Mercedes and 2022's aerodynamic bridge to the winner's circle

The 2022 Mercedes AMG F1 team– at the point of writing this post– has been an almost total disappointment. The team has almost totally lacked control of the vehicle dynamics and aerodynamics of their car. The culprit seemed from the beginning to be: porpoising, a dynamical coupling between the under-body aerodynamics introduced in the new-for-2022 regulations and the vehicle dynamics.

Porpoising is a complex phenomenon, but it's pretty closely related to phenomena we're pretty used to. Ever sing in a closed room, only to be startled by the booming and sudden echo of your voice? And then, with a change of pitch, the booming echo can be gone as soon as it arrives. This is a phenomenon known as resonance, and it's not only found in closed rooms. It also happens to unfortunate bridges:

Resonance is about the interaction between a system with a naturally oscillatory nature and input to the system from outside it– "forcing". In most intended operating conditions, systems like bridges or closed rooms or, for that matter, race cars will oscillate briefly when some input forcing comes. But nominally, that oscillation dies out. Disaster strikes- whether in the Tacoma Narrows or on the track in Miami when the oscillation doesn't die out, but instead multiplies itself.

So, porpoising is a resonance?

Precisely. And to be more specific, it's a resonance between the underbody aerodynamics and a car's suspension. When the car is nominally situated, air flows freely and cleanly under the body. When the suspension is compressed away from equilibrium due to track irregularities, the channel through which the air flows under the car gets constricted. Because mass is conserved in the flow, a smaller flow-through channel means that flow must accelerate to a faster velocity in this condition. This, in turn creates a lower pressure under the car, by Bernoulli's principle. Lower pressure under the car and the same pressure above it increases the downforce, further shrinking the gap for flow, speeding up the air, and creating more pressure. This process feeds back into itself, resisted only by the suspension, whose springs become highly loaded with potential energy.

At a certain critical point, if the suspension does not slow the ride height from shrinking, the velocity gets large enough to trigger "separation" (the process here in technical terms is really an increase in the Reynolds number, $\mathrm{Re}$). Separation represents the point at which the tendency of a flow to want to "move" reaches a critical balance– or lack of balance– with its tendency to "settle". The result is swirling, churning, and chaotic (in both the non-mathematical and mathematical sense). Lift and its autosport counterpart, downforce, are best generated by settled and predictable flow, and when separation occurs, there's a lot less of them. So, suddenly, on our racecar, the downforce drops and the loaded suspension can spring the car back to and then beyond its nominal ride height, reversing the process of decreasing gaps, increasing speeds, and decreasing pressures. The flow gap for underbody air gets big, the velocity goes down, the pressure goes up, and downforce (and therefore grip) is low, just the opposite as before. Conveniently, this allows the flow under the body to reattach, becoming regular again. But the springs have a tendency to oscillate, so once they max out, they start coming back down again.

Here is where resonance comes in: if the springs and dampers (which tamp down oscillations over time) are tuned correctly, the timing is off when the car comes down and the oscillation due to separation passes quickly. Resonance is controlled. However, if that's not the case, the process starts itself back up again every fraction of a second. With every drop in ride height, downforce increases to the crisis point, separation happens, the suspension unloads and the car bounces back up, then the car comes down to rinse and repeat. This is porpoising: an uncontrolled resonance between the suspension and aerodynamics of an F1 car.

Mercedes fixed its porpoising problem by... re-tuning the aerodynamics???

For a few months now, we've heard about Mercedes trying to "find the right balance" or "find the right setup" on the car. This, generally, means trying different springs and dampers in the suspension. But I was convinced that Mercedes had changed the approach– and actually fixed things– when I saw exactly this frame from this video:

Now this winglet directly generates downforce. But it also creates a couple of vortexes either side along through the chassis and under the floor. Now Mercedes aren't being too open about exactly where these vortexes go and what they do. And, that's sort of what you'd expect...

From here, he goes on to look at some other things, purportedly equally important for performance. I think he missed the massive importance of this part.

Flow control is an ancient form of black magic aerodynamic discipline that basically involves tricking a aerodynamic flow into doing what you want it to do (not separate) instead of what it wants to do (separate). It's generally divided into two camps: Active Flow Control, where you acoustically buzz, suck and/or  blow on, and sometimes electrocute the flow into doing what you want. Passive flow control is much less interventional and much more common; it involves modifying oncoming flow, changing what's happening upstream of the feature that wants to be controlled, in the hope that the effect of the modification induces the flow not to separate.

