2 percent of rear-end crashes involve a slowly-moving lead vehicle

photo: KPHO /KTVK
photo: KPHO /KTVK. The red pickup struck the rear end of a school bus that was already stopped.

Rear-end crashes are, by far, the most common motor vehicle crash. Looking at all MV-MV (that is, motor vehicle crashes excluding single-vehicle crashes), a whopping 47% were classified as rear-end, using 2012 Arizona data.

The explanations generally run to generic excuses: the driver of the striking vehicle was driving too fast for conditions, or “distraction” — which are more-or-less true by definition.

The driver of the pickup in the pickup pictured was seriously injured Mar 25, 2016 when he or she slammed into the rear-end of a reportedly stopped school bus (none of the bus occupants were seriously injured).

Digging into the problem, one of the Human Factors / Naturalistic driving studies:

Lee, S. E., Llaneras E., Klauer S., Sudweeks J. (2007) Analyses of Rear-End Crashes and Near-Crashes in the 100-Car Naturalistic Driving Study to Support Rear-Signaling Countermeasure Development, DOT HS 810 846

Of the 7,024 observed rear-end events, 45 percent involved a decelerating lead vehicle, 38 percent involved a stopped lead vehicle, 2 percent involved a slower moving lead vehicle, and 15 percent occurred under various other situations. Crashes were predominately characterized by situations in which the lead vehicle was stopped, whereas near-crashes and incidents were more evenly distributed across instances of both stopped and decelerating lead vehicles. The majority of rear-end crash events (59%, or 16 out of 27) involved a stopped lead vehicle, while 22 percent (6 out of 27) occurred under conditions of a decelerating lead vehicle.

i.e. few rear-end collisions involve “slow” vehicles. This study is specifically only motor vehicle; but this perhaps offers a clue as to why very few Bike-MV crashes are a motorist striking the rear-end of a bicyclist — drivers are quite good at not avoiding hitting slowly moving lead vehicle, perhaps simply because they have additional reaction time.

What about MV-Bike Rear-end collisions?

Rear-end collisions are only about 3% of all Bike-MV crashes in Arizona (and that includes incidents where the bicyclist strikes the rear-end of a MV). The incidence of fatal Bike-MV, though, is much higher, at about 25% of all overall bicyclist traffic fatalities nationally, though some like to claim the figure is higher. (although state data is available, the number of bicyclist fatalities in Arizona is generally too small to draw any meaningful conclusions from so everything below refers to US national data).

Breaking down the motorist-overtaking crash group between urban and rural, and daylight vs. not-daylight is important, as it reveals what counter-measures might be expected to help.

As expected, the urban/daylight (the largest category, by the way) has only relatively fewer, only 14%, motorist overtaking; versus rural/not-daylight at 42%. The 14% (together with the 3% figure, mentioned above) suggests things like Bike Lanes, protected Bike lanes, cycle tracks are unlikely to change the safety picture much.  The much higher non-daylight fractions suggest that lighting could be an especially important countermeasure.

BIKECGP urban/rural Daylight/not 2010 2011 2013 average
Mot Overtaking Rural Daylight 29 43 44 39
Mot Overtaking Rural DarkDawnDusk 33 35 41 36
Mot Overtaking Urban Daylight 30 30 37 32
Mot Overtaking Urban DarkDawnDusk 62 56 65 61
ALL Rural Daylight 103 122 141 122
ALL Rural DarkDawnDusk 75 89 98 87
ALL Urban Daylight 229 237 243 236
ALL Urban DarkDawnDusk 211 229 261 234
As percent Rural Daylight 28% 35% 31% 32%
Rural DarkDawnDusk 44% 39% 42% 42%
Urban Daylight 13% 13% 15% 14%
Urban DarkDawnDusk 29% 24% 25% 26%

minutia: the table is stored at FARS.xls. PBCAT data existed only for 2010, 2011, and 2013. Unknown rural/urban’s were assigned to rural. Unknown lighting were assigned to not daylight. These adjustments were very small single digits (mostly 1’s, a 2, and and two 3’s). See the spreadsheet for adjustments.

