Paper ID #26037

Measuring the Traction Limits and Suspension Forces of a Formula SAERacecar

Mr. Matthew Vincent Bartolomeo, The Cooper Union

Matthew is a senior Mechanical Engineering student at The Cooper Union who is heavily involved in theFormula SAE team. During the past four years his roles have included the team’s Chief Engineer andmost recently the lead of the Vehicle Dynamics system, overseeing the vehicle’s suspension, steering, andbrakes.

Ms. Amanda Lombardo, The Cooper Union

Amanda is a senior mechanical engineering student at the Cooper Union. She officially joined the FormulaSAE team’s body and branding systems in Fall 2018, but has also unofficially been involved in helpingthe team with rapid prototyping for several years.

Michael Colella, The Cooper Union

I am a current senior Mechanical Engineering student at The Cooper Union for the Advancement ofScience and Art. Throughout my four years as an undergraduate student, I have been an avid member ofthe Formula SAE team, working on various vehicle subsystems. For the past two years, I have been incharge of the frame subsystem.

Dr. George J. Delagrammatikas, The Cooper Union

George J. Delagrammatikas is a Professor of Mechanical Engineering at The Cooper Union for the Ad-vancement of Science and Art in New York City. He is the Director of STEM Outreach which is com-prised of four programs that immerse K12 students in hands-on, authentic engineering design experiences(cooper.edu/stem). George has been involved in undergraduate motorsports since his college days and hasbeen advising the Cooper Motorsports FSAE Team since 2005 (fsae.cooper.edu). He teaches undergrad-uate design, thermodynamics, and engineering experimentation and is the faculty adviser of the Pi TauSigma Honor Society.

c©American Society for Engineering Education, 2019

Measuring the Traction Limits and Suspension Forces of a Formula SAE Racecar

Abstract Intercollegiate competitions have established themselves as authentic engineering experiences as both extracurricular learning opportunities and hands-on supplements to traditional course instruction. The following paper describes the integration of a Formula SAE (FSAE) team project into a junior-level mechanical engineering experimentation course; it represents one of nine projects in this course. The first half of the course is divided into modules that, for all students, progressively address: 1) the measurement chain and laboratory best practices using pre-existing experiments, 2) sensor design, selection, and calibration, 3) statistical data analysis and uncertainty limits, and 4) technical communication skills. The second half tasks student teams to propose, design, build, and carry out an original experiment to an engineering problem they perceive can improve the undergraduate experience in the department. An FSAE racecar was instrumented in order to characterize its acceleratory performance and thereby inform a strategy for overall vehicle improvement. An on-board data acquisition system received data from accelerometers, a GPS system, and linear potentiometers on the four suspension systems. These data streams were then used to determine the total forces experienced by each tire; static calculations yielded suspension loads. Lateral and longitudinal accelerations over the course of a single race track were then plotted and reduced to find the traction limits of the vehicle. In addition, a novel statistical method using traction data to compare individual drivers and overall vehicle performance was applied to two different drivers on the same track. With this metric, areas for driver improvement could be identified and potentially be used to guide an event-specific driver selection process or personalize driver training. Student learning objectives linked to ABET outcomes are described in the context of how they are assessed in this course. Results from student self-efficacy surveys and student achievement on assignments are presented and discussed as they apply to ABET outcomes b, g, i, and k. Introduction Authentic engineering experiences, such as student competitions, sponsored projects, design clinics, and project-based learning modules have been incorporated broadly within the undergraduate curricula to enhance student learning. The challenges and opportunities of competitions, in particular, have been succinctly detailed by Schuster et al in 2006 [1] at a

Predominantly Undergraduate Institution (PUI). These themes resonate at the PUI discussed here, The Cooper Union for the Advancement of Science and Art, in which faculty attempt to improve the undergraduate experience and promote scholarship through design and research projects that are incorporated within the curriculum. Student competitions have been historically incorporated within upper-level design courses, with particular emphasis in the senior capstone design experience. One such popular design challenge is the Formula SAE (FSAE) Competition sponsored by SAE International (Society of Automotive Engineers). FSAE publications in the engineering education literature are abundant, with hundreds currently in ASEE conference proceedings. In a recent publication, Fathizadeh et al [2] describes the FSAE project at Purdue University, Northwest and provides insight into the competition itself while focusing on the importance of real-time data acquisition on vehicle improvement. Fletcher [3] describes his school’s involvement in the Formula Hybrid competition while providing student satisfaction and self-efficacy study results. This publication illustrates the learning gains associated in engineering skills attributed to this project and supports the approach of this project-based learning experience. Similarly, Constans et al [4] describes a 5-semester project that addresses the detailed design, fabrication, and use of a bench-scale hybrid automotive powertrain. Although not a competition per se, students in this project were immersed in a hands-on engineering project and developed a test stand for use by subsequent students. Senior capstone projects are a natural fit for these types of projects, as the courses attempt to bring together all the fundamental learning into one design exercise. Earlier experiences are also related to this work and provide a proving ground and student recruitment tool for senior project selection. Such work is performed by Singh Chawla and Leonhardt [5] who describe a project that links junior and senior work to the optimization of an FSAE chassis. Previous experimental work in the context of a junior-level experimentation course is described by A. Chambers et al [6] who experimentally determine the torsional rigidity of an FSAE spaceframe. Together, this previous work supports the need for scaffolded, multi-year experiences that immerse students in real-world engineering challenges, which develop project management skills while contextualizing learning from other courses. The focus of the current work is to describe one of nine projects performed in the spring 2018 semester in a junior-level mechanical engineering course entitled ‘Engineering Experimentation.’ The objective of this course was to immerse students in a real-world engineering design project that they defined, which was related to either their own co- or extracurricular interests, or their perceived need in the undergraduate curriculum. The problem stated at the beginning of the

course included that a final deliverable, in addition to an experimental setup, would be a review-ready manuscript for submission to an ASEE conference. In this course, the three students (co-authors) formed a team to design and research the concept of racecar traction limits and suspension forces through the design, fabrication, and implementation of an onboard measurement and data acquisition system. This work gives an overview of the project from the course perspective and details the results of the technical portion of the project as well as those of assessment linked to course ABET outcomes for the entire class. The main purpose of this publication is to disseminate a method for curricular integration of a project that many FSAE teams attempt to solely undertake as a multi-year extracurricular activity. Course Learning Objectives The ABET outcomes that were assessed for this course included:

