My twin brother wrote an article on You Suck at Racing about tire grip, and I’m going to steal some of that content to explore how tire grip and aero are related.
Braking, cornering, accelerating: everything depends on grip. Understanding how rubber tires create and lose grip is therefore fundamental. Let’s start with some theoretical laws of friction.
- Amonton’s First Law: The force of friction is directly proportional to the applied load. If this law is true, then a 4000 lb car should stop in the same distance as a 2000 lb car. It weighs twice as much, but it also experiences twice as much friction, so theoretically, the weight of the car doesn’t matter.
- Amonton’s Second Law: The force of friction is independent of the area of contact. This means that it doesn’t matter how wide your tires are. Skinny or fat, they have the same amount of grip. And grooves wouldn’t matter either.
- Coulomb’s Law of Friction: Friction is independent of velocity. Which means you should have the same amount of grip at all speeds.
- Finally, static friction is always greater than kinetic friction.
You might not believe these laws, because you’ve experienced that tires don’t really follow these laws of friction.
- If weight doesn’t matter, then why do lightweight cars like Miatas out-handle bigger cars?
- If tire width doesn’t matter, then why are wider tires faster? And by the same logic, given the same amount of rubber area, why are slicks faster than a tire with grooves?
- If static friction is always greater than sliding friction, why is it faster to have slip angle through a corner?
Four important graphs
In order to understand how tires work, you have to understand the following four graphs. Introductory physics assumes that the coefficient of friction, Mu (μ), is a constant, and that may be true for a block sliding against a table top, but when it comes to tires, μ is not a constant.
Tires generate grip from molecular adhesion, mechanical keying, and hysteresis, and those factors are based on a combination of variables. In each of the graphs below, the coefficient of friction, Mu (μ), changes due to load, temperature, speed, and slip angle:
Graph A shows μ as a function of load (weight). If doubling weight doubled grip, then the line would be flat. But when you double the amount of weight on a tire, there are diminishing returns. When cornering heavily, the outside tires experience more load, and because of that, heavier cars lose more grip than light cars.
Graph B shows μ as a function of temperature. Every tire has an optimum temperature. Both cold and hot tires have less grip than one in the optimal range. If your tires are too wide, they may never get up to optimal temperature, and a narrower tire may heat up more favorably. For this reason, wider isn’t always better.
Tire Rack did a great test where they tested a bunch of wheel and tire widths. The fastest tire wasn’t the widest. And when they went to a wet track, the fastest lap was the narrowest tire.
One thing that contributes to heat is grooves. Squirming tread blocks are a major source of heat. As a result, grooved tires heat up more quickly than slicks. One reason for using slick tires is to spread the load better, but an even more important one is to prevent the rubber from overheating.
Graph C shows μ as a function of speed. The faster the car goes, the less time there is for keying; the ability for rubber to change shape and interact with the road. Under wet conditions, where adhesion no longer applies, grip is highly affected by speed.
Graph D shows μ as a function of slip angle. Every tire has an optimal slip angle. When a tire is twisted, which it always is to some degree, some parts of the contact patch are experiencing static friction while others are kinetic. This mixed state isn’t really addressed by any of the laws of friction, but it doesn’t make this any less real.
Ian made a drawing of what is happening between the road and the surface of your tire, which can help you further understand how tires grip.
Visualizing grip
The following image shows the surface of the road as a jagged green line on the bottom. (If the road surface was perfectly smooth, then the line would be horizontal. But because asphalt has imperfections with peaks and valleys, the road surface is represented as a jagged line.)
Panel A represents a tire (squiggly line) at rest, pressing into the surface of the road (jagged line).
Panel B is what happens when you add load: the rubber goes deeper into the surface, creating more grip. But there’s only so far you can push the rubber in. This is why doubling the load on a tire doesn’t double its grip. Panel B could also be softer rubber or hotter rubber. In both cases, the rubber conforms more easily to the surface, and with more contact, you get more grip.
Panel C shows what happens at high speed. The rubber doesn’t have as much time to change shape, so it doesn’t deliver as much grip from keying.
Panel D shows what happens when a tire overheats. The rubber comes apart, providing less contact with the surface. If the rubber gets hot enough, it may liquify or sublimate, creating a slippery layer between the surfaces.
This visual model isn’t perfect, as it doesn’t give why slip angle matters so much. But hopefully it helps you visualize the interface between your tires and the road, and why some factors add grip, and other factors take it away.
Aero and tires
So that’s how rubber grips the road, but there are other dynamic factors at play here, namely the aerodynamics of the vehicle.
Most cars without aero lift at speed, because the curved surface of the top of the car is longer than the bottom. In other words, cars are shaped like airplane wings, and like wings, they generate lift. The higher the air speed, the less traction there is.
