|
Project_240: Comparative Analysis of Autocross Laps Introduction The sport of autocross presents unique opportunities for assessing various driving styles and vehicle modifications in terms of improving the capability of the driver-vehicle system in negotiating the course in the shortest possible time. The several time-attack runs throughout the event are conducted on an invariant course, under controlled traffic conditions, and timed with a displayed precision of 1/1000th of a second. The race conditions are appropriate for basic parametric analysis, which may include such factors as tire pressure, suspension settings, turn technique (Out-In-Out vs. Late-apex), or path choice (in the case of optional-direction slaloms). The basic idea behind this analysis is to identify some of the factors that affect the performance in an autocross race. These factors generally relate to either the vehicle performance potential or the driver's ability to pilot at the maximum performance level. The page is divided into several sections, each relating to a particular type of data representation or analysis. Scroll down to read the sections and click on the figures to see larger versions. Ground Track The data presented below consists of two runs from a Buccaneer region autocross event. Runs 1 and 2 are the slowest and fastest runs, respectively, so they are appropriate for analysis in determining what factors lead to the performance disparity. The only significant difference between the vehicle configuration from run 1 to run 2 is an increase in the tire pressure from 32 psi to 40 psi, respectively. The ground track of run 1 is shown in Figure 1, which shows several types of data in overlay. The background of the plot shows a series of aerial photographs of the racecourse. The photos were taken from a Cessna 152 at an altitude of 500 feet then combined into a composite image and georeferenced with the latitude/longitude data. The black '*' symbols show the locations of the GPS updates, which occur at a rate of 1Hz. The green/red line shows path of the vehicle over the course, with the green segments indicating positive acceleration (driving) and red segments indicating negative acceleration (braking). Figure 2 shows a similar plot for run 2.
Course Stages Start --> A: A --> B: B --> C: C --> D: D --> Finish: Table 1 shows the accumulated and split times for the two autocross laps at each stage. The columns labeled 'Run 1' and 'Run 2' show the time starting from the initial forward acceleration before the start gate until the finish. The times listed for each stage is the elapsed time from start, identified in the data by some characteristic feature in the acceleration data (a lateral acceleration peak at the last slalom cone, for instance). The stage split time column shows the difference in the run times of only the preceding segment. For instance, the table shows that I negotiated the B to C segment 0.45 seconds faster in run 2 than I did in run 1. The last column, lap split time, shows the difference in the elapsed time since the beginning of each run. It is important to note that my intermediate stage times will differ by what the timing van would consider correct by an amount equal to the time needed to accelerate from the starting position to the timing gate at the start grid. The final time listed at the finish is the score given by the timing van, so the last segment should be interpreted with caution.
It is obvious that my racing performance significantly improved between the runs. A nearly 1.5 second improvement in the lap time is a result of faster driving in each of the course segments. The amount of improvement presents an interesting trend, with nearly identical times in the short, first segment, followed by a dramatic outpacing in the second segment, and progressively decreasing time differences in the remaining segments. The final hairpin and skidpad are nearly equal in time for the two runs. Table 1 shows that run 2 was faster than run 1, but what are the factors that lead to such an improvement? Familiarity with the course is certainly a compelling argument, but what about the difference in tire pressure? Is it possible that the 8 psi increase helped improve the cornering stiffness and improve handling qualities in the turns? Figures 1 and 2 show a binary representation of the acceleration as the vehicle maneuvers through the course. The path is colored in green if the car is accelerating at anything above (and including) 0.0g, whereas the path is red for any moment of deceleration or braking. The lack of magnitude information doesn't help, but the frequency at which the longitudinal acceleration changes from driving to braking may be a useful measure of driving efficiency. The 240SX has limited acceleration potential, whether due to engine torque saturation or brake-pad/tire traction limits. Thus, by noting that the path for run 1 (Figure 1) shows several sections that rapidly change from green to red and back, it can be deduced that neither the driving nor the braking acceleration can be substantial in magnitude in these regions. Put simply, if the acceleration color is changing in a small space, then the magnitude of the acceleration is probably close to zero. In racing, the fastest time through a course is usually achieved by driving, turning, or braking at the maximum acceleration allowable by the tire forces or vehicle stability. In the case of run 1 where the acceleration is likely near zero in some sections, this amounts to wasted potential. Having to coast before a turn entry means that I could have accelerated forward for longer and braked harder before the turn entry, thus saving time. Run 2 shows that the distribution of acceleration color is more discrete, with longer, solid sections of green (hopefully indicating driving acceleration at the maximum rate) and somewhat shorter sections of deceleration (which could mean the braking was harder). Acceleration Probability Figures 3 and 4 show joint probability plots of a g-g acceleration plot [Milliken, 1993]. Each run produces four plots, one for each accelerometer location on the car body. The convention of the plots is listed next to each axis, where the top is driving acceleration, the bottom is braking acceleration, the right-hand-side is an accelerating turn to the right, and the left-hand-side is an accelerating turn to the left. The colorbar beneath the plots shows the mapping from colors to percentages. The yellow-colored square in the third quadrant (bottom right) of run 4, for instance, signifies that the local acceleration was 0.7g to the left and 0.4g braking for 2% of the run. Similarly, the light blue squares shows regions in which the acceleration vector resided for 1% of the time. The upper-end of the scale is saturated at 3%, so red-squares show acceleration regions of 3% or more (up to 4.5%).