(b) design and conduct experiments, analyze and interpret data (g) ability to communicate effectively (i) recognition of need for and ability to engage in life-long learning (k) ability to use technology, skills, modern tools for engineering practice

Jones [7] proposes a metric by which ABET outcome (b) could be assessed for experimental courses while also describing the accreditation framework. He applies a rubric adapted from various engineering schools to a civil engineering course he describes where students are graded on their individual outcomes. These concepts have been expanded through the rubric used in the course described here, which is presented in Appendix A. All technical writing and oral presentation assignments in the course were ranked using this scale. In addition to this rubric, students provided written critiques for peers during oral presentations, which contributed to student outcome (g). This form, shown in Appendix B, tasked students to indicate what they thought were positive during the presentation (I like…) and then what they thought could be improved (I wish…). This appendix shows a sample critique from a student, with all names and identifying information redacted. Through the course requirement of preparing a manuscript for submission to an ASEE conference, students were inherently immersed in life-long learning as they had to investigate the open literature and learn new skills as needed for their project (outcome (i)). In addition, through their development of a measurement chain, sensor selection, a calibration procedure, and data acquisition and reduction methods, they developed skills that related to outcome (k).

Finally, a voluntary and anonymous course evaluation survey was given to the students during the last week of the course and is provided in Appendix C. These questions are divided in the following sections, which are described briefly below:

1. Your understanding of class content i. Project management and designing from scratch

2. Increases in your skills i. ABET outcomes a-k

3. Class impact on your attitudes i. Confidence and comfort in material

4. Integration of your learning i. Contextualizing the course material

5. The Class Overall i. Instructional approach and assignments

6. Class Activities i. Lectures, consultations

7. Assignments, graded activities and tests i. Feedback and appropriateness

8. Class Resources i. Physical and digital resources, course management

9. The information you were given i. Adequacy of reference material

10. Support for you as an individual learner i. Individualized instruction

11. Course Summary i. Course reflection in open format

Results from these assessment tools for the overall class are presented after the technical portion is first discussed. Course Setup: Defining the Problem This 15-week ‘Engineering Experimentation’ course was divided into three modules. Module One spanned the first three weeks and consisted of experimentation on foundational knowledge experiments, where students learned basic concepts about the measurement chain, uncertainty, technical writing, and presenting. These experiments are briefly described as follows:

1. Sump Pump: the performance range of a household sump pump is characterized through the application of simulated pressure (head) loads at its outlet with a gate valve. The

head and mass flow rate measurements are used with electrical power input measurements to determine system efficiency.

2. Cantilever Beam: a series of cantilever beams of unknown material compositions are loaded and unloaded with known weights at their free tips. Deflection and dimensional measurements are taken such that material properties can be deduced from Young’s Modulus and density.

3. Flame: varying air-fuel ratios of propane-air mixtures travel through a flame tube and are ignited. Video recordings allows students to measure average flame speed, which is related to stoichiometric fuel-air equivalence ratios.

4. DC Motor Dyno: the performance map of a 12-V DC motor (commonly used in robotics projects at the institution) is determined through a Prony brake system whereby motor speed and applied torque are measured and compared against supplied electric power (voltage and current measurements) to yield efficiency.

Module Two occurred over the subsequent three weeks of the course and consisted of a rotation to a different Module One experiment for each group. This progression mirrors the scaffolded approach described by Reissman et al in 2017 [8]. Student teams were supplied with all the previous group’s data and writing and had to augment the data sets at different operating conditions for broader understanding and deeper application of the core concepts. This rotation also developed the current group’s critical thinking skills as they were critiquing the previous group’s work. Both modules concluded with a formal critique of a 10-minute presentation. The critiques were delivered by all the students in the audience and consisted of at least one presentation characteristic they thought worked well and one that they thought could be improved. This technique provided a framework such that the audience could critically assess the merits of different delivery techniques, the information that was delivered itself as it applied to the overarching narrative of the experiment, and how conclusions could be used to further student knowledge of the subject. At the conclusion of these two modules, students were asked to separate into groups of their own choosing (2-5 students in each group) and submit a written project proposal for their Module Three design project along with a presentation to the entire class for feedback using the critique sheets mentioned earlier. There were 9 projects distributed over 34 students; the following work describes one of these projects.

Problem Definition and Background The suspension of a racecar plays an important role in the overall performance of the vehicle. It is responsible for distributing the weight of the car among its tires during accelerating, braking, and cornering while ensuring the wheels have adequate contact with the road at all times. The weight on each tire determines the frictional forces it produces, thereby also defining acceleratory capability. This project implements the data acquisition system of the 2018 Cooper Motorsports FSAE vehicle to better understand the performance of the vehicle’s suspension, and the driving ability of the drivers. Improved characterization of the suspension allows for components to be designed much lighter and with smaller, more realistic factors of safety. The driver ability metric would allow for more specific driver training interventions and/or event-specific driver selection. A useful tool for analyzing the high performance level of the driver and vehicle are traction circles. These plots measure the performance limits of the vehicle-driver combination under acceleration, braking, and cornering. In addition to the operating limits outlined by traction circles, insight into the movement of the suspension and the dynamic weight transfer is also desired, since this characteristic plays a critical role in vehicle performance. In addition, the maximum weight on each tire is used to select the spring and damping constants of the suspension. Sources [9-13] were used to develop the analysis of the suspension system described here. The major goals of the experiment are to better evaluate driver performance using a metric derived from a traction circle and to better calculate suspension forces using accurate experimental equipment, thereby allowing the team to make more informed design choices in order to enhance vehicle performance. Optimizing a suspension system correlates closely to a car’s ability to handle cornering, braking, accelerating, and ability to move sharply and accurately, among other things. The Cooper Union FSAE suspension design team uses both information learned in previous years and general knowledge of vehicle specifications and rule guidelines to improve every subsequent suspension system. The suspension system as used in the 2018 competition is displayed in Figure 1.

