Aerodynamics Fundamentals: Aerodynamic Force Effects on the Tyres
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Aerodynamic Force Effects on the Tyres
06.28
| 00:00 | Before we jump into this module, as we mentioned in the introduction section, this is the point in the course at which we will start introducing some basic mathematics. |
| 00:08 | So, just to reiterate, although it's great to have this deeper understanding of what's going on, don't get too caught up in the maths. |
| 00:15 | If it flies right over your head, it's not going to stop you developing an effective aero package for your car. |
| 00:21 | So, we've now established that you can generate aerodynamic forces by manipulating the airflow around a car. |
| 00:27 | But what do these forces actually do? Despite all the complexity of a modern race car, fundamentally the only thing that makes it accelerate, brake and corner the way it does is the coupling between the tyres and the ground, and the force from the tyre contact patches. |
| 00:44 | There are smaller influences from things like exhaust flow, cooling fans and other aerodynamic forces, but these are generally speaking significantly smaller contri, butions to car performance than the grip at the tyres. |
| 00:56 | A tyre fundamentally generates its force through friction with the ground. |
| 01:00 | There are other, more complex mechanisms at work here, but that's a big rabbit hole to go down and well beyond the scope of this course. |
| 01:08 | If you're interested in learning more, check out High Performance Academy's Suspension Tuning and Optimization. |
| 01:13 | At the most basic level though, we can model friction as a linear relationship between the force applied perpendicular between two surfaces, referred to as the normal force, and what's known as the coefficient of friction. |
| 01:27 | The coefficient of friction, which I will refer to as the Greek letter mu from here on out, is dependent on the two surfaces interacting. |
| 01:34 | For example, steel on steel like a train wheel could be mu 0.5, while a street tyre on asphalt may be closer to 0.9, and higher end race tyres can be closer to 1.5. |
| 01:47 | The mu is largely determined by interactions between the roughness of the two surfaces and a traction on a molecular level. |
| 01:55 | Mu is slightly non-linear in that at higher normal loadings, the mu will typically decrease, essentially it drops away as vertical load on the tyre is increased. |
| 02:04 | So, that means that if we double the vertical load, we don't quite double the grip. |
| 02:08 | For a given tyre and track surface, there's not a whole lot we can do to change the mu. |
| 02:13 | Suspension tuning, weight reduction and weight transfer management can make small improvements, but you won't see that number change by a huge amount. |
| 02:21 | So, if we have well optimized suspension and we want more grip at the tyres, the only way to do this is to add more normal force. |
| 02:29 | If we explore the most obvious way to add more normal force, which is to increase the mass of the car, we immediately run into a problem. |
| 02:37 | Exploring the case of the car taking the corner, it will need to have lateral force turning into the corner of Fc equals mv squared on R, where Fc is what's known as the centripetal force, or the force pulling the car into the centre of the corner, m is the mass, v is the velocity and R is the corner radius. |
| 02:56 | If we rearrange this equation to find the minimum velocity we can take a corner at, it's v equals the square root of Fc multiplied by R divided by m. |
| 03:07 | Now, Fc is effectively defined by the lateral force available from the tyres, which as we discussed earlier is Fr equals mu multiplied by n. |
| 03:19 | If we sum all four tyres together, n on our tyres is going to be the mass of the car times gravity, mass times gravity, m times g. |
| 03:29 | Here lies the problem. |
| 03:31 | The grip force Fc is proportional to m, but the expression within that square root side is divided by the mass m. |
| 03:41 | This gives us an equation of v equals square root mu multiplied by g multiplied by R. |
| 03:48 | So, if we just add mass to the car, the grip available increases, but the tyres have to work harder to turn the car, so you haven't gained anything. |
| 03:57 | And of course, in the real world, as mentioned before, the mu will decrease as the mass increases, this is actually going to make you slower through the corner. |
| 04:07 | So, let's now consider adding force on the tyres through a massless force, which is what we can achieve using aerodynamics. |
| 04:15 | This provides force on the car, but doesn't increase the mass of the car in any way. |
| 04:21 | I'm going to call the aerodynamic vertical force down on the car Fz aero, which is more commonly known as downforce. |
| 04:29 | This is using the FIA standard car convention, which is x is along the car, y is across the car and z is vertical. |
| 04:37 | So, F means force, z means vertical and aero is just the aerodynamics. |
| 04:43 | Assuming a constant mu, our grip force available at the tyres now becomes Fr equals mu multiplied by in brackets m times g plus Fz aero, where we now have the vertical force contribution from the mass of the vehicle as well as the vertical force contribution from the aero multiplied by the mu. |
| 05:04 | Substituting this back into our old equation, we can see that V equals the square root of brackets mu multiplied by brackets m times g plus Fz aero brackets multiplied by r divided by m, which is quite a mouthful. |
| 05:21 | But basically, any vertical force we add to the tyre without adding mass to the car will increase our velocity through a fixed corner radius. |
| 05:30 | And this is obviously the advantage of adding downforce, or Fz to a car. |
| 05:35 | It gives you more grip and allows you to corner at faster velocities. |
| 05:39 | Now, while I've used cornering for this example, the same principles apply to accelerating or braking. |
| 05:44 | If we have more friction force available at the tyre without increasing the car mass, we'll improve our available braking and acceleration. |
| 05:53 | To summarise the main takeaways of what we've covered here, aerodynamic forces can increase a car's grip without adding mass, which allows for better acceleration, braking and cornering. |
| 06:04 | The key factors in cornering speeds is the coefficient of friction mu between the tyres and the ground, which is largely determined by surface interactions, and the vertical force applied to the tyre. |
| 06:15 | By adding downforce, a vertical aerodynamic force, the car's tyres generate more grip, allowing for faster cornering without the drawbacks of increased mass. |
