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Table of Contents

Page No.

Abstract …………………………………………………………………… 3

Introduction ………………………………………………………………. 5

Texas Proofing of vehicles ……………………………………………… 6

1940-49 War Speed Limit ………………………………………………… 10

Data available for scientific analysis …………………………………… 11

Iowa motor vehicle fatalities data ………………………………………. 16

The Montana no speed limit safety paradox ………………………….. 28

The Texas Interstate traffic fatalities-crashes …………………………. 38

Iowa statewide crash data and changing speed limits ……………….. 40

Kansas speeding related crashes-fatalities ……………………………. 45

Summary and Conclusions ………………………………………………. 50

Appendix 1: Legendre‟s Best-fit line and Einstein‟s Work function…... 54

Appendix 2 : NHTSA Workshop on Vehicle Mass-Safety……………… 57

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Abstract

Several state legislatures in the US, notably Texas, have recently voted to

increase the legal speed limits on their highways. Texas would soon have

the highest posted speed limit of 85 mph (136 kmph) in the nation and the

second highest in the world. In this context it is important to understand,

dispassionately without any socio-political and economic prejudices, the

effect of increased speed limits on traffic-related fatalities. Nearly 40,000

people die in traffic-related accidents each year, the social costs of which

cannot be overlooked.

A review of the fatalities data, or the fatality rate data (based on VMT, the

Vehicle Miles Traveled) often yield conflicting signals, depending on how

the data is “mined” and/or interpreted. Some states indicate increased

fatalities with increasing speed limits while others indicate just the opposite.

Indeed, according to NHTSA, the absolute number of fatalities has reached

a historical low in 2010 since 1949. Many statewide data reveal similar

historical lows. (The current depressed state of the US economy may

certainly be a factor here!) The fatality rates, based on VMT, have also

been decreasing year after year. Yet, there can be no doubt that crashes

occurring at higher and higher speeds, which are inevitable if the legal

speed limits are raised, will be increasingly gruesome and the US might

indeed witness an “epidemic” of traffic related deaths, as in the 1950s and

1960s, which prompted congressional hearings and historic traffic safety

legislations. Teenagers and inexperienced drivers are, perhaps, the most

susceptible.

Attention is therefore called to a new, and remarkably simple, method of

addressing this issue, as discussed here, which is based on an analysis of

well documented data on fatal crashes and fatalities in various states. It is

shown that as the number of fatal crashes, x, increases the number of

fatalities, y, increases following a simple linear law y = hx + c (see Figures

2, 11, and 13 and sidebar on page 15). The numerical values of the

constants h and c can be deduced using the classical statistical method

known as linear regression analysis. A graphical representation of the data,

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with observations made over several years that span different speed limits,

suggest no statistically significant effect of the speed limit (see, in

particular, Figures 14 to 16).

Nonetheless, the physical effects of an increase in the absolute speed

limits cannot be overlooked and the increasing amounts of energy that

must be absorbed in crashes occurring at higher and higher speeds (see

Figure 1) must be factored into any societal consensus on this important

problem that should engage our national attention – like any other major

newsworthy tragedy. The interaction of speed, safety, vehicle mass, fuel

economy and crashworthiness, and other social costs, such as insurance

and medical costs, will ultimately govern the course of vehicle

development. Innovations in materials technology, that permit the use of

highstrength, lightweight materials, might help us “Texas Proof” our

vehicles and spur a new era in high speed personal and public

transportation.

A review of the historical trends in the traffic fatality data, from 1899 to the

present, is presented in a separate write up.

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Introduction

This is the second of a two-part article prepared by the author, prompted

mainly by a recent news item about attempts by the Texas legislature to

increase the speed limit to 85 mph, at least in some parts of the state. The

speed limit in Texas now is 80 mph, with Utah being the only other state

with this high a speed limit. 85 mph would be the highest posted speed limit

in the United States and the second highest in the world. A speed of 140

kmph (86 mph) is posted in some parts of Poland.

http://en.wikipedia.org/wiki/Speed_limits_in_the_United_States

http://www.reuters.com/article/2011/04/07/us-texas-speed-limit-idUSTRE7366L720110407

http://www.huffingtonpost.com/social/Dana1982/texas-speed-limit-may-rea_n_847269_84007982.html

The problem that we are trying to address here is a very simple one. We

simply do not seem to agree on what all the data that is being compiled

meticulously, by various government and law enforcement agencies, about

highway fatalities really means, especially the effect of increased speed

limits in various states on the highway fatalities.

