, but there is room in all three to open up the driving line sufficiently to reach exactly the required 31.6 m, with a little room to spare. The top corner is undesirable as it is just after a tight section so the required speed would not be reached. The right corner is also undesirable as it is on a section with rapidly changing grade, which is not representative of the very flat competition track. This leaves the bottom corner (labelled at 19.4 m) as the best option. Combining these new adjusted radii with Figure 5 gives the following two cases:

"Representative" corner case: 13.2 m @ 14.6 ms-1

Maximum grip-limited case: 31.6 m @ 23.0 ms-1

Both of these are subject to change after the first round of on-track aerodynamic testing, probably about 11 months from now. 

These values are also unique to EV24 and are therefore expected to be faster than what EV23 can achieve. Our EV23 validation speeds for the same conditions are 13.9 ms-1 and 21.9 ms-1. 

As a note from the future, the "Representative" corner case just became known as the "median" corner case, somewhat incorrectly, but we just stuck with that naming convention. I use the terms interchangeably on this site. 

Braking

By rules the driver needs enough brake force at their disposal to lock all four wheels. This means that at higher speeds, a little extra downforce can let the tyres utilise this mandated force excess. Just as critical as pure downforce when braking is front/rear aero balance. Our lap simulation suggests an optimal average brake bias of 70% front, and average aero balance of 70% rear. That sounds achievable to me. Very little time is spent in pure braking so there's unlikely to be any optimisation for braking scenarios. We'll still set up a braking CFD case though to run occasional checks in to make sure balance isn't too pitch-sensitive, and avoid unexpected flow separation (particularly on floors/diffusers). 

There is also forward acceleration. This one is made extremely simple by a quick check of the lap simulator, which indicates that this year's car with its downsized motors and slightly more rearwards centre of mass is only grip limited below 7 ms-1 in pure longitudinal acceleration. At this speed, downforce can be assumed negligible, so there is no reason to optimise aerodynamics for a pure acceleration case. We won't be looking at combined longitudinal/lateral cases at least until there is more significant downforce on the car and a better understanding of its driveability aspects.

This makes four cases so far, when including the two cornering cases, braking, and also a simple ride-height straight-line case (solely for testing CFD-track correlation as easily as possible). The latter two were both assigned a velocity of 18 ms-1. 

Skidpan 

There's one more feature of the FSAE competition to throw a spanner in the works. Skidpan by nature is a constant radius corner for the entire event. This event offers over half the points of the entire autocross event. Given a significant proportion of corners on the autocross and endurance track also lie at or below this 9m radius (11.8 ms-1 as per Figure 5), this is the most important optimisation case. 

Summary

So, we have identified five critical scenarios under which to monitor performance of the car. These range from pure optimisation cases for maximising performance, to easy-to-correlate cases for validation, and in the case of the maximum grip-limited scenario, an opportunity to check peak cornering loads and balance where it's most influential on instantaneous performance, and most critical for safety. 

There are also various combinations of these cases, such as cornering and braking simultaneously, which will introduce further changes to incident airflow angles and suspension positions. These combination cases were considered too complex to specifically target during this first year of design.

I'll just acknowledge that on this page I have talked purely about maximum lateral accelerations (with a little on longitudinal acceleration and braking), and with respect to just pure downforce. Downforce is just 1 of 6 ways (3 axial forces, 3 axial moments) that the fluid-structure interactions of air on the car can affect the vehicle's behaviour, but with no significant frontal or lateral area being added by just a floor/diffuser design, the influence of any forces/moments other than downforce, drag, and front/rear balance were assumed negligible. There have also been no considerations yet on transient aero performance as this really relies on track data and perhaps some empirical performance prediction methods. I'm certainly not planning on waiting 2 weeks at a time for a full-car detached-eddy CFD simulation with solid-body motion...