Most cars have a coefficient of lift of around 0.3. Cars with a lot of curvature, like a fastback, have more lift than a three-box sedan or hatchback. By nature of their shape, most cars generate more lift over the rear tires than the front tires.
Cars also generate lift when in yaw, so if your car is pitched slightly sideways in a corner, it has even less traction. Nissan did some tests on this and found there is a fairly linear relationship between yaw angle and lift, and so the more sideways you get, the more the car lifts.
This means as you corner faster and faster, your rear tires have less and less rear grip. You already saw in graph C and panel C that tires have less grip at speed because they have less time for keying. So if you combine the keying losses with the lift and yaw losses, you get a car that’s lost a lot of grip on the rear tires.
And this is why it’s so important for race cars to have spoilers and/or wings.
Aero and lap times
To put some numbers on it, let’s take a look at a few NASA classes at Watkins Glen.
NASA Spec3 is a class for stock-bodied (no aero) E36 BMWs on Toyo RR tires measuring around 14.5 lbs/hp. The Spec3 lap record is 2:13.6.
NASA also has the ST5, class, which is a similar lbs/hp ratio to Spec3, but allows a splitter and wing. The ST5 record is 4.3 seconds faster: 2:09.27.
NASA also has a time trial class, TT5. TT5 and ST5 are the same formula, but the ST5 cars are racing wheel to wheel, whereas the TT5 cars are in a time trial situation with less traffic. Therefore, the TT5 laps are usually faster, but in this case, a surprising two seconds faster: 2:07.202.
If you compare the Spec3 lap record to ST5/TT5, can see that aero (splitter and wing) are worth about 4-6 seconds at Watkins Glen. Let’s call it 5 seconds for simplicity. This isn’t a difference in tire grip, as most cars are on Toyo RRs, but some cars are on Maxxis RC1 for the same lbs/hp (or Hoosiers at a significant penalty to lbs/hp).
Let’s take a look at where the difference is. On the front and back straights, there isn’t a huge difference in top speed, so the cars are pretty similar in lbs/hp. In Turn 7, where aero doesn’t make much difference, the minimum corner speeds (vMin) are pretty similar, and so we’re looking at cars with equal grip, as well. But take a look at Turn 10, the aero cars are going about 10 mph faster!
| Lap | Front | Back | T7 | T10 | |
| Spec3 | 2:13.6 | 121 | 126 | 62 | 87 |
| ST5 | 2:09.3 | 118 | 1277 | 63 | 96 |
| TT5 | 2:07.2 | 123 | 128 | 62 | 98 |
Now I’m making some pretty big assumptions on driver skill and track conditions being equal. So I’ll do some simulations in OptimumLap, and see if the computer world agrees with the real world.
I’ll start with the Spec3 car using drag and lift values of .44 and 0.3 which is probably in the right area. With these values I get a lap time of 2:13.82 which is pretty close to the Spec3 lap record. I’ll then add a splitter and wing to bring the Cd to .47 and Cl to -0.8 which are pretty fair values for the added aero. Doing only these aero mods on exactly the same car, I get a 2:08.84 lap, which is right in the middle of the 5-second delta we saw in the real world.
So that’s a pretty good verification of aero being worth about 5 seconds. So next I want to take a look at Turn 10 and see how much aero helps here, and if there’s really a 10 mph delta.
Turn 10 Watkins Glen
For the OptimumLap simulations, I’ll use four cars instead of two cars to get more granularity. I’ve given them the same tires with 1.2g of lateral grip, but different aero packages.
- No aero – This is the Spec3 car with a coefficient of lift of 0.30, and is represented by the red line.
- Zero lift – This car has some minor aero like a spoiler, which cancels out lift, and so the Cl is zero. This is represented by the orange line.
- Mild aero – This is the kind of lift and drag you’d see from a spoiler and airdam done professionally (NASCAR level). This is represented by the blue line.
- Good aero – This is a car with a splitter and wing, and is represented by the green line.
I’ll examine the grip in the middle of Turn 10, at the 16000′ mark from the start/finish line. This is not quite the minimum speed in the corner, but shows a high lateral load and is as good a place as any to look at G forces. There are a lot of spikes in the graph (like you’d see in Aim Solo data), so imagine it’s more of a smooth arc.
- Starting at the bottom of the graph, notice that the car represented by the red line is pulling only 1.14 Gs. Recall that I gave all the tires the same 1.2g of grip, but because of aerodynamic lift, they are losing traction at speed. This is a normal situation for a street car or spec racer with no aero. What the simulation doesn’t show is that most of the grip is lost on the rear tires.
- The orange line is a car with a spoiler, which mostly cancels out lift. Lateral Gs are very close to the the static 1.2g value.
- The blue line has more than 1.29g grip because tire load is increased with downforce.