Proponents of increasing the speed limits point to low fatality numbers from

Montana, for example, just 27 for the 12 month period in 1998-1999, when

Montana law only specified reasonable and prudent as the recommended

speed. This was the law from December 1995 to June 1999 and fatalities

jumped to 56 in the following 12-months when a 75 mph speed limit was

imposed. Some other states, where speed limits were increased, also

revealed a reduction in fatalities after the increase. Proponents of reduced

speed limits, on the other hand, point to data from states where fatalities

increased after the speed limits were raised.

The argument has also been made that the number of fatalities per se is

not a good measure and that fatality rates, not fatalities, must be

considered. Fatality rates could be adjusted to reflect population, or

registered motor vehicles, or licensed drivers, or vehicles miles traveled

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(VMT), the last being the most commonly used, see NHTSA http://www-

fars.nhtsa.dot.gov/Main/index.aspx . The fatality rate per 100 million VMT is

thus taken to be the relevant statistic. However, as noted in the earlier

report by the author, the fatality rates, based on the VMT, for the US taken

as a whole, have been declining year after year, since 1921. This fatality

rate has dropped to a historical low of in 2010.

Touting a low VMT based fatality rate is tantamount to the argument that it

is somehow better to die in a fatal crash after driving a thousand miles from

one‟s home than after driving a thousand yards. One of the most important

arguments against the VMT-based fatality rate is the justified criticism of

VMT inflation. VMT values can easily be inflated to arrive at a low fatality

rate, since, unlike fatality, VMT is an estimated, not a measured, quantity.

Texas Proofing of Vehicles

Ideally, we would like to reduce, if not completely eliminate, fatalities on our

highways. We know that the higher the speed at which one travels the

higher the (kinetic) energy that must be absorbed when a crash does

occur. The laws of physics teach us that the kinetic energy K of an object

(the energy possessed by an object by virtue of its motion) increases as the

square of the speed, K = ½ mv2 where m is the mass of the object and v its

speed. (The symbol v is used in physics to denote velocity, which is speed

in a given direction.)

This means that the energy that must be absorbed in a crash occurring

when a vehicle is traveling at 65 mph has increased by 40%, at 70 mph it

has increased by 62%, and so on, see Figure 1. At 80 mph, the current

speed limit in Texas and Utah, it has increased by 112% and at 85 mph,

the limit that the Texas legislature is pushing, it has increased by 139%.

In other words, vehicle design and engineering must adjust to these new

realities of the increased desire by drivers in Texas or Utah or Montana to

drive at much higher speeds than elsewhere in the nation. Very soon, car

manufacturers must “Texas-proof” the cars they sell. Just imagine the ad

campaign, with the label Texas Proof stamped to a pickup or SUV, like we

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have liquors that have higher and higher “proof” numbers depending on

their alcohol content!

Figure 1: Graph indicating the increase in the relative amounts of energy that

must be absorbed in a crash with increasing speed of the vehicle. If the kinetic

energy of a vehicle traveling at 55 mph is set at 100, its kinetic energy is 140 at 65

mph (40% increase) and 162 at 70 mph (62% increase) and so on. At 80 mph, the

current speed limit in Texas, the energy that must be absorbed has more than

doubled (112% increase). At 85 mph, which is the limit being pushed by Texas

legislature, the energy that must be absorbed has increased by 139% compared to

the energy that must be absorbed when the same vehicle is traveling at 55 mph.

