Two’s a Crowd: Factors Affecting Time-to-Collision Estimations of Multiple Approaching Vehicles

Abstract

Accurate time-to-collision (TTC) estimates are critical to maneuver through traffic safely. Studies of relative TTC judgments showed that people perceived large, far objects as arriving sooner than small, near objects. Studies of absolute TTC judgments of laterally moving same-sized objects showed that estimates of first-arriving objects affected estimates of second-arriving objects; this effect decreased with larger temporal gaps between objects. The current study measured absolute TTC judgments of two vehicles simultaneously approaching in depth separated by 2, 5, or 7 s. Vehicles were either two motorcycles, two trucks, or a motorcycle and a truck. Results indicated that the size of a first-arriving vehicle affected TTC estimates of a second-arriving vehicle. Large temporal gaps resulted in safer judgments of the second-arriving vehicle than small temporal gaps. Thus, people should be most cautious in traffic when the first-arriving vehicle is a motorcycle and when a small gap separates two approaching vehicles.

Accurate estimates of time-to-collision (TTC) are critical to maneuver through traffic safely. For example, drivers must estimate the TTC of oncoming vehicles when making unprotected left turns across traffic (Gray, 2004). Although prior research measured TTC judgments of single objects, studies of two objects are sparse. Studies of relative TTC judgments of approaching objects showed effects of object size; people perceived large, far objects as arriving sooner than small, near objects (DeLucia, 1991).

Studies of absolute TTC judgments of laterally moving same-sized objects showed effects of arrival order; people exhibited longer estimations of TTC of the object that arrived second compared to the same object shown alone (Baurès et al., 2010). In contrast, TTC estimates of the object that arrived first were comparable to estimates of the same object shown alone. In addition, the effect of the first-arriving object on the TTC estimate of the second-arriving object was diminished with larger temporal gaps, that is, when the two objects arrived further apart from each other (Baurès et al., 2011).

The current study measured the effects of vehicle size, arrival order, and temporal gap size on simultaneous TTC estimates of two vehicles approaching in a 3D traffic environment. Twenty licensed drivers viewed scenes that were recorded from a STISIM driving simulator and presented on a computer monitor. At the start of each scene, the participant’s vehicle was stationary in the center of a road while two vehicles approached at 35 mph. After 3 s, both vehicles disappeared. Participants pressed the left arrow key when the vehicle in the left lane would reach them and the right arrow key when the vehicle in the right lane would reach them.

Arrival order was varied by having the vehicle in the left lane arrive first in half of the trials and the vehicle in the right lane arrive first in the other half. The temporal gap between the vehicles was either 2, 5, or 7 s. Participants estimated the TTC of both vehicles in each scene, which contained either two motorcycles, two trucks, or a motorcycle and a truck (“vehicle size group”). Constant error (i.e., estimated TTC minus actual TTC) was measured (Baurès et al., 2010) and analyzed with a 2 (arrival order) × 3 (temporal gap size) × 4 (vehicle size group) repeated measures ANOVA, with positive and negative values indicating less safe and more safe TTC estimations, respectively. All main effects were significant (ps < .001), and there were three significant two-way interactions.

The interaction between arrival order and vehicle size group, p = .001, indicated that the size of the first-arriving vehicle affected the estimate of the second-arriving vehicle. This is consistent with Baurès et al.’s (2010) finding that TTC estimates of a (laterally-moving) first-arriving object affected those of a second-arriving object. A possible explanation of our result is that participants used a different approach to estimate TTC for each vehicle: cognitive motion extrapolation for the first-arriving vehicle and a timing mechanism for the second-arriving vehicle (see DeLucia & Liddell, 1998).

The interaction between arrival order and temporal gap size, p < .001, indicated that the size of the temporal gap did not affect mean constant error for the first-arriving vehicle. However, as the size of the temporal gap increased, the mean constant error for the second-arriving vehicle became more negative (safer). Consistent with Baurès et al. (2011), larger temporal gaps resulted in safer judgments of the second-arriving vehicle compared to smaller temporal gaps.

The interaction between temporal gap size and vehicle size group, p = .031, indicated that TTC estimates for the vehicle that was judged were affected by the size of the other approaching vehicle for all temporal gap sizes except when a judgment was made for a motorcycle in the 5-s gap and when a judgment was made for a truck in the 2-s gap.

In summary, TTC judgments of a second-arriving vehicle are affected by the size of a first-arriving vehicle and are less safe when the two vehicles are separated by a small gap. The implication for traffic safety is that people should be most cautious under such conditions.