Table 1.

Car Following Scenario

Scenario	Car Following
Description	At the start of the scenario a LV was 18 m in front of the participant vehicle. The LVs velocity was programmed to vary velocity following a pattern created by the sum of three sine waves (Andersen and Ni, 2005). After 500 meters in which the LV maintained a head way of 18 meters, the LV began to modulate its velocity according to a sum of sines function. Three sinusoids were used to create the LVs seemingly unpredictable behavior. The amplitudes of the three sinusoids were 6.072 (9.722), 2.417 (3.889), and 1.726 (2.778) mph (kph). The corresponding frequencies were 0.033, 0.083, and 0.117 Hz. The phase for each sinusoid differed. The phase for the high and middle frequency sinusoids were randomly assigned a value between 0 and 1. The low frequency sinusoid was then assigned a value that caused the sum of the three sinusoids to be zero on the first frame, thereby ensuring that the LV always started the task at a velocity of 55 mph. The random phase values caused the LVs velocity pattern to be different for each participant.
Participant Instructions	Drivers were instructed to maintain a two car length headway distance while following the LV.
Measures of interest	Cognitive constructs stressed: Attention, perception, vigilance, continuous visuomotor performance and risk acceptance/risk taking. Dependent driving variables: Following distance (mean, SD); coherence, gain, and delay are calculated using Fourier analysis (Brookhuis et al., 1994; Janacek, 2008) Coherence measures how well the subject vehicle matches LV velocity changes. The measure is similar to correlation with values ranging between zero to one. Higher values of coherence indicate closer relationships between the two vehicle velocities; when coherence is low (we use coherence ≤ 0.3) gain and delay are not reliable. In Figure 1, the top two graphs depict examples of subjects with high coherence (0.95 and 0.93) while the bottom two graphs depict examples of subjects with low coherence (0.57 and 0.54). Gain is an amplification factor measuring the amount by which the subject overshoots or undershoots the LV velocity changes. Gain is calculated as the ratio of the spectral density of the subject vehicle velocity/spectral density of the LV velocity. Gain values greater than one indicate overreactions while values less than one are indicative of underreactions to the LV velocity changes (Andersen and Sauer, 2007). In figure 1, the bottom left graph is a rare example of an underreaction to the LV changes in velocity (0.45). The top left graph is an example of slight overshoot (1.28) and the two graphs on the right demonstrate very high values of gain (4.03 and 7.34). Delay is measured in seconds and indicates the time it takes for a driver to react to LV velocity changes. Delay is calculated as the phase/(frequency * # of frames recorded per second). De Waard and Brookhuis (2000) indicate that this measure is most indicative of driving safety; a subject with slow reactions is an unsafe driver.
Data Reduction/Variable Calculation	Following distance and velocity were recorded at 60 Hz. A Fourier analysis derived coherence, gain and delay using the velocities of the LV and the subject vehicle. The values for gain, coherence, and delay were obtained for the frequency with the highest spectral density for the LV.
Implementation Variations	Variations of the task could be done by modifying the driver instructions, changing speed parameters, changing the specified following distance, etc.
Measurement Challenges	Some drivers may not perform the task as instructed. When performed over a longer period of time, measures derived with the Fourier analysis become more stable.
Validity	Drivers may have different car following behavior in the real world, e.g., because of added risk and different visual and vestibular cues. Instrumented vehicles could be used to study car following behavior on the road, however environmental variables are less easily controlled and the safety risk is greater on the road.
Useful References	Brookuis K, de Waard D, B. Mulder (1994) Measuring Driving Performance By Car-Following in Traffic. Ergonomics, 1994 vol. 37 no. 3 427–434 Andersen G J, Ni R (2005) The Spatial Extent of Attention During Driving. Proceedings of the Third International Driving Symposium on Human Factors in Driver Assessment, Training and Vehicle Design de Waard D, Brookhuis KA. Drug Effects on Driving Performance. Annals of Internal Medicine 2000 133: 656. Andersen G J, Sauer C W (2007) Optical Information for Car Following: The Driving by Visual Angle (DVA) Model. Human Factors, 2007, vol. 49 no. 5 pp 878–896