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We also know, from overwhelming statistical data, that speeding is one of

the most prevalent factors contributing to traffic crashes and the resulting

fatalities. There are three types of crashes: fatal, injury (i.e., non fatal) and

property damage only. Crash data compiled annually by the National

Highway Traffic Safety Administration (NHTSA), suggest that speeding was

a factor in 30% of all fatal crashes, as highlighted in the following reports.

http://www-nrd.nhtsa.dot.gov/Pubs/810998.pdf

Traffic Safety Facts: 2007 Data DOT HS 810 998

http://www-nrd.nhtsa.dot.gov/Pubs/809915.pdf

Traffic Safety Facts: 2004 Data DOT HS 809 915

http://www-nrd.nhtsa.dot.gov/Pubs/811402EE.pdf

Traffic Safety Facts 2009

Furthermore, as we see from the above, speeding is usually also a factor in

alcohol-related fatal crashes. It is also a factor in more than 34% of fatal

crashes that occur on wet roads (rain), in 55% of fatal crashes under snowy

conditions and over 57% of fatal crashes under icy conditions. Also, it

should be noted that speeding-related fatal crashes occur on both

interstates and non-interstate roads, under all types of posted speed limits,

from ≤ 35 mph to ≥ 55 mph.

Given these facts, it would seem that the recent attempts to increase the

speed limits on our highways are misguided. It should be noted, however,

that a number of very reasonable arguments are made by proponents of

the no speed limit laws. This is an unending debate, which pits individual

freedom against perceived societal good. Attention is called to some of the

pros and cons cited by both sides, briefly, in appendix 1.

http://www.hwysafety.com/MDT_reply_82001_section3.htm

http://safety.transportation.org/htmlguides/speeding/section01.htm

According to NHTSA, traffic fatalities in 2010 have dropped to their lowest

levels in recorded history. http://www.nhtsa.gov/PR/NHTSA-05-11

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Between 2009 and 2010, the number of traffic fatalities fell nearly 3%, from

33,808 to 32,788. Fatalities have dropped 25 percent since 2005, from a

total of 43,510 fatalities in that year. Statistical projections indicate that the

fatality rate will be the lowest on record since 1949, with 1.09 fatalities per

100 million vehicle miles traveled, down from 1.13 for 2009. This decrease

in fatalities for 2010 occurred despite an estimated increase of nearly 21

billion miles in nationwide vehicle miles traveled.

It would be tragic if this momentous trend is reversed with the recent

attempts to increase the speed limits on our highways. The significance of

these historical trends in fatality data were discussed in detail in the first

part of this article, see link below,

http://www.scribd.com/vlaxmanan

Does Speed Kill? Forgotten Facts of US Highway Deaths in 1950s and

1960s.

Between 1965 and 1966, public pressure grew in the US to increase the

safety of cars. The deaths on US highways had been increasing year after

year. In 1966 Congress held a series of highly publicized hearings on

highway safety. This led to the legislation for mandatory installation of seat

belts, which also created the US Department of Transportation (on Oct 15,

1966). As President Lyndon B. Johnson stated at the signing of the

National Traffic and Motor Vehicle Safety Act on September 9, 1966,

" ... we have tolerated a raging epidemic of highway death ... which has killed

more of our youth than all other diseases combined. Through the Highway Safety

Act, we are going to find out more about highway disease—and we aim to cure it."

Accordingly, the main purpose here is to take a fresh look at the traffic

fatality data, especially the data from Iowa, Montana that has been

prominently by both proponents and opponents in this speed limit debate.

http://www.iowadot.gov/mvd/ods/stats/2006speedstudy.pdf

A significant increase in fatalities was observed in Iowa, after the speed

limit was raised on rural interstates to 65 mph in May 1987 and also when it

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was raised once again, to 70 mph, in July 2005, see link given above.

Indeed, according to this study, all the Midwestern US states that increased

the speed limits (to 65 mph) showed an increase in fatalities ranging from 7

to 13 percent (see extract from above report in appendix 1). In Montana, on

the other hand, the number of fatalities dropped dramatically immediately

after the reasonable and prudent (i.e., no numerical limit) law was adopted.

Does the traffic fatality data, recorded immediately before and after the

changes, warrant the conclusions drawn? Is there indeed a correlation

between posted speed limits, and/or raising or lowering them, and the

traffic fatalities? This is the question that we would like to answer, using a

reliable scientific approach. In what follows here, a new methodology is

described, which is based on the analysis of both the number of traffic

fatalities (F) and the number fatal crashes (C) recorded over the years. The

merits of this approach will become obvious when we reconsider the Iowa

and Montana traffic fatality data for the past several decades.

