The question of how to develop a distribution of speeds for vehicles passing and being passed by an observer car in the vehicle stream has attracted the interest of several mathematicians, but their published work has not gone beyond the theoretical stage. In practice, the theoretical expressions that have been developed do not permit the construction of an accurate speed distribution from actual data gathered from an observer car. The standard deviation of the distributions they construct are accurate, but their inability to process a few discrete data points causes errors in estimating the mean speed of the traffic stream. An observer car was operated over Bl 7. 9 mi of Interstate highway, gathering actual data for use in this study. A simulation program was written to help test an empirical method for constructing a speed distribution. The simulation revealed that the empirical method predicted the mean speed well, but estimated the standard deviation poorly. Furthermore, it illustrated why these inaccuracies resulted. Finally, a practical method was produced by which anyone can determine good estimates of both the mean and standard deviation of the speed distribution without special equipment.

In order to avoid losing certain federal-aid highway funds or to qualify for incentive grants, each state must compile annual speed compliance data. If more than 30 percent of the vehicles on a representative sample of highways in a state exceed 55 mph, that state may have 10 percent of its federal-aid highway funds withheld. If fewer than 20 percent exceed 55 mph, the state can claim an incentive grant<.!>. Often, as one is driving on an Interstate highway, it is difficult to believe that sufficient compliance is actually taking place. This paper presents a practical method of approximating, not only the mean speed of traffic, but the distribution of speeds in the stream of traffic surrounding a vehicle driven by an individual who is curious about speed compliance levels on a given highway section. This method describes the speed of vehicles throughout the traffic stream, not just at isolated speed monitoring stations.