Using Dymola to understand the 2018 Indy 500

To the uninitiated, the Indy 500 seems like a simple event. 200 laps (500 miles) around the Indianapolis Motor Speedway, a 2.5 mile long banked oval circuit using single-seater, open wheel IndyCars. Sounds simple enough, doesn’t it?

Well… it isn’t. As with any top level Motorsport, drivers straddle the edge of adhesion, 4 rubber tyres preventing a hard, 220+ mph rendezvous with the outside retaining wall. Cars trimmed of downforce to be as quick through the air as possible. No large tarmac run-off areas to be found on an oval. It’s a colossal challenge, easily earning the moniker “The greatest spectacle in racing”.

In 2018, the annual instalment of the Indy 500 was marked by a usually high number of crashes. Whilst it is expected that some drivers will exceed the physical limit during the heat of competition, crashing accordingly, last year featured 6 separate single car incidents. Notable drivers such as Danica Patrick, Ed Jones and JR Hildebrand, former F1 driver/ChampCar champion Sebastian Bourdais and former Indy 500 winners Tony Kanaan and Helio Castroneves all found the wall in single car incidents where they lost control of their machines in similar instances.

The talk after the event often surrounded the near record race-day temperatures of 91F/32.8C. But what effect did that have on the cars themselves? I decided to investigate using Dymola and the Claytex VeSyMA suite (VeSyMA – Suspensions and VeSyMA – Motorsports).

Building a track and vehicle model

To build a representative simulation, some form of data is required. I was lucky enough to stumble upon an article written in the lead up to the 2018 race, detailing the challenges the Indy 500 competitor faces from the cockpit. It came complete with the following data picture:

A data sheet from 2018 Indy 500 practice. Image: Marshall Pruett/Andretti Autosport.
A data sheet from 2018 Indy 500 practice. Image: Marshall Pruett/Andretti Autosport.

Containing longitudinal and lateral acceleration, gear, velocity, steering and throttle traces from a single, this sheet enabled me to build a reasonably representative simulation of an Indy 500 lap, utilising the IndyCar example vehicle model found in the VeSyMA – Motorsport library. A free MatLab tool known as GRABIT was used to harvest data representations from the traces in the figure. Whilst this example is not accurate enough for a qualitative judgement, we can still use it to highlight interesting trends and observe some effects.

Specifically for track generation, the lateral acceleration and longitudinal velocity traces were of immediate interest, as they can be used to calculate the radius of curvature of the vehicle path.

The radius of curvature equation
The radius of curvature equation

Using the radius of curvature, which is an inverse of the cornering radius of the vehicle, a road model from the actual line taken by the vehicle can be generated. This is using the Suspensions.Roads.RoadBuildingFunctions.RoadFromCurvature road building function. An option to include the banking angle is present in the function. If the data sheet above also contained the vertical acceleration, then this could be used to calculate the banking angle the vehicle experienced using the Suspensions.Roads.Functions.GPS.CalculateBankingAngle function. This function is presented in an academic paper previously published by Claytex.

Alas, the data sheet does not include vertical acceleration, therefore for the purposes of this blog post I estimated the banking angle around the turns. I assumed the banking was at the peak of 9 degrees at the middle of the turn, decaying to 0 degrees by the entry/exit. Corner apex, entry and exit points were estimated from the lateral acceleration trace.

The IndyCar example model traversing the track model of the Indianapolis Motor Speedway created from the datasheet presented above

By default, the setup the IndyCar example model found in the VeSyMA – Motorsports library is equipped with a road course style setup. Given the extra aerodynamic drag from the larger road course wings, the car struggles to get close to the high speeds of a lap of the Indy 500. With a velocity and throttle position trace, I adapted the vehicle setup (reducing the downforce and drag) and modified the driver model to read a throttle position defined by distance. A fixed rear differential (spool) was also used. Steering control is closed loop, keeping the car on the racing line, with an open loop throttle. This was simple to do, duplicating the VeSyMA.Drivers.TestDrivingControl.SingleDistanceTime block and replacing the acceleratorSourceModel with a Claytex.Blocks.Tables.Lookup1D model and picking up the variable sLap, which is the distance travelled around the lap from the sensedState expandable connector. This resulted in the following speed trace:

Ballpark validation of the vehicle model, after tweaking the aero, mass and tyre models. Not accurate enough to make quantitative judgements (the vehicle setup is a guess!), we can still look at the effect of environmental changes.
Ballpark validation of the vehicle model, after tweaking the aero, mass and tyre models. Not accurate enough to make quantitative judgements (the vehicle setup is a guess!), we can still look at the effect of environmental changes.

Some like it hot…

The 2018 Indy 500 was the hottest in recent memory. Race cars, being the thoroughbred machines that they are, are very sensitive to temperature changes and fluctuations. Heat, humidity, and air pressure all effect performance of the vehicle. So, if we vary the atmospheric parameters of the experiment, what effect will that have on the vehicle?

The “Cold – baseline” results correspond to the validation/setup conditions of this vehicle, namely 20C ambient temperature, 1.013 bar atmospheric pressure and relative 50% humidity. The “Hot” results were with the same vehicle with a “32.8C ambient temperature, 0.982 bar atmospheric pressure and 40% relative humidity, which approximately correspond to the 2018 race day conditions. To account for track temperature changes (which the road does not model) and the effect a hot day has on them, I also reduced the mue value of the road in the hot conditions.

Longitudinal speed trace comparison for the two track conditions. Note the lack of apex speed in the corners.

Longitudinal speed trace comparison for the two track conditions. Note the lack of apex speed in the corners.
As the driver model parameterisation was not changed, we can conclude from the higher steering wheel angles that the vehicle was understeering or "pushing" more in the hot, slick track scenario.
As the driver model parameterisation was not changed, we can conclude from the higher steering wheel angles that the vehicle was understeering or “pushing” more in the hot, slick track scenario.

As we can see, the vehicle is now losing a lot more speed in the centre of the corner, whilst the driver is having to turn the steering wheel to a higher angle to maintain the same line. Such a high front wheel angle is reducing the speed of the vehicle through excessive scrub of the front tyres.

Steering angle peaks in the opposite direction as the vehicle enters the corner; this is the driver moving the car closer to the outside wall in order to get a better turn in angle. Such a peak on the exit of the corner is likely to be due to the estimated banking transition not being exactly correct. Open loop throttle control was kept for both the cold and the hot experiments, so the effect of the environmental changes could be observed without influence from changing the throttle input.

Yaw rate comparison between track conditions. Note the high peak values (both negative and positive). Despite understeering more, the car as a system is more unstable now.
Yaw rate comparison between track conditions. Note the high peak values (both negative and positive). Despite understeering more, the car as a system is more unstable now.

Interestingly, the vehicle is showing greater peak values of yaw rate. Instinctively, this tells us that the vehicle is more unstable in yaw, due to the overall reduction in grip. As the car is biased to understeer, this would present the driver with the issue of trying to get the car to have a more positive front end, whilst dealing with a rear end which is less stuck than before.

Clearly then, we can appreciate the challenge drivers faced in the Indy 500 last year, with vehicles tuned during the month of May under conditions non-representative of race day.

Written by: Theodor Ensbury – Project Engineer

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