Figure 1: CAD rendering of the 2018 Cooper Motorsports suspension system, with the coilovers

highlighted in orange Note that four coilover shocks are mounted using rockers to suspension members on the four polar edges of the frame. This placement is necessary to absorb impact at critical points of the suspension to prevent adverse vibration. Specifications like this are extremely important in car optimization, but very few of these specifications are currently well-known. Linear potentiometers were placed on the springs and dampers of the suspension to record their deflection during race conditions. This deflection can be used to calculate the movement of the suspension. Using known spring and damping constants, the force through the spring-damper system can be calculated, which can then be used to calculate the weight on the tire. Understanding these loads is essential to minimize the weight of the suspension. One method by which these ideal specifications can be determined is through better understanding how forces are distributed throughout the system. Knowing these forces can both help with structural integrity and make the suspension theory easier to apply to current and future vehicles. Obtaining this force data is therefore both instructive and important for more comprehensively characterizing the vehicle’s suspension system. Another aspect of improving vehicle performance is comparing how different drivers handle the same car. Determining the driver whose driving style is best suited for a given situation allows the car to be used to its absolute limits, helping to balance any potential non-optimized suspension design. Among the most straightforward ways this can be implemented is through the

generation of a traction circle. This plot measures the outer limits of real-time longitudinal acceleration and lateral acceleration, as can be seen in Figure 2.

Figure 2: Example of a traction circle [3]

This plot displays the upper limits of the driver and vehicle under braking, accelerating, and cornering. Using this information, feedback can clearly be obtained of how a car and driver perform while on a given track. Fundamentally, the traction circle has three variables: car, driver, and track. If two of the three variables are held fixed, a traction circle can directly compare vehicle performance over consecutive years with the same driver and track, driver performance on the same track and vehicle, or different tracks with the same driver and vehicle. The only variable in this experiment is driver performance, as it allows drivers to directly be compared in terms of accelerating, braking, and cornering. Such a comparison permits for more selective choice of drivers for future FSAE competitions; every decision to select a driver can be made based on a comparison of an average of each individual driver’s traction circle over the same track. In recent years, a data acquisition system comprised of a set of linear potentiometers and a data logger have been mounted to the Cooper Union FSAE car, but complete suspension and traction circle studies have yet to be conducted for a variety of reasons. This coursework has allotted the time and equipment resources necessary to do so. Tire Forces Suspension member forces are determined by first finding forces in the tires. These tire forces are then delivered through the six suspension members on each of the four corners of the vehicle. To begin finding approximate values for these forces, the tires currently used on the vehicle are mounted onto a flat track tire testing machine from Calspan. The slip angle of the tire is swept over a set number of degrees and the lateral force on the tire is measured in real-time as a

function of slip angle. Figure 3 is an example of data obtained from such an analysis, provided by the Calspan Tire Research Facility (TIRF) and the FSAE Tire Testing Consortium.

Figure 3: Lateral force v. slip angle of tire as provided by Calspan and the FSAE Tire Testing

Consortium. Here, note that only three curves are provided in the image. To find another lateral force as a function of slip angle aside from the three given, the corresponding curve can be interpolated from the curves already available. With this information, tire forces can effectively be found in a pseudo-steady state analysis, directly meaning that the other six adjacent suspension member forces can be calculated. The free-body diagram used for this analysis is presented in Figure 4.

Figure 4: Free-body diagram of the tire forces (green) and suspension member forces (orange)

When the car is physically in motion and not in simulation, however, the slip angle changes rapidly due to imperfections in the road and unsteady cornering. While the bounds for the slip angle remain the same as in the flat track, the lateral forces the tires experience vary to a much larger degree than is shown in Figure 3. To experimentally verify how correct the calculated forces are in the suspension members, linear potentiometers can be used. However, to use these potentiometers, the coilovers the potentiometers mount to must first be characterized. Coilover Characterization A coilover, or a coil spring over shock, is a part of a vehicle’s suspension and is characterized with its spring constant k and the damper constant c. Assuming that both the spring and damper of the coilover are within a linear region, the spring force exerted on the coilover by the suspension system is:

xF spring = k where x is the displacement of the suspension member the coilover is mounted to. Likewise, the damper force exerted on the coilover by the suspension system is:

xF damper = c˙ where is the velocity of the suspension member the coilover is mounted to.ẋ As the coilover model used already has a fixed specification for k, the spring force is fully characterized. To calculate c, the damper curves for the model must be interpreted. These curves are shown in Figure 5.

Figure 5: Damper curves displaying different configurations sold by the manufacturer, Penske

The curves in Figure 5 model all the settings of the tunable damper the coilover model uses (numbered 1-5) as a set of piecewise continuous functions. If the specific pair of curves used on the current vehicle is specified and the velocity of the coilover is specified by the linear potentiometer, the damper force can be fully characterized. The pair of curves used on the current vehicle is specified in Figure 6.

Figure 6: Damper curves of force v. velocity for the shocks used by Cooper Motorsports

The damper force is thereby fully characterized with displacement and velocity of the suspension member through the use of linear potentiometers. Experimental Setup The hardware used within this experiment consisted of linear potentiometers and a data logger with onboard accelerometers and GPS. The linear potentiometers were used in determining the forces on the suspension, and the data logger in the acquisition of traction circle data. Linear Potentiometers Real-time suspension displacement and velocity data were measured using linear potentiometers attached in parallel to each coilover on the racecar. These measurements converted the linear motion of each shock into an electrical signal, which was then recorded by a data logger (discussed in the next section) as a voltage between zero and five volts. This displacement data can be differentiated to determine velocity. The data can then be used in the equations of a spring

and damper, respectively, to obtain the force through the coilover. Cooper Motorsports previously used linear potentiometers on its 2017 vehicle to measure the downforce produced by the aerodynamics package, and during the early stages of this project, feasibility of implementing these potentiometers was investigated. The decision to use linear potentiometers over any other kind of sensor was made for several reasons. For example, linear potentiometers have been used by Cooper Union FSAE in previous years for this exact purpose; by using an already-established sensor, more time can be dedicated to other important areas of the project (e.g. proper mounting techniques, in-depth calibration analysis, or force determination error analysis, among others). Rotational potentiometers attached in a four-bar linkage system had been considered for analysis, but were ultimately rejected on the basis of unreliability and complexity of such a linkage. Of available linear potentiometers, the ones currently owned by the Cooper Union FSAE team are the least expensive and have previously been tested as being reliable, further justifying the decision to use the linear potentiometer. The four potentiometers are Ixthus PZ-12-A-75P linear potentiometers with a 75mm (3”) stroke. Upon initial inspection, it was found that several of the potentiometers did not actuate smoothly and exhibited signs of wear on the shafts. However, similar potentiometers cost approximately ~$250 each to purchase, which was outside the budget of this project. In order to assess the functionality of the potentiometers before installation on the vehicle, a static calibration was performed. To establish a relationship between the voltage output of the linear potentiometers and their displacement on the racecar, the potentiometers were calibrated. Each potentiometer was supplied with 5 V, as that is the power they receive while attached to the car, and the voltage output for each was recorded from a voltmeter at several extension lengths. A diagram and photo of this setup can be seen below in Figure 7 and Figure 8. This calibration was performed both by lengthening and shortening the potentiometer to account for any variation due to hysteresis. The upper and lower limits for the range of motion of the potentiometer were determined, and six points (not including the limits) were chosen for calibration testing at approximately 0.5 inches apart from one another. At each point, the displacement and voltage were recorded and calculated.

