As car speeds increase, the chance that collisions will kill bicyclists and pedestrians increase proportionally. While not focused on speed as a factor in collisions, the Wikipedia article on Pedestrian safety through vehicle design covers the damage that a vehicle impact can do to a human body.
The relation between speed and crashes is a 2012 fact sheet by SWOV, Netherland’s road safety research institute. It pulls from a few European studies to derive pedestrian fatality risk as a function of vehicle speed.
Impact Speed and a Pedestrian’s Risk of Severe Injury or Death, published in 2011 by AAA (a typically car-positive institution), only studied four years between 1994 and 1998 but standardized the data for 2007 to 2009. It neatly summarized its findings in the abstract:
Results show that the average risk of severe injury for a pedestrian struck by a vehicle reaches 10% at an impact speed of 16 mph, 25% at 23 mph, 50% at 31 mph, 75% at 39 mph, and 90% at 46 mph. The average risk of death for a pedestrian reaches 10% at an impact speed of 23 mph, 25% at 32 mph, 50% at 42 mph, 75% at 50 mph, and 90% at 58 mph.
The Propublica article Unsafe at Many Speeds visualized this data as a line chart showing fatality risk vs. car speed.
Relationship between Speed and Risk of Fatal Injury: Pedestrians and Car Occupants, published in 2010, looked at three datasets from Europe. It finds that fatality risk increases slowly until impact speeds above 30 mph and after that, between 3.5 to 5.5 times more likely at 40 mph. Despite this, half of the pedestrian fatalities occurred below 30 mph.
Literature Review on Vehicle Travel Speeds and Pedestrian Injuries, prepared by the NHTSA in 1999, reviews literature available at the time and summarized the General Estimates System for speed-dependent lethality, which are lower than other studies. Unfortunately, the data tables are presented as bitmap images.