Brake-lead tests—Table 2 provides a summary of the results of these studies for both equal and split coefficients of friction.

Table 2
Summary of Brake Lead Tests

Test description Positive 54.8-mm Scrub radius Negative 20.2-mm Scrub radius Maintain straight line, no brake bias 0.17 N•m (0.13 lb•ft) at steering wheel (clockwise) 0.11 N•m (0.08 lb•ft) at steering wheel (clockwise) Hands off wheel, no brake bias 2.2 m (7.2 ft) of vehicle drift (left) 0.15 m (0.49 ft) of vehicle drift (left) Maintain straight line, 60/40 brake bias 0.34 N•m (0.25 lb•ft) at steering wheel (clockwise) (counterclockwise) 0.11 N•m (0.08 lb•ft) at steering wheel Hands off wheel, 60/40 brake bias 8.5 m (27.9 ft) of vehicle drift (left) 0.46 m (1.51 ft) of vehicle drift (right)

Wheel torque data— Note that the left tire brake torque is ~1500 N•m (1105 lb•ft), which is greater than the right tire at approximately 1200 N•m (885 lb•ft). With a total front brake reaction of 2700 N•m (1500+1200), the right side provided 44% of the braking torque and the left 56%. This difference resulted in vehicle pull or drift to the left (as noted) at 2.2 m (7.2 ft) for a 63.1-m (207-ft) braking distance.

The right wheel's brake reaction torque averaged ~750 N•m (553 lb•ft). The left wheel provided ~1350 N•m (995 lb•ft) of brake reaction. With a total front brake reaction of 2100 N•m (750+1350), the right side provided 36% of the braking torque and the left 64%. This difference results in an increased vehicle pull or drift to the left of 8.5 m (28 ft) for a 66.1 m (215 ft) braking distance.

Brake-lead data—The difference in left and right brake reaction torque at the tire patch has an impact on the driver's handling perception.

During the normal (unbiased) brake test, an average 0.18 N•m (0.13 lb•ft) of torque is felt at the steering wheel and a 6-8° steering position correction was needed to maintain a straight line path. The higher brake reaction torque at the left tire results in a steering pull to the left and a steering position correction to the right. On the steering position and torque charts, the positive Y-axis denotes driver right hand changes and the negative Y-axis the opposite.

The brake-lead test with 60/40% left-to-right bias resulted in a greater pull to the left and a much larger steering wheel position change to steer right (clockwise). To maintain a straight vehicle path, the driver initially made a 24° steering wheel overcorrection and then maintained a 12° correction to the right for the remainder of the braking event.

The test results correlate with the conceptual and theoretical expectations for the impact of a positive scrub radius. The intent was to reproduce as closely as possible the brake reaction torque at the tire patch and then study the effect of varying the scrub radius. At a positive scrub radius of 54.8 mm (2.16 in.), a slight difference in brake reaction torque at the left tire resulted in a slight torque at the steering wheel to the left, causing the driver to turn away by moving the steering wheel to the right (clockwise). With the increased bias to the left, simulating a left-to-right driving surface split coefficient, the same effects required much greater corrective action.

The normal (unbiased) brake-lead test, for the modified vehicle with a negative 20.2 mm (-0.80 in.) scrub radius, had an average 0.12 N•m (0.9 lb•ft) of counterclockwise torque at the steering wheel. To maintain a straightline path, only a 2-4° steering position correction to the right (clockwise) was required. During this normal brake-lead test, even though the scrub radius has a negative value, the driver still made a small clockwise steering correction.

The brake-lead test with the 60/40% left-to-right bias for the modified vehicle at a scrub radius of negative 20.2 mm (-0.80 in.). To maintain a straight path, the driver initially made a 24° steering wheel overcorrection and then maintained a 6° correction to the left for the remainder of the braking event. The important difference to note is that the direction of the steering wheel correction for a vehicle pull to the left was a steering correction to the left (counterclockwise).

Summary of Brake Lead Tests
(vehicle drift with hands off the steering wheel)

Scrub radius No brake bias 60/40% brake bias 54.8 mm (2.16 in.) 2.2 m (7.2 ft) left 8.5 m (27.9 ft) left 24.9 mm (0.98 in.) 1.0 m (3.3 ft) left 5.4 m (17.7 ft) left -9.8 mm (-0.39 in.) 0.52 m (1.7 ft) left 1.8 m (5.9 ft) left -20.2 mm (-0.80 in.) 0.15 m (0.49 ft) left 0.46 m (1.5 ft) right

The test results correlate with the conceptual and theoretical expectations for the comparison of positive and negative scrub radii (Table 3). The bias testing for positive scrub radius shows a steering wheel correction clockwise, or away from the drift direction. The negative scrub radius setting resulted in a counterclockwise steering wheel correction for the same left side bias. At negative scrub, the driver had to turn into the drift direction, to maintain a straightline path at the bias setting.

Steady-state cornering — Lateral acceleration data were collected and compiled into standard understeer graphs. The constant radius method was used in which a constant radius circle of 15.2 m (50 ft) was navigated at increasing velocities up to, and including, incipient skidding. Steering wheel position was then crossplotted against lateral acceleration levels to obtain a graph for each scrub radius.