Figure 7: Diagram of potentiometer calibration setup

Figure 8: Photo of potentiometer calibration setup, with the potentiometer extended 1.6675

inches and outputting 2.665 V Noting that these potentiometers are expected to lengthen and shorten accurately and quickly, the expectation for these results is that the calibration curve is linear with as little hysteresis and variance as possible. The results of the calibration are shown in Figure 9.

Figure 9: Calibration results for the four shocks used on the 2018 Cooper Motorsports vehicle

From Figure 9, given the fact that only two of the points are visible over the course of the entire calibration, it is clear that the linear potentiometers work well without any discernible hysteresis. The error bars associated with the analysis can be seen in Figure 10.

Figure 10: Error bars for a data point from each linear potentiometer

As the displacement axis is measured on the order of thousandths, it is clear that the points are all extremely close together. An uncertainty analysis showed that this change is not reflected in the overall calculation of the suspension member force.

In order for the linear potentiometers to be installed on the vehicle, mounting pieces were designed to attach the potentiometer to the shock. Initially, the potentiometer was to be attached using threaded standoffs on the bolts holding the shock in place. The main advantage of this configuration is its ease of installation and lack of any custom-designed parts. However, due to the tight packaging of the 2018 vehicle’s suspension, this configuration was not feasible. When the shock is fully compressed, the distance between the attachment bolts is shorter than the length of the potentiometer. This would cause the potentiometer to exceed its travel when the shock is compressed, likely damaging the potentiometer. In order to solve this problem, 3D-printed clamps were designed. This manufacturing method was chosen due to the ease of manufacturing and the ability to quickly iterate through several designs of the clamps. One clamp attaches to the head of the shock and provides an attachment point for the shaft of the potentiometer. The second clamp attaches to the base of the shock and clamps on to the body of the potentiometer. This configuration allows the body of the potentiometer to be shifted relative to the shock, and prevents the potentiometer from bottoming out during full compression of the shock.

Figure 11: Photo of the linear potentiometer mounting

Figure 12: Photo of a linear potentiometer mounted on the front suspension, with the mounts

highlighted in orange

Figure 13: Photo of linear potentiometers mounted on the rear suspension, highlighted in orange Data Logger Recording the voltage output from the linear potentiometers and vehicle acceleration is handled by the vehicle’s onboard data logger. For the 2015 through the present (2018) Cooper Motorsports vehicle, the AiM Evo 4 Data Logger has been implemented. The development of a new data logger for this project was considered, but implementation with the existing Evo 4 was chosen due to the features of the data logger that make it highly desirable. For example, it has input channels for 0-5V analog sensors, allowing the output voltage of the linear potentiometers to be recorded. It also contains an internal three-axis accelerometer, which eliminates the need to purchase and install separate accelerometers. All data is recorded by the data logger at a sampling rate of 10 Hz. Within the data logger’s software (Race Studio 2), math channels were created to convert the voltage recorded from the linear potentiometers (in volts) to the length of the potentiometers (in inches). This conversion was done using the calibration curves generated for each potentiometer. The data from the static calibration was plotted as displacement versus voltage for each potentiometer, and best-fit lines were fit to the data. The equation for each potentiometer was entered into Race Studio 2 to convert the recorded voltage to the length of the potentiometer. The conversions from potentiometer length to speed, and subsequently to suspension member force, will be detailed in a subsequent section.

The three-axis accelerometer in the data logger is configured using Race Studio 2. Upon opening the software, the Device Configuration menu is selected. After selecting the model of the data logger (Evo 4), the orientation of the data logger can be chosen. This orientation allows the data logger to automatically assign the three axes of the accelerometer to longitudinal, lateral, and vertical accelerations. However, the list of pre-defined orientations does not include the orientation of the data logger in the vehicle. Therefore, one of the default orientations was chosen, and the channels were manually renamed to correspond with the data logger’s orientation in the vehicle. Race Studio 2 also allows the readings to be zeroed while the car is stationary. However, the software assigns 1g of acceleration to the vertical accelerometer while stationary. As the accelerometers were manually renamed to match their orientation in the vehicle, the acceleration had to be zeroed properly. In order to correct this, a math channel was used within Race Studio 2 to subtract 1g from all the vertical accelerations measured.

Figure 14: CAD of Cooper Motorsports 2018 suspension and frame, with the data logger

mounted and highlighted in orange

Figure 15: Photo of the data logger mounted on the car frame and highlighted in orange

Analysis Traction Circle Plot Generation The primary assumption in this analysis is that both the lateral acceleration data and the longitudinal acceleration data are normally distributed. That is, the data has a well-defined variance and the probability of a data point existing a certain distance away from the mean is defined by a Gaussian distribution. The benefit of using this distribution is that the size and orientation of the traction circle can be characterized for any shape of data to be analyzed. In general, the equation of an ellipse with a major axis length of 2a and a minor axis length of 2b centered at the origin and aligned with the x-axis and y-axis is:

) )( xa2 + ( yb

2 = 1 In the case of the experiment performed, if the acceleration data also happens to align with the x-axis and y-axis, the above equation can be written as:

