MAE 494598 Racetrack Optimization Group 3 Fabian Gadau

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

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

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

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

Track Geometry 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 Spring 2015 MAE 494/598 • Created gates – λLower =0 – λUpper =1 • Initial guess: – Center of the Track • λ =0. 5 Prof. Max Yi Ren Constraints: • Lower bounds • Upper bounds Optimization: • Gradient Method • Armijo Lineseach 5

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

Tire Model MAE 494/598 • 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 2015 Prof. Max Yi Ren 7

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

Vehicle Dynamics • MAE 494/598 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 2015 Prof. Max Yi Ren 9

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

Powertrain Decision Model MAE 494/598 • 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 – – Spring 2015 Velocity constraints based on track geometry Motor limited to 7000 RPM First 4 Gears of Gearbox How quickly RPMs increase Prof. Max Yi Ren 11

Results MAE 494/598 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 Optimization Results y (m) Lap Time Sampled Racing Lines Iteration Number x (m) Spring 2015 Prof. Max Yi Ren 12

Results • VD + Powertrain Results Path 1 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 y (m) Spring 2015 Percent of Track Completed Path 1 Result y (m) Path 2 Result Velocity(mph)/ Gear *10/ Throttle Position (%) • • MAE 494/598 x (m) Prof. Max Yi Ren x (m) 13

Further Work MAE 494/598 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 2015 Prof. Max Yi Ren 14

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