# Professional Motorsport Data Analysis: Suspension Stiffness & Balance

## Suspension Stiffness & Balance

### 16.38

00:00 | - So far in this section, we've mainly talked about analysing drivers during cornering. |

00:05 | But if we have damper position data available, this opens up some more opportunities to understand how the chassis is behaving. |

00:13 | Which itself obviously has a large impact on the balance of the car. |

00:18 | One way we can use the damper positions is we can estimate the roll angle of the chassis using the difference in the displacements of each damper. |

00:27 | To be clear, in the examples we're going to go through in this module, we're not going to include the vertical deflection of the tyres in the roll angle calculation. |

00:36 | This is because adequately modifying the loaded radius of the tyres, takes quite a lot of work. |

00:42 | And as long as you're running on the same tyres all the time, this can be reasonably ignored while still being able to make use of the simplified calculations. |

00:51 | This means we're only considering the roll angle of the sprung mass with respect to the unsprung mass which is another way of saying the roll angle of the chassis with respect to the suspension. |

01:02 | Looking at the data without considering the tyre deflection can still be very useful. |

01:08 | We just need to keep it in mind by remembering that we're not calculating the absolute roll angles with respect to the road surface. |

01:16 | In this diagram we can see the different contributions to roll that I'm talking about. |

01:20 | When the car is cornering, the sprung mass will roll, which we can see here. |

01:25 | Because the tyres are flexible, their loaded height also changes during cornering as shown here. |

01:32 | This vertical deflection of the tyres is what we're ignoring. |

01:36 | There are a few pieces of information that we need before we can calculate the roll angle. |

01:41 | First we need the track width of each axle of the car and also the motion ratio between the wheel and damper for each end of the car. |

01:51 | Which we already discussed the calculation of in the advanced sensor section. |

01:55 | The standard way to define the track width is the distance between the centre of the tyre contact patch with the car at rest. |

02:02 | We do this for the front and rear axles separately as they're usually different. |

02:07 | We need the motion ratio to convert between damper position and wheel position. |

02:12 | Because in this case we're interested in the position of the wheel rather than the damper itself. |

02:18 | As you'll hopefully remember from the advanced sensors section, the definition of the motion ratio is the amount of wheel movement relative to the amount of damper movement. |

02:28 | Now that we have all the basic information we need, here's how we'll use these values to define roll angle for each end of the car separately. |

02:37 | We're interested in the difference in wheel position from one side to the other. |

02:41 | Looking from the front of the car, we can simplify the roll of the sprung mass into a simple triangle and use Pythagoras to solve for the roll angle which we'll do with a math channel. |

02:52 | As we can see in the diagram, we use the difference in vertical displacement of each wheel as the height of the vertical part of the triangle and we use the track width as the horizontal part of the triangle. |

03:03 | Now, Pythagoras can be used to solve for the roll angle of the sprung mass. |

03:07 | This is done using this expression. |

03:10 | We take the difference in wheel position and divide this by the track width. |

03:13 | Taking the arc tangent of this, gives us the roll angle. |

03:17 | And this needs to be done for the front and rear of the car separately. |

03:21 | There's an intermediate step we need to take in order to make this method of roll calculation useful. |

03:27 | As we're using the difference between the wheel positions and therefore the damper position, it's important we know the values of each damper position when the car has no roll angle. |

03:37 | There are a number of different approaches here, one of which is that we can zero the damper potentiometers when the car is on the flat patch during setup. |

03:46 | An issue with this that needs to be considered is that the changes in static ride height or different weight distribution throughout the day, save from fuel loads, can give you an offset in the roll calculation if both sides aren't changed by the same amount. |

04:00 | There are a number of different ways this can be accounted for but one is to calculate the average position of each damper when the car is travelling in the pit lane. |

04:09 | Assuming that the pit lane is level, and then use this as the reference position. |

04:15 | Using this reference position we can then employ a similar method that was used in the advanced math channels module for finding the steering offset. |

04:23 | Using this offset we can create a corrected damper position channel from which we'll do all of our roll angle calculations. |

04:32 | Using this method of virtually zeroing the car using the date from each outing, means that any suspension changes are automatically accounted for. |

04:41 | The first step is to identify when the car is in the pit lane. |

04:44 | There are plenty of ways you can do this and if you have a pit limiter, you can easily use this to trigger the condition. |

04:51 | But in this case, I'm assuming there is no pit limiter. |

04:54 | So the condition I'm using are, the speed must be greater than 38 km/h but less than 40 km/h and the absolute values of longitudinal and lateral accelerations must be less than 0.05G. |

05:09 | You should use whatever combinations of conditions make sense for your application. |

05:13 | The important thing is that we're trying to capture the points in the pit lane when the car is travelling steadily. |

05:19 | When these conditions are met, this channel will be equal to 1. |

05:23 | The offset value to virtually zero each damper is calculated by taking the average of all damper position values when our steady state pit lane condition is true. |

