1. MAE 494/598 Group 3: Fabian Gadau Lucas Jaramillo Myrtle Lin Bryce Thompson Racetrack Optimization

2. MAE 494/598 Introduction Objective – Optimize driving path and vehicle inputs for a given racetrack in order to minimize the given vehicle’s lap time. Spring 2015Prof. Max Yi Ren2

3. MAE 494/598 Subsystem Flow Chart Spring 2015Prof. Max Yi Ren3

4. MAE 494/598 Track Geometry Spring 2015Prof. Max Yi Ren4

5. MAE 494/598 Track Geometry Spring 2015Prof. Max Yi Ren5 Process: Found a Local Track Scaled the track Gathered Points Cubic Spline Interpolation – Match first and second derivatives with the first and last data point Created gates – λ Lower =0 – λ Upper =1 Initial guess: – Center of the Track λ =0.5 Constraints: Lower bounds Upper bounds Optimization: Gradient Method Armijo Lineseach

6. MAE 494/598 Tire Model Spring 2015Prof. Max Yi Ren6

7. MAE 494/598 Tire Model Objective​ – Relate tire pressure and vehicle speeds to frictional coefficients between the tire and the pavement. ​ – Optimize tire pressure to produce fastest lap times.​ Method​ – Meta Model​ Data from US Department of Transportation​ Goodyear Eagle LS tires​ Constraints​ – 17 psi ≤ Pressure ≤ 35 psi​ – 0 mph ≤ Velocity ≤ Max velocity of engine​ Spring 2015Prof. Max Yi Ren7

8. MAE 494/598 Vehicle Dynamics Spring 2015Prof. Max Yi Ren8

9. MAE 494/598 Vehicle Dynamics Objective​ – To optimize the suspension spring rate to provide an ideal engine power to traction relation for the given projectile path and velocity​ Assumptions​ – Lumped System​ Body roll modeled as a mass/spring system​ – Simplified Physical Tire Analysis​ No heating/cooling effects​ Constant contact area​ No “slip area”​ – Simplified Suspension System​ Instantaneous Damping​ No internal oil viscosity compression effects​ No fluid heating/expansion (causing a change in stiffness)​ Variables​ – Suspension Spring Stiffness [k]​ Constraints​ – Lateral tire friction​ – Powertrain delivery output Spring 2015Prof. Max Yi Ren9

10. MAE 494/598 Powertrain Spring 2015Prof. Max Yi Ren10

11. MAE 494/598 Powertrain Decision Model Objective​ – To optimize driving decision such as the timing of gear shifts, throttle position and break position to reduce the time in takes for a 2010 Subaru Sti with a Cobb Stage II tuning kit​ Assumptions​ – State Dependent​ Actions to be taken based on the previous time step’s values.​ Actions are limited either by traction in corners, or how quickly the engine can accelerate ​ Variables​ – Gear, throttle position, brake position​ Constraints​ – Velocity constraints based on track geometry​ – Motor limited to 7000 RPM​ – First 4 Gears of Gearbox​ – How quickly RPMs increase Spring 2015Prof. Max Yi Ren11

12. MAE 494/598 Results Simplified Model of a track to Validate Results Results converge to – 62.6 s (IG outside of Track) – 64.3 s (IG inside of Track) Can sample only realistic racing lines Spring 2015Prof. Max Yi Ren12 Iteration Number Lap Time Optimization Results x (m) y (m) Sampled Racing Lines

13. MAE 494/598 Path is on expected ideal racing line Either at Full Throttle, shifting gears, or limited by vehicle dynamics 2 known local solutions – Ideal locations for overtaking in a racing situation Usually bounded by either track geometry or powertrain – shown by 100% or 0% in most driving scenarios Results Spring 2015Prof. Max Yi Ren13 x (m) y (m) Percent of Track Completed Velocity(mph)/ Gear *10/ Throttle Position (%) VD + Powertrain Results Path 1 Path 1 Result Path 2 Result x (m) y (m)

14. MAE 494/598 Further Work Bettering Product Make better models for physical systems Add 3 rd Dimensions to incorporate hills Add Aerodynamic Model Add diminishing tire performance Applications Racing Teams can compare driver inputs with ideal inputs during practice laps – Give precise feedback to increase performance – Simulate Lap before the race day Spring 2015Prof. Max Yi Ren14

15. MAE 494/598 Thank You! Questions? Spring 2015Prof. Max Yi Ren15