The benefits of decreasing the speed limit (to just 35 mph) in Utah, during

the war years, were unequivocal. The only county, where fatalities

increased, seems to have been the county with chronic speeders.

1940 - 1949 / War Speed Limit

http://publicsafety.utah.gov/highwaypatrol/history_1949/war_speed_limit.html

On October 28, 1942, a War Speed Limit of 35 mph came into effect in an attempt to conserve

gasoline and save on tires. Enforcement began on November 10, 1942. Many cars were operating

with unsafe tires because people were unable to buy new tires.

With the implementation of the War Speed Limit of 35 mph, Patrolman Russ Cederlund was

featured on the cover of the November 1942 issue of Public Safety, a national magazine devoted

to promoting public safety. Patrolman Cederlund and Matt Haslam of the state road shop are

shown replacing a 50 mph sign with a 35 mph sign. Because all of Utah’s 40, 50 and 60 mph

signs were reflectorized, all of these signs had to be replaced. The old signs were stored in

anticipation that the speed limit would be raised following the war.

Despite a 5 percent increase in motor vehicles in Utah from 1941 to 1943, Utah had a significant

decrease in accidents, injuries, and fatalities. The following chart represents this decrease:

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Although vehicle miles traveled decreased 11 percent, fatal accidents in Utah decreased by 50

percent, the ninth lowest in the United States. Utah was the only state in the nation with an

increase in motor vehicle registrations during this period of time. The only area of the state

which showed an increase in fatal accidents was Utah County. Colonel Pete Dow immediately

transferred two patrolmen from the southern district to assist the Utah County personnel in

slowing down the many "chronic speeders" in Utah County.

Data available for scientific analysis

The following three pieces of pertinent data are readily available from

various sources on the Internet and can be used in a scientific analysis of

the effect of increasing speed limits on the number of fatalities in our

roadways. This also highlights areas where improvements are needed in

our data collection and/or organization.

Number of Fatalities, F

Number of fatal crashes, C

Fatality rates (based on VMT)

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However, if one wishes to seriously study the effect of increasing the

(legal) speed limits, which is usually restricted to interstate highways, it is

important to look at these three numbers ONLY as they apply to rural

and urban interstates. Fatality and crash data on other types of roadways

are less relevant. For example, the following F and C data is readily

available for Texas at the TxDOT website. However, corresponding values

of the VMT, for rural and urban driving, is not available. This is the single

most important shortcoming in data reporting (both state and nationwide).

Table 1A: Texas Interstate Traffic Fatalities-Crashes Data (2003-2009)

Year 2003 2004 2005 2006 2007 2008 2009 Rural, C 218 188 221 206 149 174 130 Rural, F 259 238 292 242 178 212 150 Urban, C 279 284 285 272 306 270 236 Urban, F 327 321 319 286 338 300 250

Only fatal crashes and fatalities occurring on interstate highways are included here.

Source: Texas Department of Transportation (TxDOT), Motor Vehicle Crash Statistics

ftp://ftp.dot.state.tx.us/pub/txdot-info/trf/crash_statistics/2009_update/12_2009.pdf

ftp://ftp.dot.state.tx.us/pub/txdot-info/trf/crash_statistics/2003_update/12_2003.pdf

In many cases, only fatalities (F) are reported without recording the

corresponding number of crashes (C), see data for Alabama, given below.

Fatalities in urban areas are generally lower than in rural areas, see

Alabama data, because crowded driving promotes greater alertness and

caution. Rural driving, with reduced traffic, on the other hand, promotes

inattentiveness, tendency to dose off and/or veer off the road and also risk

taking at super high speeds. The Texas data, however, defy this logic.

