Tires are rather complex, as there are a number of different characteristics and a number of different variables that can affect them. 

• Slip Angle refers to the angle between the heading of the vehicle and the heading of the tire, causing deformation of the rubber, enabling the tire to generate forces. 

• Lateral Force refers to the the horizontal force generated by the tire, which enables a vehicle to corner.

• Inclination Angle, also referred to as Camber Angle, is the the angle between the tire's central axis and the vehicle's central axis from a front view. 

• Self-Aligning Moment is the tendency for tire forces to generate a centering torque about its central axis and is associated with steering feel. 

• Cornering Stiffness is the derivative of the lateral force curve with respect to slip angle, representing how rapidly grip changes with incremental changes in slip angle, and is associated with the driveability of the tire. 

Teamwide goal setting was based on a quasi-steady state lap time simulator, which allowed us examine how changing vehicle parameters correlated with points scored in FSAE events. From a vehicle dynamics point of view, and more specifically a tires point of view, the lap simulator indicated that increasing lateral coefficient of friction was the most impactful parameter by far. More specifically, improving cornering performance was four times as impactful as an equivalent improvement in straight line traction. For this reason, I determined that increasing lateral performance should serve as a primary goal for this year's design. This started with tires, and throughout the tire analysis and optimization process, I focused on maximizing peak lateral force in as many conditions as possible to extract maximum performance in a variety of driving scenarios. Doing this also served another purpose: developing quantifiable guidelines to base suspension design on. This meant finding combinations of camber, normal load and temperature where the tire performs best, and then transferring these goals into later suspension development.

To evaluate the six tire choices, I elected to compare all the tires against a control tire in a set of standardized conditions. This method was chosen for its consistency and efficiency, as all tires were compared under the same conditions and comparison to the known control allowed for conclusions to be made more definitively than comparing two unknown tires. In the previous year, the team utilized Tire A, so I selected this as a the control tire. 

Tire data was loaded in from the TTC, and plotted in OptimumTire2 (tire modeling software). The TTC performs tests in sweeps, holding some variables constant while modulating another, meaning the data is not easily useable for my purposes. Therefore, before performing any analysis, I used OptimumTire2 to sort and fit the data to a Pacejka Model, a standardized curve used to model tires. Lateral force was the parameter evaluated most closely, where tires with a higher peak lateral force were generally considered to have higher performance. To derive test conditions, I utilized drive data from the previous year to calculate load transfer to each tire, which enabled me to simulate inside and outside tire conditions. I compared Tire A to the other five tires, and observed that out of the six total choices, Tires A and C were capable of the highest peak lateral force in all test cases. Since the goal was to maximize lateral performance, these two tires represented the highest chance of achieving this.

The baseline comparison showed that Tire A and C demonstrated the highest capability to generate lateral force, which warranted more in depth analysis and characterization. In addition to examining load cases that were used in the baseline comparison, I now did pressure and camber (inclination) sweeps for both tires, and also conducted analysis on cornering stiffness. These steps provided a more detailed comparison, and enabled me to examine the operating range for both tires. Ultimately, a tire that had both high performance and a wide operating window would, on average, perform better in FSAE events which often have changing ambient conditions.

Tire pressure is a variable that changes while the car is driving, as friction between the road and tire creates heat, which in turn increases the air pressure in the tire. Examining the consistency of lateral force across multiple pressures can be thought of as analyzing the change in grip throughout the course of an autocross or endurance event.

Camber angle is another variable that changes during driving. As the car corners, the body of the vehicle rolls, which in turn influences the camber of the wheels. Changes in camber can affect the amount of contact the tire has with the road, and also affects something called camber thrust, which supplements lateral force. 

Examining these graphs showed that Tire A performed the best in a number of pressure and camber combinations, and ultimately that was the tire chosen for the second year running. This also meant the team saved a large sum of money that would've been required if replacing the existing tires.

The next phase of this project, optimization, was very important in establishing goals for future suspension design. I started by analyzing how lateral force correlated with camber variation during cornering. I modeled the tire under several pressures and normal loads, and recorded peak lateral force values for a variety of camber angles. This enabled me to simulate how the peak tire grip fluctuated in different cornering scenarios at different points during a lap. The data was charted in a 'heat map' which allowed me to identify the regions where lateral force was highest. To achieve maximum lateral performance, and points, this green range was where the tire needed to be. The next phase of vehicle dynamics, suspension design, would enable the car to maintain these optimal conditions.

Another key part of suspension and steering design is Ackermann angle. This is the relationship between the steering angle of the inner and outer tires, which is not always equal. In a corner, the inside tire travels along a tighter radius, which demonstrates the need for different steering angles. However, it's not as simple as adjusting for traveled radius, as there are a number of different ways to optimize lateral force and maneuverability through Ackermann geometry. To quantify what kind of Ackermann setup would achieve maximum cornering performance, I recorded the slip angles at which maximum lateral force was achieved for an inside and outside tire load. Observing the difference between slip angles for inner and outer tires illustrates the required Ackermann angle for peak lateral performance. Another consideration was maneuverability, as pro-ackermann generally allows the car to follow a tighter radius. In FSAE courses, there are many tight corners and slow speed slaloms, so the decision was made to target neutral steer as a compromise between maximizing grip and maneuverability.

During the course of a run, the tires heat up as friction acts on the tire during cornering and acceleration. The behavior of the tire compound often change when the tire temperature changes, making temperature another critical aspect of tire performance optimization. To find the most ideal tire temperature, I plotted normalized lateral force against core temperature of the tire. The lateral force values are normalized with respect to vertical load, since this would be a confounding variable. The plot on the right shows a region where higher lateral force values are more consistent, which is what we aimed to achieve with car setup during testing.

While it is important to design a vehicle that is theoretically fast, it's far more useful, and successful, to design a vehicle that is easy to drive in the real world. To achieve this, the driver must be able to feel how the car is behaving, and one avenue for this is through the steering wheel. Tires produce a self-centering moment which fluctuates with changes in slip angle. At some point in the slip angle range, the self centering moment is maximized, and this is when the driver will feel the most resistance in the steering wheel. To help the team's drivers get a better feel for when they are approaching the limit of grip, I wanted to align this peak in steering feedback with the peak in lateral force. This first started with modeling self-centering moment as a function of slip angle, and then comparing this to the lateral force versus slip angle plots. Determining the delta in slip angle between self centering moment and peak lateral force would set a design target for suspension design, where there are a number of variables that can be changed to fix this.