05:34 | Now we can define the corrected damper position channel. |

05:38 | The exact way we implement this channel will depend on the direction of our damper position data. |

05:43 | Regardless, the end result we're looking for is an offset of the raw logged damper position value so that is approximately zero when the car is at rest on all 4 corners. |

05:54 | In the case of this data, I'm subtraacting the damper position offset value from the raw logged damper position channel. |

06:01 | Now if we look at these channels on a plot, you can see that we have values approximately equal to zero when the car is in the pit lane, which is exactly what we want. |

06:11 | These values will never be perfect but all we're looking for is a decent approximation. |

06:17 | Now that we have the corrected damper position channels, we can calculate the difference between each wheel position with more confidence. |

06:24 | The calculation for the front roll angle is implemented as a math channel here. |

06:28 | Note that the output expression is in terms of radians. |

06:31 | And we'd normally want to look at this in degrees. |

06:34 | The output units of the channel can easily be changed like we have here to display the result in degrees. |

06:42 | Finally we can plot the front and rear roll angle data. |

06:46 | Looking at our new roll angle channels along with the speed and steering channels, we can see the chassis roll in and out of each corner as you'd expect. |

06:55 | Now we have a way to calculate the roll angle for each end of the car which can be used for a number of things. |

07:01 | WIth this, we can start to do some really useful calculations to understand the setup and balance of the car. |

07:08 | One way this can be done is by using the roll angle to calculate the roll gradient for each axle. |

07:13 | The roll gradient is defined as the amount of chassis roll per unit lateral G force. |

07:18 | Which is calculated simply by dividing the roll channel by the lateral G channel. |

07:24 | The reason this is useful is that the roll gradient can tell us something about the relative weight transfer that's occurring at each end of the car. |

07:32 | Looking at the calculation for roll gradient, we can see that a higher value of roll angle for a given amount of lateral G results in a higher value of roll gradient. |

07:41 | Just considering the elastic component effects on body roll, meaning springs and anti roll bars for example, we know that softer suspension results in more chassis roll. |

07:52 | So a higher roll gradient means a softer suspension and roll. |

07:56 | One common tool that's used to change the steady state weight transfer distribution are the elastic elements. |

08:02 | Most commonly the springs and anti roll bars. |

08:06 | Getting into the meat of calculating the effects of changing these elements properly is outside the scope of this course but by using the concept of roll gradient, we can come at it from the opposite direction by measuring the resultant deflection and therefore the stiffness we're actually getting on track as opposed to calculating them theoretically. |

08:26 | What's important in understanding chassis balance when looking at the effect of the elastic parts of a suspension system, is the relative stiffness between the front and rear axles. |

08:37 | By comparing the front and rear roll gradients, we have an extremely useful tool for tracking and understanding changes to our springs, anti roll bars and suspension geometry. |

08:48 | And in turn seeing how they are affecting our car. |

08:51 | What we're interested in at the end of this is the amount of weight transfer happening at the front of the car relative to the rear and how this changes with different setups. |

09:01 | Simply because this is the dominant factor in determining the mechanical balance of the car. |

09:06 | This is not an absolute measurement, we're tracking differences, not absolutes, the stiffer one end of hte car is, the higher the proportion of elastic weight transfer is happening at that end of the car. |

09:19 | By calculating the roll gradients, we're able to get a global overview of how our front suspension is behaving relative to the rear with respect to weight transfer. |

09:28 | One way to visualise the roll gradient is to plot the lateral G force vs roll angle on a scatter plot as shown here. |

09:36 | We can see a clear pattern with the points showing a close to linear relationship, the gradient or slop of this relationship is the roll gradient. |

09:45 | To calculate the roll gradient at each end of the car, we simply need to divide the roll angle for each end of the car by the lateral G force. |

09:53 | Plotting the roll gradients on a time/distance plot next to the scatter plot for each end of the car individually can also be useful. |

10:01 | Here in this example, I'm doing to dig into some of the roll gradient data, just having a look at a specific point on track between two different setups we ran on the same car within the same session. |

10:13 | Looking here on my laptop screen I've got a couple of different pieces to this layout, I've got a time/distance plot on the left hand side and I've got an XY plot in the right hand side. |

10:20 | In the time/distance plot it is simply steering angle, this is the chassis roll angle and the roll gradient plotted over distance and on the XY plot I've just got chassis roll angle vs lateral acceleration. |

10:32 | Now the combination of looking at the lateral acceleration vs the roll angle, that's essentially giving us a graphical representation or a different graphical representation vs the time/distance plot looking at that roll gradient. |

10:44 | So we know that when the roll gradient number is higher that's indicating a softer suspension and roll. |

10:51 | That's because we're getting more degrees of roll for a given amount of G force. |

10:55 | Here we've got 2 different setups plotted against each other. |

10:57 | So you can see here by looking at the legend in the roll gradient plot, we'll look at the time/distance to start with. |