Table 1B: Fatalities in Alabama Interstates (1998-2007)

Year 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Total 1023 1028 1118 1110 1033 1040 1082 1113 1142 1190 Rural 634 665 754 742 661 722 727 749 757 772 Urban 389 363 364 368 372 318 355 364 385 418

Source: 1997 ALABAMA TRAFFIC ACCIDENT FACTS. Note that information

on the corresponding fatal crashes or the fatality rates (interstate VMT) is missing.

http://documents.crdl.ua.edu/docs/1997FactBook.pdf

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Also, methods must be developed to improve VMT estimates, specifically

as it applies to interstate highways, to avoid the criticism of VMT inflation/or

deflation, to arrive at a desired fatality rate. With these caveats, we will now

take a fresh look at the fatality data in three states: Iowa, Montana, and

Texas, because of some unique aspects of the data and all because this

data has also been analyzed before by other authors.

Before we proceed, let us quickly review the Utah war-years data since this

reveals an important property of traffic fatality statistics.

Figure 2: Graph of accidents versus fatalities in Utah during the war years when

the war speed limit of 35 mph was adopted in the state. The number of fatalities

appears to increase at a fixed rate as the number of accidents increase. Here

―accidents‖ includes all types – not just those that led to a fatality. The slope of the

straight line through the three points can be estimated using classical linear

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regression analysis. However, here we use the average value of the three slopes

obtained by consider any two of the three points in the data set. This average slope

h = 0.0475. (The slope of the best-fit line h = 0.478.) Since the straight line must

pass through all three points, the intercept c can be fixed by considering any one

data point. The equation of the straight line is y = hx + c and considering the (x, y)

values for 1942 we get c = - 86.23. This line can be seen to pass very close to the

(x, y) pairs for 1941 and 1943.

Notice that the both the VMT, x, and the number of fatalities, y, decreased

during the war years. The fatality rate, determined by the ratio y/x, also

decreased each year, from 13.58 in 1941 to 9.83 in 1942 and to 7.6 in

1943. The fatalities/accidents ratio also decreased from 0.034 to 0.03 to

0.026. The average value of this latter ratio is 0.0301. The x-y graph, of

accidents versus fatalities, reveals a nice linear trend, see Figure 2, with

the three data points falling almost on a perfect straight line. The equation

of this line is of the type y = hx + c = 0.0475x – 86.23, where the numerical

values of the slope h and intercept c were determined as described in more

detail in the figure caption. The fixed slope h = 0.0475 means that fatalities

increase at a constant rate as the number of accidents increase: we expect

475 additional fatalities per 10,000 additional accidents, or about 5

additional fatalities per 100 additional accidents. (The graph of VMT versus

fatalities, on the other hand, does NOT reveal such a nice linearity.)

The near-perfect linear trend observed in the war-years is almost certainly

due to the low speed limit. Vehicles of this era were obviously built very

differently from modern vehicles and had few safety features (not even

good tires, as noted in the article cited). Even a collision at a low speed led

to fatalities. However, even today, fatalities are observed at all speeds in

our roadways; see, for example, the annual Traffic Safety Facts 2009 by

NHTSA, link below, Tables 59 and 60 and Figure 24, even at ≤ 30 mph.

http://www-nrd.nhtsa.dot.gov/Pubs/811402EE.pdf

The greater predictability in the war-years data is certainly due to less

variability in road and driving conditions. It also suggests that the universal

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law describing the relation between the number of accidents and the

number of fatalities is a simple linear law, y = hx + c where x is the number

of accidents (or fatal crashes) and y is the number of fatalities. As we will

see shortly this universal law appears to be confirmed when we consider

the more recent data for the states of Iowa, Kansas, Montana, and Texas.

From the nature of the trends observed, there is little doubt that the same

would also be confirmed if we consider the data for every state and also the

national data, or even international data from other countries. This linear

law was already alluded to in the earlier report (see conclusions and also

discussion of Figure 4 in that first report).

Finally, when we consider all types of

accidents, or crashes (which includes those

resulting in injuries only and property

damage only), the constant h, as we see

here for Utah, has a very low value (less

than 1, or even 0.10, ≈ 0.05). Its value

cannot be predicted theoretically.

However, if we consider only fatal

crashes, and the law y = hx + c still applies,

the slope h = 1, ideally, since a single

crash must produce one fatality, 2 crashes

2 fatalities, and so on. Also, ideally, the

constant c = 0, since the number of

fatalities y must go to zero as the number of

crashes x goes to zero.