) )( xσx22 + ( yσy2

2 = k

where is the variance of the lateral acceleration data points, is the variance of theσx2 σy2 longitudinal acceleration data points, and k is the scale of the ellipse. As the data points in this analysis are assumed to follow a sum of squared independent Gaussian distributions in the x and y directions, the data follows a Chi-Squared distribution with two degrees of freedom. This distribution lumps the individual Gaussian probabilities in the x and y directions into a single overall probability. In this case, the number k mentioned above creates a direct correlation between the probability that a data point exists on the longitudinal-lateral acceleration graph and

the size of the ellipse given in the above equation. In other words: the bigger the ellipse, the higher percentage of points are within the ellipse. The major advantage of using a Chi-Squared distribution is that it is easy to correlate a probability with a corresponding k value. According to Hoover et. al. [9], it can be shown that probability is related to k by:

k = √− (1 )2 ln − p where p is the probability of a point existing in the ellipse. For example, if 95% of the acceleration points are to fit inside the ellipse, the k value becomes 2.4477, meaning that the equation for the ellipse where the ellipse is aligned with the x-axis or y-axis becomes:

) ) .4477( xσx22 + ( yσy2

2 = 2

A plot demonstrating the correlation between k and p is shown in Figure 16.

Figure 16: Correlation between the scale of an ellipse, k, and the probability of a point existing

in said ellipse, p [2] Note from Figure 16 that most of the major scaling and variation in probability changes most near the rightmost side of the graph, indicating that a finalized k value to ubiquitously compare drivers will be driven largely by the average variance of the data obtained for each driver over several trials. After many of these trials, it is determined that a constant k value of 3.2552 maintains the shape of the ellipse without being too big to make accurate comparisons or discounting too many outliers. This k value corresponds to a probability of 99.5%, meaning that only 0.5% of all data points are neglected in the analysis. Now, consider the case where the ellipse is not aligned with the x-axis or y-axis. In this case, provided the coordinate axes can be rotated such that the ellipse is aligned with the adjusted coordinates, the ellipse can be oriented in the same way as the data is trending. This allows the curvature of the ellipse to better fit the data and to obtain more precise ellipse measurements.

There are two random variables associated with this analysis: lateral acceleration and longitudinal acceleration. According to probability theory, a 2x2 covariance matrix of the data can be created by calculating the variance of each random variable and the covariance between the two variables. The diagonal entries of the matrix are the variances of lateral acceleration and longitudinal acceleration, respectively, and the off-diagonal entries are both the covariance of lateral and longitudinal acceleration. The eigenvectors of this matrix dictate the directions of the largest spread of data, and the eigenvalues detail the variance of the data in the direction of the eigenvectors. The ellipse is plotted by creating the covariance matrix of the acceleration data and finding the associated eigenvectors and eigenvalues of said matrix. The angle the ellipse rotates to relative to the x-axis is defined by:

an ( )θ = t −1 v(x)v(y)

where v(y) is the largest eigenvector associated with the y-axis and v(x) is the largest eigenvector associated with the x-axis. The major and minor axis lengths are calculated as:

, andajor axis length 2 M = √(3.2552)λ1 inor axis length , M = 2√(3.2552)λ2

where and are the first and second eigenvalues of the covariance matrix, respectively. Withλ1 λ2 the lengths of the major axis and minor axis, and the angle the ellipse makes with the x-axis, the ellipse can be fully characterized for any orientation of data. Suspension Member Force Calculations As mentioned in the Experimental Setup section, the data logger was configured to output the length of the potentiometer as a function of time. This data was converted to displacement by subtracting the length of the potentiometer when the car is stationary from the recorded lengths. A MATLAB script was used to convert these displacement data points into the force through the coilover. First, the displacement data was multiplied by the spring constant to calculate the force due to the spring. The force due to the damper is dependent to the velocity of the shaft, which was calculated by differentiating the displacement of the linear potentiometer. This can be calculated by subtracting adjacent data points and dividing by the time separating them. Since the data logger samples at 10 Hz, this length of time corresponds to 0.1 seconds. Therefore, the velocity can be calculated using the following equation:

(t)v = 0.1sx(t)−x(t−0.1s)

The total force through the coilover can be calculated by summing the force through the spring and the force through the damper. Therefore:

(t) F (t) (t) x(t) x(t)F coilover = spring + F damper = k + c˙ (t) kx(t) F coilover = + c 0.1s

x(t)−x(t−0.1s)

This force represents the total force taken by the spring and the damper. The vertical load on the tire can be calculated using the motion ratio of the suspension. According to Milliken [10], the motion ratio is defined as the “the rate of change of spring compression with wheel movement”. The vertical load on the tire (the Fz), is given by:

F /(MR)F z = F z,static − coilover where Fz,static represents the weight on the tire when the vehicle is stationary. The front and rear suspensions of a vehicle are often not identical, so the appropriate spring constants, damping constants, and motion ratios must be used. The forces through the rest of the suspension members can be calculated using the 3D equations of static equilibrium. The suspension linkages for each tire represent a system of nine forces: six produced by the suspension links, two frictional forces produced by the tire, and the vertical load on the tire. During skidpad testing, which can be modeled as pure lateral acceleration, the longitudinal frictional force (Fx) produced by the tire is approximately equal to zero. The vertical load on the tire can be calculated using the aforementioned equations. Lastly, the force through the coilover can be used to calculate the force in one of the suspension links, the pushrod or the pullrod (depending on the configuration of the suspension). These links are connected to the upright (which holds the wheel to the rest of the suspension) and a rocker. The rocker connects the coilover to the pushrod or pullrod, and rotates as the suspension moves through its travel. Using the distance between the push/pullrod attachment point and the coilover attachment point (rpush/pullrod and rcoilover), the force in the push/pullrod can be calculated as follows:

FF push/pullrod = coiloverrcoilover

rpush/pullrod

This results in a total of three forces that are known (Fz, Fx,, and Fpush/pullrod), which can be used to solve for the forces in the remaining five suspension members and the lateral frictional force produced by the tire (Fy). Results The data included in this paper was collected on 4/21/2018 during a test day at Rutgers University (a neighboring institution with a parking lot). The logger recorded data for the full 20 km, which consisted of five different drivers on an autocross, acceleration, and skidpad course. The GPS data recorded was used to produce the map of the courses shown in Figure 17. From left to right, the courses are autocross, acceleration, and skidpad.

