# Professional Motorsport Data Analysis: Traction & Drive Slip

## Traction & Drive Slip

### 08.39

00:00 | - In a perfect world in which tyres with unlimited amounts of grip existed, we'd all have as much horsepower as we wanted and a very heavy right foot. |

00:09 | But racing would probably be pretty boring. |

00:12 | In reality, most times when we're exiting the corner, we're going to be traction limited which simply means that the limiting factor for accelerating the car is how much drive force the tyres can supply. |

00:24 | Rather than the engine torque. |

00:26 | Ignoring the effect of aerodynamics on traction, the fundamental reason we're more traction limited in lower gears than higher gears is because in lower gears as the speed of rotation of the drive wheels is low, for a given engine power output we have relatively high torque output. |

00:44 | Propulsive force is simply a term for the force that the drive tyres are providing to accelerate the vehicle. |

00:51 | Which is a function of the torque available to the drive tyres and their effective driving radius. |

00:57 | Looking at this plot of propulsive force output from the tyres, we can see that as we move up the gears, the output speed of the wheels increases which comes with a necessary reduction in the force output. |

01:09 | This plot can be quite a useful way to think about many of the concepts involving traction. |

01:15 | When we add the effective downforce, and knowing that downforce generating from lifting surfaces is roughly proportional to the square of the road speed, we know that at low speed, we aren't going to gain much extra traction where we need it most. |

01:28 | We introduced the concept of slip ratio in the braking section. |

01:32 | All the same fundamentals that affect a tyre producing longitudinal force for braking also apply here for drive. |

01:40 | The main difference being the tyre torque is in the opposite direction. |

01:45 | Looking at the same longitudinal force vs slip ratio plot, we looked at in the braking section, we move from looking at a negative slip ratio to a positive slip ratio with positive slip ratio being the normal convention for drive. |

01:59 | It's worth keeping in mind that the slip ratio behaviour of a tyre isn't necessarily the same in drive as braking as the construction may not be symmetrical. |

02:09 | In the same way as braking, the optimum slip ratio is dependent on many other factors. |

02:14 | Vertical load, slip angle, camber angle, inflation pressure, temperatures and vehicle speed. |

02:22 | This plot is only valid for a single constant value of each of these parameters. |

02:27 | For cars that are only driving on one axle, we have the ability to estimate the slip ratio which is actually much simpler than doing so for braking. |

02:35 | As discussed in the braking section, the instrumentation to properly measure the slip ratio is usually prohibitive but in a car where we have 1 axle that is not driving, we can use the non driven axle as an approximation for the free rolling speed. |

02:50 | This means we have a reference by which we can estimate the slip ratio by comparing the wheel speeds of the driven vs non driving wheels. |

02:58 | The sensor layout on each car will determine the data we have available to calculate the slip ratio. |

03:04 | In the case where we'd only been measuring the wheel speed of undriven wheels, we can estimate the driven wheel speed by using the engine speed, gear ratios, final drive ratios and tyre radius. |

03:17 | Although this isn't preferable because there's a lot of scope for errors to creep in. |

03:22 | If we're measuring the speed of at least one driven and one undriven wheel, we can start to calculate things a little more accurately. |

03:29 | With that said, unless we have a spool rather than a differential, our accuracy will be limited by the slip in the differential. |

03:37 | The ideal is to be logging each wheel speed separately. |

03:40 | This gives us the best chance to estimate the slip as accurately as possible. |

03:44 | Not only does it remove some of the errors of calculating the slip from the differential, we can also account for the tyres taking different paths through a corner. |

03:53 | If we look at a car from above and plot the path of each wheel as the car follows an arc, it's clear that the inside and outside wheels are travelling different distances which in itself is the reason we make use of differentials. |

04:07 | This difference in speed is greatest in tighter corners so this effect will diminish in faster corners. |

04:13 | So to improve the estimation of slip, one way we can simply account for the wheels on each side of the car following different paths, is to compare each driven wheel speed with the wheel speed of the undriven wheel on the same side of the car. |

04:27 | With this method of estimating slip ratio, the formula looks like this. |

04:32 | We take the speed of the driven wheel and divide it by the speed of the undriven wheel then subtract one. |

04:39 | In the case where the car is accelerating, this will be a positive number, say the driving wheel has a speed of 110 km/h and the non driving wheel is rotating at 100 km/h. |

04:50 | Using this equation, this gives us a slip ratio of 0.1. |

04:54 | Going back and looking at our slip ratio plot, that puts us here which in the case of this specific tyre and in these conditions, is greater than the peak slip ratio. |

05:04 | This method is not perfect as there are a number of sources of error. |

05:09 | However, its' still a useful way of estimating the relative slip level we have in the tyre on drive by putting a number on it. |

05:16 | Here is an example of the calculation of slip ratio implemented inside our data project for the rear left wheel. |

05:23 | We only want to calculate the slip when we're on part throttle as the throttle ramp phase is the part where we're going to be most traction limited, so we're only looking at ranges between 5 and 95% throttle. |

05:36 | Obviously we only care about the parts of the track where the car is accelerating. |

05:41 | So we only look at points where the longitudinal acceleration is greater than 0. |

05:46 | We can then implement the calculation discussed earlier with the ratio of the wheel speeds which we have defined here. |

05:53 | Plotting this on a time distance plot straight away we can see the points where the slip ratio is high. |

05:59 | If your analysis software has the ability, you can also add in some reference lines to help gauge the magnitude of the slip. |

06:06 | Here I have one added in at 0.05 or 5% to help me see where I'm exceeding that. |

06:13 | If we now add in the longitudinal acceleration into the same plot, we start to see something interesting about the traction force. |

06:20 | Zooming into an area where heavy acceleration is taking place, out of a slow corner, we can see that the longitudinal acceleration is dropping off here. |

06:29 | Looking at the throttle, we can see it's continuously increasing and the gear position is constant so there's no gear change taking place. |

06:38 | So this is telling us that the drive force is dropping away for another reason. |

06:42 | This is likely the tyre exceeding the peak slip ratio and beginning to flare up into wheel spin. |

06:49 | We can also visualise this in another way by using a scatter plot to plot longitudinal acceleration against the new slip ratio channel. |

06:56 | Note that the axes are limited to only showing positive values of acceleration and slip ratio. |

07:03 | Looking at the same part of the data as we did before, we can see some interesting behaviour that looks a lot like the theoretical slip ratio curve we showed earlier. |

07:12 | Looking at these side by side we can see the linear region of the slip ratio building, followed by a clear peak and a drop off as the slip ratio continues to increase. |

07:23 | In this loading condition, the peak slip ratio for this tyre is around 0.04 or 4% slip. |

07:30 | Notice that the features of the logged data follow the theoretical behaviour we looked at earlier. |

07:38 | This is a relatively small amount of slip for the tyre to be breaking away at but bearing in mind this tyre is not loaded purely longitudinally. |

07:45 | There is also a lateral component of force as the car is exiting a corner which has the effect of reducing the longitudinal compliance of the tyre. |

07:55 | Everything we've looked at with the longitudinal traction of the tyre so far has been for reviewing the logged data post session. |

08:02 | Having a logger that's capable of calculating math in real time gives us the option to display information like wheel slip to the driver while inside the car. |

08:11 | Every car and driver combination will have a different sensitivity to picking up wheel slip in drive by making use of a set of lights to indicate drive slip can be helpful. |

08:21 | Typically these would be set up in 2 or 3 stages to indicate the magnitude of the slip. |

08:27 | This is particularly useful in any situation where looking after the driven tyres to extend their life over a full stint or race is required. |