In the real world, h > 1, see sidebar, and

the greater the deviation from 1, the higher

the rate at which fatalities increase due to a

variety of factors (speed limits, road

conditions including weather, type of roadway, vehicle infrastructure, driver

behavior, and so on). Also, the constant c will be non-zero and can be

either positive or negative.

Fatal crashes at County Level

If we consider data at the

county level, for example, in

2009, in Michigan, there were

2 fatal crashes and exactly 2

fatalities in Manistee county,

i.e., (C, F) = (2, 2). In Alcona it

was (3, 3), Isabella (9, 9),

Jackson (12, 12). In other

counties, there were more

fatalities per fatal crash.

Example Macomb (37, 41),

Oakland (51, 53), Wayne

(149, 173). For the state as a

whole it was (806, 871).

http://www.michigantrafficcr

ashfacts.org/doc/2009/quick_

2.pdf . For the US a whole, it

was (30,797, 33,808) in 2009.

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Iowa Motor Vehicle Fatalities data

From 1970 to 1974 the speed limit on Iowa rural Interstates was 75 mph. In

1974, following the Arab oil embargo of 1973, a National Maximum Speed

Limit (NMSL) of 55 mph was imposed and adopted throughout the US

(reluctantly by some states). The Iowa speed limit was 55 mph.

Table 2: Fatal Crashes and Fatalities in Iowa

Year Crashes, x (fatal)

Fatalities, y F/C ratio, y/x

Comments on speed

limits

1970 38 57 1.50 75 mph day 1971 25 31 1.24 and 65 mph 1972 35 37 1.06 speed limit 1973 41 48 1.17 at night. 1974 23 24 1.04 NMSL takes 1975 29 40 1.38 effect in 1974 1976 20 27 1.35 I speed limit 55 1977 19 21 1.11 mph until 1978 27 28 1.04 1986. 1979 19 20 1.05 1980 22 30 1.36 1981 28 35 1.25 1982 15 22 1.47 1983 17 21 1.24 1984 13 15 1.15 1985 13 18 1.38 1986 13 14 1.08

1987 21 23 1.10 Up 65 mph on May 12, 1987

Average (1970-1986)

1.23

Last 4-yr. avg. 35 43 At 75/65 mph First 4-yr avg. 23 28 At 55 mph Last 4-yr avg. 14 17 At 55 mph

Source: http://www.iowadot.gov/mvd/ods/stats/2006speedstudy.pdf

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In 1987 the NMSL was partially repealed and speed limits were allowed to

increase to 65 mph. In 1995, the NMSL was fully repealed and each state

could set its own speed limit. In 2005, Iowa increased its rural interstate

speed limit to 70 mph.

Table 3: Fatal Crashes and Fatalities in Iowa

Year Crashes, x (fatal)

Fatalities, y F/C ratio, y/x

Comments on speed

limits

1988 28 35 1.25 Speed limit 1989 26 28 1.08 was 65 mph 1990 23 27 1.17 from 1988 1991 25 32 1.28 to 2004 1992 25 29 1.16 on all rural 1993 29 34 1.17 Interstates 1994 26 36 1.38 I in Iowa 1995 19 26 1.37 1996 20 30 1.50 1997 29 32 1.10 1998 25 34 1.36 1999 32 38 1.19

2000 35 41 1.17 2001 30 39 1.30 2002 22 25 1.14 2003 24 38 1.58 2004 16 23 1.44

2005 38 47 1.24 70 mph on July 1, 2005

Average (1988-2004) 25.53 32.2

1.27

First 4-yr avg. 26 31 At 65 mph Last 4-yr avg. 23 31 At 65 mph

The fatality-crashes data for the period 1970-1987 and for 1988-2005 are

reproduced in Tables 2 and 3 were obtained from a report released by Iowa

Department of Transportation, see links given below.

