Aerodynamics Fundamentals: Aerodynamic Coefficients & Effects
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Aerodynamic Coefficients & Effects
09.12
| 00:00 | We've discussed the concepts of downforce and drag, but now I want to introduce some terms that will help us with the quantification of these forces. |
| 00:08 | A force is essentially an influence that when applied to a body will cause it to accelerate, unless it's counted by other forces in the opposite direction. |
| 00:16 | Think of it like when we push our hand against a wall, we're applying force to the wall, and the wall is applying force back to us, so we don't accelerate. |
| 00:26 | If we apply a pushing force to a block and it slides away from us, it's accelerating as a result of the force that we've applied to it not being fully counterbalanced by the friction of the block against the ground. |
| 00:38 | If we hold an object in the air, Earth's gravity pulls it to the ground with a force proportional to the mass of the object. |
| 00:46 | The units used for forces are Newtons, which is the amount of force required to accelerate a one kilogram body at one meter per second per second. |
| 00:55 | The formula, which describes the relationship between force, mass, and acceleration is force equals mass multiplied by acceleration, F equals ma. |
| 01:06 | The strength of gravity is such that if we have a one kilogram block, gravity will attract it to the Earth with a strength of 9.81 Newtons down, and thus one kilogram force is 9.81 Newtons. |
| 01:18 | This will cause a one kilogram block to accelerate at 9.81 meters per second per second down to the Earth. |
| 01:27 | Similarly, a 100 kilogram block will have 981 Newtons of force applied to it due to gravity, accelerating a 100 kilo object, so will also accelerate at 9.81 meters per second per second. |
| 01:41 | The general rule for any aerodynamic force is that it will scale as a function of velocity squared. |
| 01:48 | So, if I have a wing that generates 100 Newtons of downforce at 50 meters per second, it will generate a force of 100 Newtons of force, multiplied by 50, multiplied by 50, times 100 multiplied by 100, equals 400 Newtons at 100 meters per second. |
| 02:08 | And if it was at 150 meters per second, it would be a hundred divided by 50 squared multiplied by 150 squared equals 900 Newtons. |
| 02:20 | Firstly, you'll notice my units. |
| 02:22 | Newtons and meters per second instead of mass in kilograms or pounds or speed in kilometers per hour or miles per hour. |
| 02:31 | Arrow doesn't like using strange units as we have to put conversion factors into a bunch of equations and it gets very messy very quickly. |
| 02:40 | It's much cleaner to stick with SI units, which is just an abbreviation for International System of Units. |
| 02:47 | To convert kilometers per hour to meters per second it's simple. |
| 02:50 | Divide by 3.6 to convert kilograms to Newtons multiplied by 9.81. |
| 02:56 | To convert pounds to kilos divide by 2.2. |
| 03:00 | Remember that 9.81 number for converting a kilogram of force to Newtons of force is the strength at which gravity pulls a one kilogram block towards the Earth's surface. |
| 03:10 | The second thing you'll notice is that quoting raw downforce numbers becomes quite meaningless. |
| 03:16 | If I say a car makes newtons, then that's true. |
| 03:18 | If I say a car makes newtons, then that's a newton. |
| 03:18 | 900N of downforce, it tells you very little about the car. |
| 03:22 | Was it 900N at 50m per second, or at 500m per second? This becomes even more complicated once we start bringing air density into the picture. |
| 03:32 | Density is a measure of how much mass an object contains within a certain space. |
| 03:37 | For example, if I have an 100mm cube of styrofoam, it will weigh significantly less than a 100mm cube of steel. |
| 03:45 | Air has density just like these solid objects. |
| 03:48 | However, as air is a gas, its density can vary quite significantly depending on factors like temperature and pressure, which we'll talk about more soon. |
| 03:57 | If the density of the air is higher, the force on any air surface is higher, and then we can start to ask the question of is that 900N of downforce from before at sea level, or on top of Pike's Peak? You can immediately see that we need a better number that can tell us all we need to know about air force on a car in a single axis, and this is what is known as an aerodynamic coefficient. |