Figure 17: Tracks driven overlayed on map of Rutgers University parking lot

Traction Circle Analysis Acceleration data recorded from the autocross course was used to produce traction circles for the two drivers who drove that course: Driver One and Driver Two. The traction circles produced for each driver are shown in Figure 18 and Figure 19, and the two circles are plotted together for comparison in Figure 20. The traction circles for both drivers demonstrate a bias towards negative lateral acceleration, which corresponds to right turns. This suggests that the course is biased towards right turns, which is in agreement with the course map presented in Figure 17 (the autocross track was run clockwise). A comparison between the two drivers indicates that, while the two drivers had similar lateral accelerations, Driver One was capable of achieving higher longitudinal accelerations. This analysis suggests that Driver Two is not at the limits of the car’s longitudinal acceleration and therefore has room for improvement in autocross.

Figure 18: Traction circle for Driver One on the autocross course

Figure 19: Traction circle for Driver Two on the autocross course

Figure 20: Comparison of traction circles for Driver One (red) and Driver Two (blue) on the

autocross course In order to characterize the overall performance limits of the vehicle (independent of the driver), acceleration data was compiled for all five drivers over the course of the entire test day. By combining the data from several drivers, the resulting traction circle demonstrates the overall performance the vehicle is capable of independent of an individual driver. This overall traction circle is shown in Figure 21. The overall traction circle shows a maximum lateral acceleration of approximately 1.5 g’s, which agrees with the predicted maximum lateral acceleration used to design the 2018 vehicle’s suspension.

Figure 21: Overall traction for the 2018 vehicle

Suspension Member Force Analysis Data from the linear potentiometers was analyzed for the skidpad course, as the course represents quasi-steady lateral acceleration, which simplifies data analysis. The raw data indicated a maximum suspension travel on the skidpad of approximately 0.6”, which is well within the 1.5” travel limit of the suspension. The vertical load on each tire (found using the methods described in the Analysis section) is shown in Figure 22 and Figure 23. Although the data exhibits the general trends expected from a figure-eight skidpad, the weight on the front tires drops to approximately -200 lbs. Since the front tires were not observed to lift off the ground during testing, the weight is expected to always remain positive, and the data for the rear suspension demonstrates this. A possible cause for this is an offset in the front suspension data, which would shift the weight on the tire from positive to negative.

Figure 22: Weight on the tires for the front suspension

Figure 23: Weight on the tires for the rear suspension

The lateral force produced by the right tires was also calculated using the skidpad data, and is shown in Figure 24. As before, the calculated values for the front suspension vary widely from positive to negative, while the rear suspension remains positive at all times. However, using the vertical loads calculated above, the data suggests that the tire has a friction coefficient greater

than 2, which is unrealistic for FSAE tires. Generally, the tires used by Cooper Motorsports have a lateral friction coefficient around 1.6. This is likely caused by the error in the data mentioned previously.

Figure 24: Lateral force produced by the right tires

Course Assessment Results and Discussion There were 34 students in the course who were divided into nine groups, each composed of 3-5 students. Each project’s scope and breadth were monitored and adjusted weekly by the instructor during weekly consultations to ensure that workload was distributed evenly among individual students. Four of the nine projects were related to the FSAE vehicle. At the end of the semester, ABET outcomes b, g, i, and k were assessed according to the Mechanical Engineering Department’s outcomes mapping strategy on key class assignments, where at least 75% of the groups had to perform at or above an 80% threshold of achievement. This class achieved the following results above the threshold: (b) 8/9, 7/9 (g), (i) 8/9, and (k) 9/9, which all represent greater than a 75% threshold. The IRB-approved course assessment instrument in Appendix C was administered during the last week of the semester, and 8 of the 34 students responded. The results from the ABET outcomes questions are illustrated in Table 1 and, though sparse, show favorable student self-efficacy in outcomes b, i, g, and k, scored on a 5-point Likert scale. All ABET outcome results are shown in Appendix D.

Mean Standard Deviation

An ability to design and conduct experiments, as well as to analyze and interpret data (ABET outcome b)

4.1 0.64

An ability to communicate effectively (ABET outcome g) 4.0 1.31

A recognition of the need for, and an ability to engage in life-long learning (ABET outcome i)

3.6 1.51

An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice (ABET outcome k)

3.9 1.25

Table 1: Student self-efficacy survey results on ABET outcomes (b, g, i, and k) [15] Of particular interest to the department faculty was student confidence and ability in undertaking open-ended problems that resulted in a physical embodiment of their work. Offered in their second semester junior year, this course has been considered the training ground for the senior capstone design experience. The relevant survey results are shown in Table 2. Not surprisingly, students felt that the course improved their abilities to manage a project. This skill was developed weekly during consultations where timelines, tasks, and purchasing were discussed. In addition, it appears that students felt that the subject matter became more contextualized with respect to their other courses, as did their abilities and confidence in building an experiment from start to finish. One result that stands out is that the outcome of lifelong learning may need to be addressed in a way that students either better understand the meaning of that outcome or assignments are modified to improve achievement in that outcome.

Mean Standard Deviation

Project Management 4.4 1.41

Researching publications/texts outside class material to learn on your own.

3.2 1.49

Learn how to work on a team (consider the skills of delegating tasks, managing time, respecting others' opinions, meeting regularly, etc).

4.0 1.31

Design and build an experiment from concept to product 4.1 0.99

Confidence that you understand the material 3.9 0.99

Confidence in approaching open-ended problems 4.1 1.36

Your comfort level in working with complex systems 3.7 1.28

Connecting key class ideas with other knowledge 4.0 1.07

How studying this subject helps in addressing real world problems

3.9 0.83

How concepts from this course relates to other mechanical engineering concepts

4.2 1.04

Table 2: Survey results for non-ABET outcomes The open-ended questions offered the faculty tremendous insight. For aspects of the class that the students thought were positive, students provided the following feedback:

“I like that we got to see the work that everyone else did. I like that there were a lot of resources already available in the Team Drive. I like the diversity of projects done throughout the semester.” “I like the team communication that was necessary to complete the projects throughout the semester.” “The extremely fast pace of the class forced me to dedicate a lot of my effort into organizing the project, and setting realistic, yet ambitious goals. This also included delegating tasks between group members.”

“I think I learned the most about how much work it takes to make a good project vs.a mediocre project. Planning a project takes a decent amount of time and effort, but executing that project well takes much, much more time and effort.”

For aspects that may be improved, students answered:

“I wish assignments were more clear. I wish submissions were easier.”