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http://www.iowadot.gov/mvd/ods/stats/2006speedstudy.pdf

http://www.topslab.wisc.edu/workgroups/TSC/Speed_Limit_Lit_Review-

Updated_071405.pdf Impact of Raising Speed Limits onTraffic Safety, by

Arup Datta and David A. Noyce

Let us first consider the data for the more recent period, 1988-2005, in

Table 3. The authors of the above report compared the fatalities after the

speed limit was increased on July 1, 2005 with the average fatalities in the

first and last four year periods (1988-1991) and (2001-2004), see last two

rows, before the increase. An average of 26 crashes, with an average of 31

fatalities, were observed during the first-four year period at 65 mph. Fewer

crashes, 23, with exactly the same average number of fatalities were

observed in the last-four year period of the 65 mph era. The number of fatal

crashes and fatalities jumped to 38 and 47, respectively, when the speed

limit was raised to 70 mph.

Can we now say, unequivocally, based on these four-year-average-fatality

calculations, that the jump in 2005 was entirely due to the higher speed

limit? Or, are there other factors, besides the increased speed limit, that

must be considered to assess this situation?

Or, consider the situation before the adoption of the NMSL of 55 mph. In

the last-four year period (1970-1973) before the NMSL, the average

crashes and fatalities were 35 and 43, respectively. In the first four-year

period after adoption of 55 mph, the number of crashes had dropped to 23

and the fatalities had dropped to just 28. Was this again entirely the result

of the lower 55 mph speed limit? Likewise, in the last-four year period

(1983-1986) of the 55 mph speed limit, the average number of crashes and

fatalities had dropped even more to 14 and 17, respectively. Was this again

the beneficial effect of the 55 mph speed limit over a long and sustained

period? It then increased again in 1987, after the partial repeal of NMSL.

A careful examination of all of the data in Tables 2 and 3, at both the 65

and 55 mph speed limits, suggests the following.

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1. The number of fatalities, y, is always greater than the number of

crashes, x. By definition, a fatal crash is a crash where there is at least

one death. Often, however, more than one person dies when there is a

fatal accident. The fatalities/crashes ratio F/C ratio, or y/x, is always

greater than 1.0. This is indicated in the calculations in the fourth

column. The average value of the F/C ratio, or y/x ratio, is 1.27 in the

more recent period (1988-2005) and 1.23 in the earlier era (1970-1987).

2. The higher the number of crashes the higher the number of fatalities.

Considering the period 1988-2005, Table 3, with 20 crashes, there were

30 fatalities. With 30 crashes, there were 39 fatalities. With 25 crashes,

there were only 34 fatalities. With 35 crashes, there were 41 fatalities.

And so on. This suggests that the x-y scatter graph must have a nice

upward trend. The data here suggests that with x = 10, y = 9, and the

rate of change h = y/x = 9/10 = 0.9. Many such values of the slope h

can be calculated and an average determined. The classical statistical

method, known as linear regression analysis (also called least squares

method), permits a determination of the slope of the so-called best-fit

line through many such (x, y) pairs.

The graphical representation of the fatalities-crashes data from Table 3

indeed reveals a nice upward trend, see Figure 3. The best-fit line through

the data points has the equation y = hx + c = 1.215x + 0.118 where the

slope h = 1.215 and the intercept c = 0.118. Ideally, the intercept c = 0

since we know that y = 0 when x = 0, i.e., when the number of crashes

goes to zero, the number of fatalities must also be zero. The small positive

value of the intercept is the result of statistical variations (see also the brief

discussion in appendix 1 on this point). Many factors besides being in a

crash determine if the occupant will actually die – age and prior health also

being significant factors that cannot be overlooked. Also, the rapid access

to emergency medical services (EMS) determines whether a severely

injured occupant can survive. Furthermore, the age and condition of the

vehicle and how well it is maintained (apart from the basic manufacturer‟s

vehicle design and engineering) could be contributing factors that make a

IoKsMTxStudy Page 20 of 60

bad situation worse in the event of a crash. All such factors introduce

statistical “noise” and affect the numerical value of the constant c in the

linear law y = hx + c revealed here.

Notice also that the slope of the best-fit line h = 1.215 is comparable to the

average slope h = 1.23 determined from the seventeen values of the y/x

ratio in Table 2. Indeed, it can be shown that as the number of data points

increases, the average slope h would ultimately tend asymptotically to the

value determined using the linear regression analysis.