| 04:21 | Before I demonstrate the coefficients, I want to remind you of our FIA axis system. |
| 04:27 | The x is along the car, with positive x being further rearwards, y is across the car, with positive to driver's right, and z is vertical, with positive being up. |
| 04:38 | With this in mind, let's consider a formula to get downforce, or downforce. |
| 04:42 | We know it's related to the square of the speed v, as before, and we also know it's related to the size of the device, as in, if we have the same wing, but scaled up to twice the size, it will make twice the downforce. |
| 04:57 | Let's call the surface area of that device s. |
| 05:01 | It's also related to the air density, which we'll use the Greek letter rho for. |
| 05:06 | When you do the maths and derive the equation, it comes out like this. |
| 05:10 | Fz equals a half times rho times v squared times s times cz. |
| 05:17 | I've introduced here the term cz, which we refer to as the coefficient of downforce. |
| 05:23 | This coefficient of downforce is how we characterise how much downforce a given aero package is producing. |
| 05:30 | Typically, when it comes to race cars, we're only interested in the overall coefficient of downforce. |
| 05:36 | We aren't going to be scaling the car up and down, so the value we're looking at is s multiplied by cz or scz. |
| 05:45 | Knowing this value will allow us to calculate the expected downforce on the car given a speed and an air density. |
| 05:53 | For example, if I have a car with scz equals to 2, and I want to see how much downforce it's going to make at 180km per hour with an air density of 1.225 kg per m3, what I first do is convert my speed into meters per second by dividing it by 3 .6, giving me 50. Meters per second. |
| 06:13 | I then plug it all into my equation. |
| 06:15 | A half times 1.225 times 50 squared times 2 equals 3062.5 newtons. |
| 06:26 | If we want to express this downforce as a mass in kilograms, which is probably a bit more meaningful for most people, we simply divide this by 9.81, which you will remember is the acceleration due to gravity that we discussed earlier. |
| 06:38 | This gives a downforce of 312 kilograms. |
| 06:43 | I can run this same calculation for different speeds or different air densities assuming the same aero package. |
| 06:50 | Drag is calculated exactly the same way, except instead of scz, we use scx, which is the drag coefficient. |
| 06:59 | You'll note I've changed the subscript from z to x. |
| 07:03 | This is because we changed the axis from z to x. |
| 07:07 | You may have also heard these terms referred to as CLA or CD. |
| 07:12 | It's the same number, but just with a different name. |
| 07:15 | Those numbers are commonly referred to as the lift and drag coefficients, respectively. |
| 07:20 | One hundredth of a coefficient is typically referred to as a point and 1 ,000th is referred to as a unit. |
| 07:27 | Now, that we've established the coefficients we can also work out power requirements for a given speed. |
| 07:33 | The drag force is given by a half times rho times v squared times scx. |
| 07:39 | And to get the theoretical power requirement, it's just going to be the force multiplied by the velocity. |
| 07:45 | So, it becomes power equals a half times rho times V cubed times SCX, which will output a power in watts using our standard units. |
| 07:56 | If we know the power at the wheels, we can estimate the top speed using this. |
| 08:02 | Rearranging my previous equation, we have V equals the cubed root of P over a half times rho times SCX. |
| 08:12 | This is only an approximate top speed due to inaccuracies in power measurement and measurement of other car and atmospheric parameters, but it should get us into the ballpark for our theoretical top speed, and will allow us to predict how our top speed will change as a result of air density and drag changes. |
| 08:32 | So, to briefly summarize what we've covered in this module, aerodynamic forces scale with the square of velocity, so the downforce and drag increase significantly as speed increases. |
| 08:43 | To quantify these forces effectively, we use aerodynamic coefficients, such as the downforce coefficient SCZ and the drag coefficient SCX, which account for factors like speed, air density, and surface area. |
| 08:58 | These coefficients allow calculations of the expected downforce or drag at different speeds, and can also be used to estimate power requirements and top speed for a vehicle. |
