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Professional Motorsport Data Analysis: Longitudinal Tyre Forces

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Longitudinal Tyre Forces


00:00 - Before we get into braking technique, we need to have a brief discussion about the basics of how longitudinal tyre grip works.
00:08 Tyres are in my opinion among the most complex parts of most racecars and as such, we'll only touch on some introductory aspects in this course.
00:18 While yes, you are still in the braking performance section of this course, many of these concepts apply to tyres generating force in either braking or acceleration.
00:27 Like most things on a car, the longitudinal force we get from the tyre is a function of many parameters.
00:35 Some of the basic ones relevant to our discussion are vertical load, slip ratio, slip angle, camber angle, inflation pressure, temperatures and vehicle speed.
00:46 Of these, the slip ratio is the one we have direct control over with the brake pedal.
00:51 And is one of the most dominant parameters in a tyre producing longitudinal forces.
00:56 When a tyre is loaded longitudinally, it generates a slip ratio.
01:01 One way to help visualise the slip ratio is to think about the tyre winding up, being twisted between the rim and the road.
01:08 We have a non zero slip ratio when the forward speed of the vehicle does not match the rotational speed of the tyre.
01:15 In the case of braking the tyre is rotating slower than it should be for a given vehicle speed.
01:21 This difference is taken up by distortion in the tyre both within the construction and the tread to road interface as the tread surface expands and contracts as it meets and leaves the road surface.
01:34 When a tyre is free rolling, then the slip ratio is equal to 0 and during braking, the slip ratio is negative.
01:42 Slip ratio is most often expressed as a ratio or pecentage.
01:47 For example, if the slip ratio is -0.1, this means that the tyre is rotating 10% slower than if it were free rolling.
01:55 It's important to emphasise that a slip ratio does not necessarily imply that the surface of the tyre is slipping or skidding on the road surface.
02:05 This slip is being taken up by tyre deformation rather than the surface of the tyre potentially slipping or skidding on the track surface.
02:14 Accurately calculating the actual slip ratio in braking is not practical for the level of instrumentation and logging we're discussing in this course but the important thing to understand about slip ratio in relation to braking is the concept rather than being able to actual calculate it properly.
02:31 To help illustrate, here is a typical plot of slip ratio vs longitudinal tyre force.
02:37 With slip ratio on the horizontal axis, and longitudinal force on the vertical axis.
02:43 A slip ratio of 0 indicates that the tyre is free rolling.
02:48 Starting from a free rolling condition, and moving to the left, we can see that initially as the magnitude of the slip ratio increases, the longitudinal force also increases quickly.
02:59 Then as the slip ratio continues to increase, the increase in force reduces until it peaks and the longitudinal force begins to drop off.
03:08 There are 3 distinct areas we can break this plot down into that are highlighted here.
03:12 The first is the linear range where the force increases linearly with the slip ratio.
03:17 The second is the transitional range and the third is the frictional range.
03:21 Because we can build braking force so quickly due to the nature of hydraulic brakes, we tend to move through the linear region quite quickly.
03:30 We get the peak force within the transitional range and this is the area we're aiming for at least in initial braking when the car is travelling in a straight line.
03:39 The frictional range is where we're using too much brake pressure which means we have too much slip ratio.
03:46 Causing the maximum longitudinal force we can create with the tyre to reduce.
03:50 This part of the plot is called the frictional area as this is the point where more and more of the tyre's contact patch is beginning to slip against the road surface because the construction and the tread are not able to deform any further.
04:04 If the slip ratio continues to increase, the entire contact patch will start to slip against the road surface.
04:11 At this point, the tyre is considered locked and the longitudinal force will drop off.
04:16 This plot is for a specific tyre at a specific vertical load, slip angle, camber, inflation pressure and speed.
04:25 As such, the exact slip ratio to aim for is different for every car and tyre combination as well as each part of the circuit.
04:34 However for modern tyres, the shape of this plot and general behaviour is always the same and it's helpful to keep in mind when discussing braking technique in the following section.

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