“I wish the projects were student driven rather than instructor driven. I wish the project was given more time and attention...” “I wish peer evaluations were implemented throughout the semester so that not only would group members be motivated to write the paper, but they would be held accountable if they didn't. [Another Cooper Union professor] does this. ”

“I wish that the course was more organized; especially during the final project phase, I felt that there was no focused direction from [the professor]. He provided useful feedback, but a lot of it was all over the place, and didn't help to focus the project in a certain direction.”

This improvement feedback is particularly helpful, and modifications to the syllabus for the spring 2019 offering have already been implemented as a result. These changes include syllabus modification, increased time for the final project, more frequent peer assessments, detailed task responsibilities (to identify ownership), and various stages of assignment review. Moreover, the instructor’s role was defined as that of a consultant to the engineering team who would advise different project directions but leave it to the student groups to develop a narrative for their project using engineering decision-making. Conclusions and Future Work This paper detailed the design, fabrication, and implementation of an experimental system used to determine the suspension forces, traction limits, and driver performance of the Cooper Motorsports’ 2018 vehicle. This project was one of nine in a junior-level engineering experimentation course aimed at delivering ABET student outcomes b, g, i, and k in the mechanical engineering curriculum. Accelerometers, a GPS tracker, and linear potentiometers on all four coil-over suspension shocks were used in conjunction to determine the traction limits of the vehicle under typical racing conditions. The data were then plotted on an aerial map to help the team determine strategies to improve vehicle performance. In addition, a novel statistical method was used to compare driver ability, thereby establishing a metric that would help individualize driver training for enhanced performance or allow for selective placement of drivers in different events. The assessment results for the entire class indicate that student confidence in addressing open-ended problems has improved through this course and that their project management skills have improved markedly. Although some felt uncomfortable with the structure of the course, real-world problems of this nature do not have clear solutions. Using student feedback, course modifications have already been made by: 1) defining ABET outcomes and their application to this course early on so that students can implement that thinking into their design project, 2) shifting the schedule to afford more time for the final project, 3) discussing educational goals through the lens of Bloom’s taxonomy, 4) assigning more frequent peer assessments so that students are held accountable for their workload, 5) defining ownership of different duties in the team so that assessment is more individualized, and 6) re-evaluating how life-long learning is addressed in the course.

References 1. P. Schuster, A. Davol, & J. Mello, “Student Competitions The Benefits And Challenges,” Proceedings of the 2006 ASEE Annual Conference & Exposition, Chicago, Illinois. June 2006. https://peer.asee.org/1055 2. M. Fathizadeh & A.I. Ayyad, “Students’ Participation to Improve Formula SAE Car,” Proceedings of the 2018 ASEE Annual Conference & Exposition, Salt Lake City, Utah. June 2018. https://peer.asee.org/31023 3. R.W. Fletcher, “Designing and Building Competitive Hybrid Electric Racing Vehicles as a Valued Teaching and Learning Method for Undergraduate Engineering Students: A Two-year Review with a Projection of Future Plans,” Proceedings of the 2012 ASEE Annual Conference & Exposition, San Antonio, Texas. June 2012. https://peer.asee.org/21166 4. E. Constans, S.I. Ranganathan, & W. Xue, “Integrating the Mechanical Engineering Curriculum Using a Long-term Green Design Project - The Planetary Gearset,” Proceedings of the 2015 ASEE Annual Conference & Exposition, Seattle, Washington. June 2015. https://peer.asee.org/24331 5. T.S. Chawla & E. Leonhardt, “Two Approaches to Optimize Formula SAE Chassis Design Using Finite Element Analysis,” Proceedings of the 2018 ASEE Annual Conference & Exposition, Salt Lake City, Utah. June 2018. https://peer.asee.org/31162 6. A. Chambers et. al, “Development of a Test Stand for Determining the Torsional Rigidity of a Formula SAE Space Frame,” Proceedings of the 2016 ASEE Annual Conference % Exposition, New Orleans, LA. June 2016. https://peer.asee.org/26814 7. A.L. Jones, “A Metric for Assessment of ABET Student Outcome "b" – Experimental Design and Analyzing the Results,” Proceedings of the 2015 ASEE Annual Conference & Exposition, Seattle, Washington. June 2015. https://peer.asee.org/23408 8. M. Reissman & T. Reissman, “Scaffold Approach to Teaching Experimentation” Proceedings of the 2017 ASEE Annual Conference & Exposition, Columbus, Ohio. June 2017. https://peer.asee.org/28811 9. W.E. Hoover, “Algorithms for Confidence Circles and Ellipses.” U.S. Dept. of Commerce, National Oceanic and Atmospheric Administration, National Ocean Service, 1984. 10. W.F. Milliken et al., Race Car Vehicle Dynamics. SAE International, 1995. 11. L.T. Borg, “An Approach to Using Finite Element Models to Predict Suspension Member Loads in a Formula SAE Vehicle.” 28 May 2009. 12. C.W. Mitchell, et al., “Training Test Drivers with Data Acquisition.” SAE Technical Paper Series, 2000, doi:10.4271/2000-01-3568. 13. D. Robertson & G. Delagrammatikas, "The Suspension System of the 2009 Cooper Union FSAE Vehicle: A Comprehensive Design Review," SAE Int. J. Passeng. Cars – Mech. Syst. 3(1):366-380, 2010

https://peer.asee.org/1055https://peer.asee.org/31023https://peer.asee.org/21166https://peer.asee.org/24331https://peer.asee.org/31162https://peer.asee.org/26814https://peer.asee.org/23408https://peer.asee.org/28811

14. R. Weingart, “On-Track Testing as a Validation Method of Computational Fluid Dynamic Simulations of a Formula SAE Vehicle.” 19 Feb. 2015. 15. ABET, Criteria for Accrediting Programs in Engineering in the United States, Effective for Evaluations During the 2018-2018 Cycle, Engineering Accreditation Commission, Accreditation Board for Engineering and Technology, Inc., 2018, Baltimore, Maryland. Acknowledgements This work was made possible through the assistance of Douglas Thornhill and Estuardo Rodas from the Department of Mechanical Engineering at The Cooper Union for the Advancement of Science and Art. Funding for this project was supplied by the Department of Mechanical Engineering. Special thanks to the Rutgers University Formula SAE Team for allowing the Cooper Union Motorsports Team to use their parking lot for testing.

