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 compared to the same car without downforce.

2. If you're rocking some serious Newton-metres, you'll be spinning up wheels at corner exit (particularly RWD cars), or at least limiting torque to the ground if there is some form of traction control. Downforce like always will increase the tyre normal force and give you more grip here too. It's not just lateral acceleration that benefits. 

3. Just like forwards acceleration, braking also benefits from maximising available longitudinal grip, both for performance and stability.

Different racing series will have different styles of tracks that they race at, with some more open than others. In FSAE, more time is spent turning the steering wheel than going straight, and full throttle for anything more than 2-3 seconds is rare. So we should focus on optimising downforce for tight corners, right? Well the flip-side is that most of the time spent cornering happens at 30-50 kph, where you're lucky to be making more than 15 kg of downforce; much less than 10% of the car's total mass. Further, FSAE cars typically weigh around 250 kg including the driver and are capable of around 1000 Nm at the wheels, suggesting corner exit could still hold some big performance gains. The question of where to focus is therefore still not obvious, so some simulation will come in handy. We'll come back to straights vs corners later; for now let's just look at what we can find out about corners first.

Validation of lap simulator

We have GPS data of the 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 software (a point mass moving around a track with weight transfer, suspension position, and inertia effects) and we can start to see how cornering affects performance, and vice-versa. We could plot something like the relationship between velocity and lateral acceleration:

This plot at first looks like a mess of spaghetti, because it's including every single data point. I'm just interested in where the performance is grip-limited. Let's throw in some conditional requirements that only pick out points where |accel[long]| < 0.001 ms-2 and |accel[lat]| > 10 ms-2 Given the lap sim works by assuming maximum grip is achieved in pure lateral acceleration, this filters out all the points we need with a bit of buffer for numerical precision, to which an interpolating curve can be fitted. 

This plot looks much nicer, but the density detail has been removed. I could bring it back with a histogram, but I'll save that for later. For now, Figure 1 is still useful. 

The first thing to note about Figure 1 (and more clearly in Figure 2) is the decreasing trend of lateral acceleration as velocity increases. This is from a combination of suspension parameters (mostly steering angle and toe, and the resulting slip angles), and also a small amount of lift force on the bare car. 

The second thing to note is that I've chosen these specific variables to plot because they are reliably obtained in the real world. 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, but is generally a bit less extreme. Peak accelerations are matched and even exceed in a few instances by the real data, but velocity densities are reduced by around 1 ms-1 and lateral acceleration drops off with velocity much faster. We expect the reasons for this are a combination of over-simplified suspension in the lap sim, and amateur drivers pushing the car less at higher speeds. We're still working on validating the suspension to figure out exactly where we can improve predictions, but these plots already give us plenty to work from. It shows we can predict the velocity that the densest window of lateral acceleration is centred around within about 10% of reality. The estimated highest speed where lateral grip is the limiting factor also lies within 12% of track data. 

Selecting design cases

The end goal of analysing this data is to determine what corner radii and associated velocities should be selected to both optimise performance for, and to set test and validation cases for. For now, we have shown using data from the previous year's vehicle that the lap simulation program gives us a sufficiently accurate idea of both instantaneous cornering performance, and cornering trends across different speeds. Now we can look at simulating this year's vehicle using our current best estimates based on our overall vehicle design targets. 

The exact vehicle parameters aren't important here, and there are many changes between last year and this year such that the plots for this year's car are not directly comparable. What is important is identifying the following key values for our estimated 2024 vehicle performance:

• median corner radius and its grip-limited velocity

• most open grip-limited corner radius and its grip-limited velocity

The first value is used as a metric to identify a "representative" corner, and the second value is the most extreme performance-critical cornering case. The choice of a representative corner is due to the obvious limitation of not being able to simulate, test, or optimise for hundreds of slightly different cornering scenarios. The extreme case is of interest less for optimisation, and more for assessing aerodynamic stability (see the final paragraph on this page) and suspension behaviour. 

I'm not so interested in the velocity-lateral acceleration plot now, that was mostly for validation purposes. Here are some more useful plots to give us those two key values:

Median grip-limited corner radius: 12.0 m

Maximum grip-limited corner radius: 31.6 m

Practical considerations and adjustments

So is that it? Are we done? Are those our two design cases? No. 

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 local 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.

Figure 6 reveals that both cornering cases 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 m radius is the 13.2 m radius corner at the bottom right. This will have to be our "representative" case. There are three candidates for the maximum 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 @ 14.8 ms-1

Maximum grip-limited case: 31.6 m @ 23.2 ms-1

These values are for EV24 and are therefore expected to be faster than what EV23 can achieve. Our EV23 validation speeds for the same conditions are 14.0 ms-1 and 22.3 ms-1. 

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 excess of braking force. There's a limit to the brake force though, and therefore a limit to how much downforce can be utilised before there are no additional returns in braking performance. Just as critical as pure downforce when braking is front/rear aero balance. On downforce cars this can get quite complex, as the amount of weight transfer under braking will change with speed due to the differing normal force on the tyres, as will the total normal force reduce as the aero load backs off. This is where brake migration comes in for the likes of F1 and modern LMP cars. We also have a form of brake migration in our car, but fully analogue (still within rules). It allows us to slam on the brakes and reach maximum deceleration while keeping stable, but also to use exaggerated trail-braking and rotate the car into tight corners by oversaturating rear tyre grip. We might keep that design to ourselves for now though...

Anyway, because we have no previous aero data to go off, it's not really possible to accurately predict an aero map of a car before we've even started to design it. As such, I'll be ignoring the effects of changing weight transfer and just assume an intermediate-speed steady-state braking. Our lap simulation suggests an optimal average brake bias of 70% front, and average aero balance of 75% rear. That sounds achievable to me. Choosing between optimising for corners or optimising for braking is too open-ended to answer quantitatively, so it will be more of a case of setting up the design cases and monitoring to make sure performance and driveability are at least at acceptable levels under all driving scenarios, while comparing different optimisation paths in the lap simulator as they arise. 

Finally, there is 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 5 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, which was set to a medium speed of 18 ms-1. For simplicity, this speed was also used for the braking case.

Skidpan 

Finally, 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. Performing well at this event with one radius and speed yields a maximum of over half the points of performing well across the entire autocross track with its whole range of radii and speeds. Given a significant proportion of corners on the autocross and endurance track also lie at or below this 9m radius (12.0 ms-1 as per Figure 5), it stands to reason that this is the most important optimisation case. 

So, we have identified five critical scenarios under which to monitor performance of the car. These range from important 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 for suspension simulation purposes and any sensitivities or driveability concerns. 

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 and optimise for during this first year of design, but will still be investigated passively for aero-map purposes for future optimisation and utilisation in a more aerodynamically fleshed-out update of the lap simulation software. 

In future posts I will discuss how these four cases were further investigated, incorporated into CAD and CFD, and eventually optimised for, tested for, and validated against. 

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 I'll save discussing these until later during the actual design and testing processes. 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 something like a full-car detached-eddy CFD simulation with solid-body motion...