By dividing the steering wheel position by the vehicle's steering ratio and by taking a moving average of the understeer data, normalized understeer plots were generated for all four cases.

Examination of these curves shows two expected areas of difference: maximum obtainable lateral-acceleration level and the understeer coefficient, K. There are also some slight differences in the initial y-offsets of the graphs, but these were deemed too small to be of consequence and can be explained by not having achieved exactly equal ackerman steering for all cases.

While it is difficult to pick out the varying understeer coefficients due to the scaling of the graph, the understeer coefficient, K, defined as the differential of wheel road angle with respect to lateral acceleration at the ackerman steer angle, was estimated by using a linear best fit method between acceleration levels of 0 and 0.5 g.

Variances in the understeer coefficient were as expected and can be qualitatively explained by the equations derived for theoretical determination of understeer. One contributor to the overall understeer coefficient, K, is the roll steer rate of the vehicle such that:

K_rollsteer = (e_f - e_r) (dΦ/da_y)

where
e_f is the front roll-steer coefficient,
e_r is the rear roll-steer coefficient,
Φ is the vehicle roll angle, and
a_y is the vehicle lateral acceleration.

From the theoretical analysis it can be seen that an inverse relationship exists between the roll-steer percentage and scrub radius. Therefore, decreasing scrub radius causes the front roll-steer coefficient to increase—and consequently affects K.

The maximum obtainable acceleration on the skid pad is represented by the sections of the curves approaching vertical. Analysis of the data provides the skid pad numbers of Table 4, indicating that a reduction in scrub radius results in higher obtainable levels of lateral acceleration.

Table 4
Understeer Coefficients and Maximum Obtainable Lateral Acceleration

Scrub radius K (deg/g) Max. accel. (g) 54.8 mm (2.16 in.) 4.74 0.68 24.9 mm (0.98 in.) 4.78 0.70 -9.8 mm (-0.39 in.) 5.28 0.74 -20.2 mm (-0.80 in.) 5.82 0.79

Transient handling maneuvers— Due to varying lead times and driver differences in performing the transient cornering maneuvers, all data collected in the time domain were transferred into frequency domain for analysis.

Results of the analysis for all maneuvers show some fundamental characteristics. The large dominating peak amplitudes at low frequencies that are characteristic of each individual maneuver are affected by changes in scrub radius. Results for all peak values for each of the eight tests performed on four different scrub radii are shown in Table 5.

Examination shows that for all cases, reducing scrub to a lower positive number reduces the peak magnitude. However, differences arise depending on the particular maneuver performed. By plotting average peak magnitude against scrub radius, some further insight can be gained.

Table 5
Amplitude Responses

Peak Magnitudes Scrub = 54.8 mm (2.16 in.) Scrub = 24.9 mm (0.98 in.) Scrub = -9.8 mm (-0.39 in.) Scrub = -20.2 mm (-0.80 in.) 22.8 m (74.8 ft) Slalom 56.3 km/h (35 mph) 2.51 2.42 1.66 2.79 Same slalom 64.4 km/h (40 mph) 2.01 1.85 1.78 2.43 Double lane change 80 km/h (50 mph) 1.91 1.01 1.22 1.31 Double lane change 88.5 km/h (55 mph) 1.81 1.06 1.26 1.73 Single lane change 72 km/h (45 mph) 1.71 1.49 1.01 1.68 Single lane change 80 km/h (50 mph) 1.30 1.26 0.96 1.68 Obstacle avoidance 48.3 km/h (30 mph) 1.77 1.56 1.27 1.47 Obstacle avoidance 56.3 km/h (35 mph) 2.60 2.03 1.46 1.72

For three of the four transient maneuvers, there is a distinct low point in the graphs. For all but the double lane change maneuver, this low point occurs at 9.8 mm (-0.39 in.) scrub radius. Logically, the low point of each curve should fall at zero scrub for all the maneuvers. In the vehicle tests performed, only four discreet scrub radius settings were analyzed. Therefore, the low point at zero cannot be absolutely confirmed. It can be said that scrub reduction toward zero will require less steering wheel effort for transient maneuvers. As scrub radius increases, detrimental increases in steering effort occur for transient maneuvers.

Unintentional sources of variance—Several sources of unintended variance exist for the four different scrub radii vehicle setups tested. While attempts were made to reduce them, it was a practical impossibility to remove such factors completely.

Vehicle suspension and wheel alignments performed for each vehicle setup were not exactly repeatable. For example, minor differences in camber are possible. Additionally, the alternate rim and tire selections used produced minor variations in track width and center of gravity height.

Testing data collected are also affected by driver-induced variance. However, multiple testing runs were made and the data transference to the frequency domain should minimize testing inaccuracies.

Each scrub radius vehicle setting had complete brake and handling data recorded. Brake and handling test routes run for each of the four scrub radius settings were completed in one day for each setup, for a total of four test days. However, an extended period of time occurred between vehicle setup changes. Weather and track conditions were similar, but not identical for each of the four test days.

All the above-described variables have a potential influence on the test results. It is not known what percentage of the experimental results are attributable to scrub radius and what percentage attributable to other variances. However, scrub radius is still the most variable factor for all four situations. The researchers believe that the results shown reflect accurately the trends scrub radius variation imposes on vehicle handling and dynamics issues.