11:05 | You can see that while the front roll gradients are really similar, 0.33 to 0.34, we've got quite a big difference in the rear roll gradient, that's 0.31 vs 0.27. |

11:14 | So what' going on there is that we've fitted a stiffer rear anti roll bar in this case quite a lot stiffer rear anti roll bar. |

11:22 | And that's what we're seeing as you can see that the front roll stiffnesses or the front roll gradients are almost sitting on top of each other but there's quite a bit offset in the rear here and that's coming from that difference in rear anti roll bar. |

11:35 | We actually see something really similar reflected in the XY plots here so if we look, we've got the front and the rear plots, we look at the rear, you can see that I've got this linear line of best fit running through them, that's just something that's automatically done by the software for us. |

11:50 | We can see here that that is a significantly lower gradient than what we've got in the first run which is the coloured run so the white run there is just showing quite a lot lower roll gradient. |

12:00 | So that's how the roll gradient will look when you've got quite a different elastic stiffness suspension at one end of the car. |

12:07 | One helpful way to visualise the roll gradients is by comparing the front to rear in terms of a ratio. |

12:14 | Giving us a way to measure the relative front to rear roll stiffness distribution. |

12:18 | In a simplified and theoretical case, only considering the elastic components of roll, a car with a 50/50 front to rear weight distribution and identical tyres front and rear, that's cornering in stead state on a skid pad, would need a front ro rear roll gradient ratio of approximately 50%. |

12:39 | Meaning that the front and rear suspension would have equivalent roll stiffness. |

12:44 | In pratice, taking into account the compliance in the chassis, suspension elements, tyres and suspension kinematics, even in a steady state case, the measured ratio will not be 50%. |

12:57 | The actual ratio number we measure is almost arbitrary and is specific to each car in kinematic arrangement. |

13:04 | It's a change in this roll gradient ratio from one setup to another than we're most interested in. |

13:10 | Over time, as you experiment with different setups, you'll tend to find a roll gradient ratio that works well for a given circuit and tyre. |

13:18 | Which is a very helpful reference to keep track of. |

13:21 | Here I've got the exact same data I looked at before when I was looking in terms of roll gradient and now I'm just looking at it in terms of roll gradient ratio. |

13:30 | The beauty of looking at something in terms of a ratio rather than the two individual values is it gives me a relatively measure between both of them so this just gives me one number to look at the stiffness distribution between the front and the rear axle. |

13:43 | So over here on my laptop screen I've got the exact same data I showed in the previous example. |

13:49 | Here I've just got this addition of the roll gradient ratio. |

13:52 | So that's just looking at the difference between the front and the rear roll gradients as a ratio. |

13:58 | Here I've got the white and the coloured data as shown before and now we know that the white data has a higher stiffness rear anti roll bar so we know we're going to get less roll per G in the rear axle, that means we're going to have more roll stiffness on the rear axle relative to what we see in the coloured data. |

14:17 | And with the way the maths works out because we're dividing the front roll gradient by the total roll gradient, that ends up with a higher number when we have a higher stiffness in the rear axle. |

14:28 | Now you can invert that, there's lots of different ways you can do that to make it make sense for you but the way we've got it making sense here is that a higher number is telling us that we have shifted the roll stiffness distribution towards the rear axle. |

14:40 | So we can see here the difference between them, let's pick a point somewhere, so we've got 54% vs 51%. |

14:47 | So having a 3% difference in roll gradient ratio is actually a really big shift, this was actually a big shift in roll stiffness. |

14:54 | This particular change was actually for a completely different anti roll bar fitted to the rear axle. |

15:00 | 3% is a big change but that just gives you an idea of what you'd expect to see in the difference in the roll gradients from making a different elastic change, either a spring or an anti roll bar on the car. |

15:09 | Now if you were to make a change in your spring or anti roll bar, you have a reference roll gradient ratio to aim for. |

15:16 | Let's take the example where we've decided to make a front spring change to increase the front spring rate because the splitter is touching the ground too much in a heavy braking zone.. |

15:27 | Because we've added stiffness to the front axle, and assuming we want to keep a similar balance to what we had before, we now need to account for this by reducing the stiffness of your front anti roll bar. |

15:37 | In a professional environment, we would have software tools to pre calculate any combination of components so we would know ahead of time which anti roll bar settings we needed. |

15:46 | In the situation where it's not an option to calculate this, which is the case in most amateur racing, this is where we can use our roll gradient ratio to find the right anti roll bar adjustment to match our new spring combination. |

16:00 | Even in the case where this was pre calculated the change would be validated using the roll gradient after the run by comparing the previous roll gradient to the one we have with our new settings. |

16:12 | There's plenty you can do with damper potentiometers to help in understanding how your suspension and chassis is working. |

16:18 | While this simple example is just scratching the surface of what's possible, hopefully it's something you feel confident to implement for yourself. |