SELECT eBIKECGP, sUrbanRural, sLighting ,count(1) FROM 
((( 2011_incident as i JOIN 2011_person AS p_bike ON (i.ST_CASE = p_bike.ST_CASE AND p_bike.eINJ_SEV LIKE ('Fatal%') AND p_bike.ePER_TYP IN ('Bicyclist', 'Other Cyclist') )) JOIN 2011_vehicle as vehicle ON (i.ST_CASE = vehicle.ST_CASE AND vehicle.VEH_NO=1 )) JOIN 2011_PBType AS pbtype ON (i.ST_CASE = pbtype.ST_CASE AND p_bike.PER_NO=pbtype.PER_NO))
WHERE eBIKECGP LIKE ('Motorist Over%') GROUP BY 1,2,3;

SELECT sUrbanRural, sLighting ,count(1) FROM ((( 2011_incident as i JOIN 2011_person AS p_bike ON (i.ST_CASE = p_bike.ST_CASE AND p_bike.eINJ_SEV LIKE ('Fatal%') AND p_bike.ePER_TYP IN ('Bicyclist', 'Other Cyclist') )) JOIN 2011_vehicle as vehicle ON (i.ST_CASE = vehicle.ST_CASE AND vehicle.VEH_NO=1 )) JOIN 2011_PBType AS pbtype ON (i.ST_CASE = pbtype.ST_CASE AND p_bike.PER_NO=pbtype.PER_NO)) GROUP BY 1,2;

SELECT count(1) FROM ((( 2011_incident as i JOIN 2011_person AS p_bike ON (i.ST_CASE = p_bike.ST_CASE AND p_bike.eINJ_SEV LIKE ('Fatal%') AND p_bike.ePER_TYP IN ('Bicyclist', 'Other Cyclist') )) JOIN 2011_vehicle as vehicle ON (i.ST_CASE = vehicle.ST_CASE AND vehicle.VEH_NO=1 )) JOIN 2011_PBType AS pbtype ON (i.ST_CASE = pbtype.ST_CASE AND p_bike.PER_NO=pbtype.PER_NO));

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Solomon U-shaped Curve

Normally cited by those wishing slow-moving vehicles should never use the roadway, even though it is perfectly legal, is the Solomon u-shaped curve, the claim is typically something to the effect of it’s safest when all traffic travels at the same speed; ergo a vehicle must never go slower than speed of traffic and must not be on the roadway in the first place. A corollary to this line of thinking is the belief that posted speed limits are really minimum speed limits.

A USDOT paper, Synthesis of Safety Research Related to Speed and Speed Management 1998 has a good backgrounder on the theoretical basis of these ideas:

In a landmark study of speed and crashes involving 10,000 drivers on 600 miles (970 kilometers) of rural highways, Solomon (1964) found a relationship between vehicle speed and crash incidence that is illustrated by a U–shaped curve. Crash rates were lowest for travel speeds near the mean speed of traffic, and increased with greater deviations above and below the mean.

however:

Excluding these (vehicles entering or vehicles slowing to leave the roadway) crashes from the analysis greatly attenuated the factors that created the U–shaped curve characteristic of the earlier studies. Without vehicles slowing to turn, or turning across traffic, the investigators found the risk of traveling much slower than average was much less pronounced. Crash risk was greatest for vehicles traveling more than two standard deviation above the mean speed.

It’s also wasn’t clear to me how or if any of this has to do with urban or suburban streets — where by definition, traffic starts and stops for a variety of necessary reasons.

There was an article published Jan 2015 in fiverthirtyeight discussing these concepts as well as some background of NYC’s move to make the default city-wide speed limit 25mph, down from 30mph.

(note to self: for some reason i mix up Solomon’s Curve and Smeed’s Law, and i also sometimes think it’s Sneed’s law, which although it related to traffic safety doesn’t have to do with the issue at hand. I also sometimes think it’s Sneed’s Law, which is completely incorrect — but now i can google for it! Smeed’s Law, named after R. J. Smeed… is an empirical rule relating traffic fatalities to traffic congestion as measured by the proxy of motor vehicle registrations and country population

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