For decades, at least until the 2022 (formerly 2021) regulation change, the goal of conditioning the flow was, more often that not, to guide where the flow goes. Of course there are also plenty of ways that teams use vortex generation, mostly to manage tire wakes. My hypothesis is that Mercedes, and I suspect before then also Ferrari, Red Bull, and Alpine– who famously claimed they could turn porpoising on and off– have leveraged this winglet as a big passive flow control mechanism to tame the porpoising problem. It all starts with the underfloor, which is new for the 2022 (formerly 2021) changes. Here's an image from racefans.net, showing the return of venturi sections.

Now, we envision nominal aerodynamic use of the driver's right-hand-side venturi in the next diagram.

We can see here that at a nominal ride height flow enters the "venturi plenum"– a technical name for the gap between the ground and the underbody of the floor and leaves through the expanding diffuser, with a high-velocity, low-pressure region that generates downforce through the middle of the car. It's worth noting that in this nominal situation, the downforce generated is resisted by the suspension, which is loaded in this situation with a nominal amount of potential energy which is set by the force equilibrium between the downforce and the force of the staticly loaded suspension. If the car is disturbed in a way that increases the suspension loading, the ride height will decrease. As noted above, this process can feedback if the suspension is not tuned to prevent it, leading to a crisis. A cartoon of the flow at the point of crisis– called separation– is shown below.

This is exactly the process that the F1 teams want to prevent with a winglet. An the flow in the underbody is envisioned in the diagram below in the presence of a vortex-generating winglet.

This diagram captures what I envision the driver's right-hand-side plenum of the underbody to look like. There's a vortex with the diameter on the order of the gap between the car's floor and the ground, kicked off by the winglet at the entry. This vortex has the effect of mixing flow– pictured as streamlines in the diagram– vertically in the plenum. This mixing carries some fast, high-energy flow from near the ground into the inner boundary layer, and carries some slow, low-energy flow out of the inner boundary layer.

This process moves flow with stream-wise inertia– the tendency to keep flowing–  into the inner boundary layer, where the flow has low stream-wise inertia and is likely to attempt to reverse itself and separate.

If this is the mechanism which Mercedes and their peers have used, and I suspect it is, it's fairly brilliant. Rather than attempting to tune the suspension, taking it off of an optimal-for-driving setup, they've tuned the aerodynamics of the underfloor with a passive flow control vortex generator, allowing the suspension to be tuned much more optimally for maximizing driving performance and delivering laptimes. And in the case of Mercedes, they certainly managed to find some mechanism to get the car to go faster. Looking at the top ten lap times, it seems like Mercedes was absolutely in control of their car's porpoising.

Lap Time Delta Driver Team Lap No. Tire Tire Life
1:24.108 0.000 PER Red Bull Racing 55 SOFT 5
1:24.253 0.145 HAM Mercedes 51 SOFT 6
1:24.636 0.528 RUS Mercedes 53 SOFT 4
1:25.106 0.998 HAM Mercedes 50 SOFT 5
1:25.207 1.099 HAM Mercedes 55 SOFT 10
1:25.257 1.149 HAM Mercedes 53 SOFT 8
1:25.262 1.154 RUS Mercedes 54 SOFT 5
1:25.389 1.281 HAM Mercedes 54 SOFT 9
1:25.456 1.348 VER Red Bull Racing 46 MEDIUM 2
1:25.551 1.443 RUS Mercedes 55 SOFT 6

They delivered 8 of the top 10 laps, which is nuts compared to their season so far. It's probably not a perfect comparison, since Lewis Hamilton was pushing hard at the end of the race, when the cars are fastest due to fuel burning off and lightening their load, while Verstappen and Russell had no strategic reason to be anything but conservative in their last few laps; however, the tenth-and-a-half gap between Perez's overall fastest lap– run like a qualifying lap to win an extra championship point– and Hamilton's fastest indicates that Mercedes has real pace, and I suspect that they will be a real threat for the rest of the season, in no small part due to their newfound passive flow control device.