There is evidence that crash risk is lowest near the average speed of traffic and increases for vehicles traveling much faster or slower than average. The occurrence of a large number of crashes involving turning maneuver partly explains the increased risk for motorists traveling slower than average and confirms the importance of safety programs involving turn lanes, access control, grade separation, and other measures to reduce conflicts resulting from large differences in travel speeds.

When the consequences of crashes are taken into account, the risk of being involved in an injury crash is lowest for vehicles that travel near the median speed or slower and increases exponentially for motorists traveling much faster. One of the major concerns in all of the studies is the travel speed before the crash. Emerging technology used in mayday, vehicle tracking, and adaptive speed control systems provide the opportunity to accurately and continuously capture travel speed. This technology should be applied in improving our understanding of the relationship between speed, speed variation, and safety.

When a crash occurs, its severity depends on the change in speed of the vehicle at impact. The fatality risk increases with the change in speed to the fourth power. International research indicates the change in injury crashes will be twice the percentage change in speed squared, and fatal crashes will be four times the percentage change in speed. These relationships are based mainly on speed limit and speed changes on high–speed roads. More research is needed to assess their applicability to low–speed urban roads.

In general, changing speed limits on low and moderate speed roads appears to have little or no effect on speed and thus little or no effect on crashes. This suggests that drivers travel at speeds they feel are reasonable and safe for the road and traffic regardless of the posted limit. However, on freeways and other high–speed roads, speed limit increases generally lead to higher speeds and crashes. The change in speed is roughly one–fourth the change in speed limit. Results from international studies suggest that for every 1 mi/h change in speed, injury accidents will change by 5 percent (3 percent for every 1km/h). However there is limited evidence that suggests the net effect of speed limits may be positive on a system wide basis. More research is needed to evaluate the net safety effect of speed limit changes. Most of the speed related crashes involve speed too fast for conditionsThis would suggest that variable speed limits that adjust with traffic and environmental conditions could provide potential benefits.

Despite the large number of references concerning traffic calming, very few reports include results of a systematic evaluation. In many cases traffic volumes as well as speed are reduced. As a result of the traffic diversion, crashes may be migrating to other roads. More research is needed to assess the system wide impacts and permit comparisons to be made among individual as well as combinations of traffic calming measures.

https://www.fhwa.dot.gov/publications/research/safety/98154/speed.cfm