Mathematics and the Internet: A source of enormous confusion and great potential
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The objective of this study was to calculate the effectiveness of a pedestrian injury mitigation system that autonomously brakes the car prior to impact at reducing fatal and severe injuries. The database from the German In-Depth Accident Study (GIDAS) was queried for pedestrians hit by the front of cars from 1999 to 2007. Information on vehicle and pedestrian velocities and trajectories were used to estimate the field of view needed for a vehicle-based sensor to detect the pedestrians one second prior to the actual crash. The pre-impact braking system was assumed to provide a braking deceleration up to the limit of the road surface conditions, but never to exceed 0.6g. New impact speeds were calculated for pedestrians that would have been detected by the sensor. These calculations assumed that all pedestrians that were within the given field of view and not hidden by surrounding objects would be detected. The changes in fatality and severe injury risks were quantified using risk curves derived by logistic regression of the accident data. Summing the risks for all pedestrians, new casualty numbers were obtained. The study documents that the effectiveness of reducing fatally (severely) injured pedestrians reached 40% (27%) at a field of view of 40°. Increasing the field of view further led to only marginal improvements in effectiveness.
Republished as a chapter in The Best Writing on Mathematics 2010, M. Pitici, Ed., Princeton University Press, Princeton, NJ, 2010.
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