- The green line is even more dramatic, with 1.4G grip. This is significantly more grip than the car with no aero.
You might be wondering how an increase in lateral Gs plays out in speed through the corner, which is the next graph. I’ve chosen the same 16000′ spot on track to measure the speed, and you can see it’s a difference of almost 10 mph between fastest and slowest.
Turn 10 is a very fast corner, and you’d see a smaller delta on a slower corner, but this is still pretty remarkable. By increasing the load on the tires, tire grip went from 1.14 to 1.4 Gs, and the car with good aero went about 10 mph faster in the middle of the corner.
Downforce and tire wear
Most people imagine that aerodynamic downforce will make your tires wear out faster. More grip = more wear, right? No. Oddly, downforce makes tires last longer.
Tires wear by abrasion; from sliding or spinning. Have you ever flat spotted a tire? Then you know that sliding a tire can wear it out in a couple seconds! Aero increases the load on the tire, giving you more grip, which makes it less likely to spin or lock up.
Aerodynamic downforce also loads the tires more equally. When cornering, the outside tires get loaded more, as a normal byproduct of mechanical grip. However, aero loads are based only on air, and is balanced across the car, left to right, helping to balance the car better.
One could even imagine an active aero device that would split the wing in half and only load the inside tires. Or rudders or vanes that help the car turn using air alone, and use the tires even less.
But let’s jump back from fantasy land… in reality, you get more aerodynamic downforce from rear aero than front aero, and this helps a lot in braking zones, increasing rear load and rear grip. The same is true in acceleration, and more rear grip reduces tire wear (on rear wheel drive cars).
Another way aero increases tire life is when you drive under the limit of the tire. For example, take Turn 10 at Watkins Glen again. Miatas can usually go through at full speed or with a slight lift on entry, and that’s because there isn’t much of a straight between Turn 9 and Turn 10 and Miatas are dog slow. If you’re going through at 85 mph without aero and on the limit of traction, you’ll go through it with aero at the same speed, but well under the limit, and you’ll wear the tires less.
The uphill esses are another place where a Miata is flat out while cornering. You can’t ever reach the limit of lateral grip because the car can’t accelerate fast enough to get there. So you slip less and use less tire.
Now this isn’t going to be true at every race track, most of the time when you have a higher limit, you fuggin use all of it. But sometimes there’s a corner or two where aero now puts you under the limit, and in a long endurance race, this can be the difference between changing tires mid race, or simply saving money. The point being, aerodynamic downforce can make your tires last longer if it keeps your car from sliding.
A good real-world example is the 2000-2002 Corvette SCCA cars, which went from a 315 rear tire in 2000 to a 275 tire in 2001. To increase grip, a rear wing was added in 2001, but it wasn’t enough and tires would only last about 4 laps before starting to go off. After optimizing the aero in a wind tunnel to create more downforce, the same tires in 2002 would last an entire race.
Aerodynamic balance
At this point I’ve only looked at how aerodynamic downforce affects grip and longevity due to increased tire load. But there are other aero factors at play that are important.
Earlier in this way too long blog post, I by mentioned that cars without aero lose rear grip from lift and yaw. In truth, the car loses both front and rear grip, but it loses more rear grip. As a consequence, as the car goes faster, it transitions more and more to oversteer. Most people find this an unsettling situation.
Personally, I don’t mind if a car oversteers at low speed, in fact, I like it. But if it does that at high speed, it scares the shit out of me. Ideally, I like a car that rotates easily at low speed and then transitions to understeer at high speed. This is ridiculously easy to do: add a big wing, and then tune the amount of understeer by adding or removing wing angle.
This is the magic of dynamically balancing the load on your tires using downforce. It’s so easy, and it’s so tunable. However, rear wings and end plates also increase stability by increasing the static margin.
Static margin is the distance between the center of gravity and the center of pressure. Anything that adds rear drag increases the static margin, sort of like streamers on a kite tail. In addition, horizontal areas on the back off your car, like big end plates, shark fins, or even bodywork like a hatchback or station wagon, increases the static margin through sideways resistance to air.
A greater static margin makes the car harder to turn, but also makes the car more stable. When a car goes over the limit of grip, the driver must make steering corrections. Cars that have a higher static margin require fewer steering corrections to bring the car back into line, which is easier on the driver. This also ends up being easier on the tires, and can make the car faster, if a bit less exciting to drive.
Conclusions
Tire grip is arguably the most important factor on a race car. Understanding how tires make grip is therefore one of the most important things a racing driver needs to know. Aerodynamic downforce can greatly influence the balance and grip of the tires at different speeds, and can be used for tuning the car’s handling and ultimately make the car turn faster lap times, and/or stay on track for a longer duration.
Occam's Racer 