https://www.abet.org/accreditation/accreditation-criteria/criteria-for-accrediting-engineering-programs-2017-2018/#1https://www.abet.org/accreditation/accreditation-criteria/criteria-for-accrediting-engineering-programs-2017-2018/#1https://www.abet.org/accreditation/accreditation-criteria/criteria-for-accrediting-engineering-programs-2017-2018/#1https://www.abet.org/accreditation/accreditation-criteria/criteria-for-accrediting-engineering-programs-2017-2018/#1https://www.abet.org/accreditation/accreditation-criteria/criteria-for-accrediting-engineering-programs-2017-2018/#1

Appendix A: Assignment grading rubric used for all written and oral work

Appendix B: Student peer critique form used for all oral presentations

Cooper Union Department of Mechanical Engineering

Overall Score: ____5_____

Presentation Review Form Date:_____******____ Project: _________Flame tube________ Reviewer:______*******__________

Score basis: 5 = promotion (highly professional, well-prepared …) 4 = renew contract (adequate job) N = No score (Presentation was not of sufficient quality to be accepted at this time)

Feedback on Individual Presenters

Presenter I like… I wish… Student One Strong intro, gesturing at relevant

parts of diagram

Student Two Well organized Less repetition of “Chris will talk about this later”

Student Three Good explanations Clarification re: use of data from previous group Transitions into next slide were smoother

Student Four Strong projection

Feedback on Group Performance

I like… I wish… Demeanor Lively

Introduction Comprehensive

Organization Solid layout and structure overall A bit of “putting off” concepts for more explanation later.

Balance More even time distribution

Visuals Nice diagram Show visuals piece by piece as you start talking about them? Got a bit dense (a lot of text) later on; could space it out with visuals? Mute first video

Conclusion Could finish more strongly; discuss implications, further work possible

Additional Comments:

Appendix C: End-of-Semester Course and Instructor Evaluation Survey The following questions were provided to students during the last week of the course. This survey was anonymous and voluntary. Your understanding of class content

1 As a result of your work in this class, what GAINS DID YOU MAKE in your UNDERSTANDING of each of the following?

1.1 Project Management

1.2 Researching publications/texts outside class material to learn on your own.

1.3 Learn how to work on a team (consider the skills of delegating tasks, managing time, respecting others' opinions, meeting regularly, etc).

1.4 Design and build an experiment from concept to product Increases in your skills

2 As a result of your work in this class, what GAINS DID YOU MAKE in the following SKILLS?

2.1 An ability to apply knowledge of mathematics, science, and engineering (ABET outcome a)

2.2 An ability to design and conduct experiments, as well as to analyze and interpret data (ABET outcome b)

2.3

An ability to design a system, component, or process to meet desired needs within realistic constraints such as economic, environmental, social, political, ethical, health and safety, manufacturability, and sustainability (ABET outcome c)

2.4 An ability to function on multi-disciplinary teams (ABET outcome d)

2.5 An ability to identify, formulate, and solve engineering problems (ABET outcome e)

2.6 An understanding of professional and ethical responsibility (ABET outcome f)

2.7 An ability to communicate effectively (ABET outcome g)

2.8

The broad education necessary to understand the impact of engineering solutions in a global, economic, environmental and societal context (ABET outcome h)

2.9 A recognition of the need for, and an ability to engage in life-long learning (ABET outcome i)

2.10 A knowledge of contemporary issues (ABET outcome j)

2.11 An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice (ABET outcome k)

2.12 Optionally, add other skills students may have gained as a result of work in this course

Class impact on your attitudes

3 As a result of your work in this class, what GAINS DID YOU MAKE in the following?

3.1 Enthusiasm for the subject

3.2 Interest in taking or planning to take additional classes in this subject 3.3 Confidence that you understand the material 3.4 Confidence in approaching open-ended problems 3.5 Your comfort level in working with complex systems

3.6 Your willingness to seek help from others (teacher, peers, TA) when working on academic problems

Integration of your learning

4 As a result of your work in this class, what GAINS DID YOU MAKE in INTEGRATING the following?

4.1 Connecting key class ideas with other knowledge 4.2 How studying this subject helps in addressing real world problems

4.3 How concepts from this course relates to other mechanical engineering concepts

The Class Overall

5 HOW MUCH did the following aspects of the class HELP YOUR LEARNING?

5.1 The instructional approach taken in this class 5.2 The pace of the class

5.3 How the class topics, assignments, reading and other activities fit together 5.4 The emphasis on lab experiments

5.5 Please comment on how the INSTRUCTIONAL APPROACH to this class affected your learning.

Class Activities

6 HOW MUCH did each of the following aspects of the class HELP YOUR LEARNING?

6.1 Attending lectures or team consultations 6.2 Critiquing other presentations Assignments, graded activities and tests

7 HOW MUCH did each of the following aspects of the class HELP YOUR LEARNING?

7.1 The number and spacing of presentations and technical writing assignments 7.2 The fit between class content and papers/presentations

7.3 The feedback on my work received after presentations and during consultations

7.4 Please comment on how the feedback you received during presentations and consultations affected your learning.

Class Resources

8 HOW MUCH did each of the following aspects of the class HELP YOUR LEARNING?

8.1 The textbook (though required, it was supposed to be used as directed during

team consultations) 8.2 Online public sources and/or library sources 8.3 How helpful was using the Google Team Drive to collaborate?

8.4 Please comment on how the textbook, course notes, and other resources in this class helped your learning.

The information you were given

9 HOW MUCH did each of the following aspects of the class HELP YOUR LEARNING?

9.1 Information given in class (appropriateness, relevance, usefulness) Support for you as an individual learner

10 HOW MUCH did each of the following aspects of the class HELP YOUR LEARNING?

10.1 Interacting with the instructor during class and/or laboratory sessions 10.2 Interacting with the instructor outside of laboratory/class time 10.3 Interacting with the instructor during other class activities Course Summary 11 Please reflect on your overall course experience:

11.1 Please comment on the most valuable thing you learned in this course. Include all the things you 'liked' about the course.

11.2 Please comment on aspects of this course that could be improved. What do you 'wish' was different?

Appendix D: ABET Outcomes Assessment (Full Data Set Reduced)