According to [Milliken, 1993] and the SCCA Solo2 Novice Handbook, a race driver should be always be accelerating that maximum level allowed by the vehicle. A perfect driver who is able to drive precisely at the machine limit would produce an acceleration probability chart that is strictly populated along a circle or an ellipse. The top of the ellipse would be at the maximum driving acceleration, the right side of the ellipse would be at the maximum right turning acceleration, and the arc length between them would be composed of the maximum combined lateral and longitudinal accelerations. Comparing the joint acceleration plots for runs 1 and 2, it is evident that the region inside the rough ellipse shape is lighter for run 2 than it is for run 1. Thus, run 2 spent less time accelerating at levels below the maximum. Furthermore, the perimeter of the ellipse is more clearly defined for run 2, meaning that I was able to better take advantage of combined turning and driving/braking potential. The concentration of accelerations along the axes of the run 1 plots (red clusters instead of yellow arcs, as in run 2) indicates that my driving strategy was concentrating on a single motion at a time. The extreme case would be a driver who accelerates only in a straight line, then takes turns at the limit without any trail braking or accelerating after the apex. The probability for such a driver would be a 'plus' sign, with the lateral and longitudinal accelerations completely uncoupled. The data presented in Figures 3 and 4 is suitable for developing metrics by which to score the driving technique. For instance, the maximum acceleration performance potential could be simplistically described by an ellipse spanning the maximum measured accelerations. All the probability points that fall inside this ellipse detract from the score, whereas all points on the ellipse increase the score. A 100% score would be assigned to a driver whose accelerations fall strictly along the performance ellipse. This method appears similar to the method used by the manufacturer of the G-cube. The distribution of acceleration trends showed how my driving in run 2 was closer to the performance limit than my driving in the first run. However, the question of where exactly this performance limit lies remains an open question. In practice, it is very difficult to describe the acceleration envelope exactly, since it depends on many factors that are not easily measured. A simple comparison of maximum measured accelerations is one method to make a relative comparison between runs. In particular, it is desirable to know to what extend the change in the tire pressure affected the performance potential. A close comparison of Figure 3 and 4 reveals that run 4 showed that the populated acceleration blocks spanned roughly 0.1g farther in the lateral direction. This can be thought of as increasing the size of the performance potential by increasing the tire pressure (and thus reducing load deformation), although granted the difference may also have resulted from more aggressive driving. Throttle Management Figure 5 shows the distribution of throttle position probabilities for both runs 1 and 2. The 240SX in stock configuration is quite power-limited, so it is expected that a good driver should always be accelerating at the maximum rate allowable, which means a throttle position of 1. The peak at the far right of the plot shows what percentage of the lap used full throttle. Run 2 shows that 30% of the time, I had the throttle pedal on the floor, while for run 1 the percentage is only 20%. Run 1 also features a prominent set of peaks near the mid-throttle range. Such peaks are pointless in racing, since any time not spent accelerating hard should be spent braking hard. The throttle management trend improved for run 2, where the dominant peak at full throttle is opposed by a large peak near 0, presumably during the time that the brake pedal was depressed.
|
