The Pennsylvania State University The Graduate School College of Engineering FORMULA 1 RACE CAR PERFORMANCE IMPROVEMENT BY OPTIMIZATION OF THE AERODYNAMIC RELATIONSHIP BETWEEN THE FRONT AND REAR WINGS A Thesis in Aerospace Engineering by Unmukt Rajeev Bhatnagar © 2014 Unmukt Rajeev Bhatnagar Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science December 2014 The thesis of Unmukt R. Bhatnagar was reviewed and approved* by the following: Mark D. Maughmer Professor of Aerospace Engineering Thesis Adviser Sven Schmitz Assistant Professor of Aerospace Engineering George A. Lesieutre Professor of Aerospace Engineering Head of the Department of Aerospace Engineering *Signatures are on file in the Graduate School ii Abstract The sport of Formula 1 (F1) has been a proving ground for race fanatics and engineers for more than half a century. With every driver wanting to go faster and beat the previous best time, research and innovation in engineering of the car is really essential. Although higher speeds are the main criterion for determining the Formula 1 car’s aerodynamic setup, post the San Marino Grand Prix of 1994, the engineering research and development has also targeted for driver’s safety. The governing body of Formula 1, i.e. Fédération Internationale de l'Automobile (FIA) has made significant rule changes since this time, primarily targeting car safety and speed. Aerodynamic performance of a F1 car is currently one of the vital aspects of performance gain, as marginal gains are obtained due to engine and mechanical changes to the car. Thus, it has become the key to success in this sport, resulting in teams spending millions of dollars on research and development in this sector each year. Although F1 car aerodynamics is at a highly advanced stage, there is always potential for further development. With the under-body aerodynamics banned by the FIA, the only significant changes that can be made to improve the aerodynamic performance of the car are by modifying the front and rear wings cross-sections, i.e. airfoils, or by developing new diffuser to modify the air flow underneath the car. Airfoil design is one of the important factors to consider while designing the car. Design of the most optimum airfoils is track-dependent, as each track has different aerodynamic requirements. The development of the F1 car is regulated by the rules sanctioned by the FIA. In recent years, the FIA has reduced the allowable operational hours for development at the wind-tunnel by a F1 team. From the 2015 season onwards, use of Computational Fluid Dynamics (CFD) software for the development of the F1 car is also being limited. This rule change will result in limited test-runs every season. This study, thus, focuses to provide a preliminary estimate of the most optimum aerodynamic loads acting on the front and rear wings for achieving the best lap times possible around a particular track. This will effectively focus the area of development leading to targeted use of CFD simulations. iii To perform the optimization, a genetic algorithm (Covariance Matrix Adaptation Evolution Strategy – CMA-ES) is used. In order to obtain all the telemetric information, a lap simulation tool called AeroLap is used. For simulation, the Sepang F1 race track, which annually hosts the Malaysian Grand Prix (GP), is selected. This track provides a perfect conundrum of whether to design the car for high downforce or low drag configuration, as it contains fast-turning corners and long straights. The optimization is performed for a given F1 car setup used for the 2010 season, with the aerodynamic loads acting on both the front and rear wings as well as the racing line being optimized. First, an optimum racing line is derived for this particular race track using CMA-ES. It is observed that the lap time is reduced by a margin between 0.542 to 1.699 seconds when compared with the best lap time for the actual race during the 2010 Malaysian GP. For this racing line, the optimum values of the aerodynamic loads in the form of lift and drag coefficients for the front and rear wings are calculated. The optimum values of lift coefficients for the front and rear wings are calculated as 1.123 and 1.651 respectively. The optimization of drag coefficients for the obtained lift coefficient values led to the conclusion that the best lap times always occurred for the least value of the drag coefficient that had been set as the lower limit for the simulation. As a result, a parametric study is performed by varying the drag and lift coefficients for the front and rear wings. The results are summarized in form of contour plots, displaying the change in lap times with variation in the aerodynamic loads for the front and rear wings. The best lap time for the minimum set of drag coefficients and the optimized lift coefficients is observed to be at least 2.02 seconds better than the lap time performed by an actual F1 car that raced in the 2010 season. iv Table of Contents List of Figures ............................................................................................................................................. vii List of Tables ............................................................................................................................................... ix Acknowledgment .......................................................................................................................................... x Abbreviations Used ..................................................................................................................................... xii Chapter 1 INTRODUCTION ........................................................................................................................ 1 1.1 History of Development of Aerodynamics in Formula 1 .............................................................. 2 1.2 Problem Statement ........................................................................................................................ 7 1.3 Research Objective ........................................................................................................................ 9 1.4 Thesis Overview............................................................................................................................ 9 Chapter 2 LITERATURE REVIEW ........................................................................................................... 11 2.1 Aerodynamics of Race Cars ........................................................................................................ 11 2.2 Ground Effect Aerodynamics...................................................................................................... 22 2.3 Role of Optimization ................................................................................................................... 23 2.4 Motivation for this study ............................................................................................................. 25 Chapter 3 TOOLS USED ............................................................................................................................ 27 3.1 Covariance Matrix Adaptation – Evolution Strategy: ................................................................. 28 3.2 AeroLap – Lap Simulation software ........................................................................................... 31 3.3 Optimization Process .................................................................................................................. 32 Chapter 4 OPTIMIZATION OF RACING LINE AROUND THE TRACK .............................................. 35 4.1 Study of a Straight Track ............................................................................................................ 36 4.2 Study of the Circular Track ......................................................................................................... 36 4.3 Study of the Oval Track .............................................................................................................. 41 4.4 Optimization of the Sepang F1 Race Track ................................................................................ 46 Chapter 5 OPTIMIZATION OF AERODYNAMIC LOADS ON FRONT AND REAR WINGS ............ 55 5.1 Variation in time with respect to change in aerodynamic loads .................................................. 56 5.2 Derivation of aerodynamic coefficients for the wings and F1 car body without wings .............. 58 5.3 Optimization of Aerodynamic Coefficients ................................................................................ 67 5.4 Results of Parametric Study ........................................................................................................ 72 v Chapter 6 CONCLUSION AND DISCUSSION ........................................................................................ 79 6.1 Summary and Results .................................................................................................................. 79 6.2 Assumptions ................................................................................................................................ 81 6.3 Discussion and Conclusion ......................................................................................................... 81 6.4 Drawbacks ................................................................................................................................... 83 6.5 Future Research ..........................................................................................................................