Figure 3: Graphical representation of the fatalities-crashes data for the period

(1970-1987). A nice upward trend is revealed here which simply means that the

higher the number of (fatal) crashes, the higher the number of fatalities. The

classical statistical method known as linear regression analysis yields the best-fit

equation y = 1.215x + 0.118. The correlation coefficient r2 = 0.831 implies a

IoKsMTxStudy Page 21 of 60

strong positive correlation between the variables x and y considered here. One can

now extrapolate using this equation to predict the number of fatalities with higher

or lower number of crashes, x. This also permits an unbiased assessment of the

effect of increased speed limits on our highways. The best-fit equation can be used

to predict the number of fatalities for 35 crashes, the average number of crashes in

the last-four year period (1970-1973) before the adoption of the NSML of 55 mph.

It can also be used to predict the number of fatalities immediately following the

repeal of the NSML and the new higher speed limit. Amazingly, for x = 35, the

best-fit prediction yb = 42.64 or 43 fatalities, exactly what was calculated in the

earlier report. Also, for x = 21, yb = 25.63 or 26 fatalities. The actual number of

fatalities observed after the partial repeal of the NSML in May 1987 was just 21.

Since the number of fatalities will increase or decrease, as the number of

crashes increase or decrease, we can estimate the number of fatalities by

simply extrapolating from the best-fit line. Predictions of the number of

fatalities based using the best-equation suggest that the higher fatalities

observed in the four-year period, before the adoption of the NSML of 55

mph, and in the year immediately after its partial repeal in 1987, are

consistent with the predictions of the best-fit equation for the period when

the speed limit was 55 mph.

The number of fatalities increased in 1987, and again in 2005, because

the number of fatal crashes also increased. The increase in fatalities

is consistent with the predictions based on an extrapolation from the

best-fit equation deduced for the 55 mph era. Thus, it is clear that the

higher speed limits in 1970-73, or in 1987, did not play any statistically

significant role.

This is confirmed by the graphical representation of the pre-NSML data

(with speeds limits of 75/65 day/night) and 1987 data following the partial

repeal of NSML in 1987 (65 mph). The five solid dots in Figure 4 represent

this data and are simply superimposed on to the earlier plot of Figure 3.

With just one exception, (38, 57) for the year 1970, the other four data

points lie on or very close to the best-fit line deduced from the analysis of

the data for the 55 mph speed limit. This implies that the universal law y =

IoKsMTxStudy Page 22 of 60

hx + c holds at all speed limits and the number of fatalities y increase or

decrease as the number of crashes x increase or decrease. The higher

fatalities observed after the speed limit was increased are not significantly

higher than the fatalities that would have been observed, at the lower

speed limit. Hence, the speed limit per se does not affect the number of

fatalities and is not a significant contributing factor.

Figure 4: Graphical representation of the fatalities-crashes data for the period

1970-1987. The five solid dots represent the data for the four years prior to NSML

(1970-1973) and the single year following the partial repeal of NSML (1987). Four

out of five data points fall at or close to the best-fit line deduced by considering

only the data for the NSML era. This means that the speed limits per se do not

affect the number of fatalities observed here, or account for the increased number

of fatalities. We are merely observing the universal law y = hx + c with fatalities

increasing as the number of (fatal) crashes increase. Factors other than the speed

IoKsMTxStudy Page 23 of 60

limit are probably the reason for the higher number of fatalities observed in 1970

and can be investigated to arrive an improved understanding of this problem.

The reason why the 1970 data point (38, 57), at the higher speed limits

(75/65) appears as an outlier on this graph certainly needs further

investigation. The higher fatalities in this instance are most likely due to

factors unrelated to the speed limit per se, some of which have been

mentioned briefly already. Notice also that for the year 2005, when higher

speed limits (70 mph) were again introduced, 38 crashes produced 47

fatalities, see Table 3, and also the data graphed in Figure 5.

Figure 5: Graph of the Iowa fatalities-crashes data for 1988-2005. The average

value of the F/C ratio for these years is 1.273. A linear regression analysis can

once again be carried out to determine the best-fit line through the data points.

This is presented in Figure 5. Instead, here we first consider first the dashed line

IoKsMTxStudy Page 24 of 60

with the equation y = 1.273x with the slope being the average value just

determined. This passes through the origin (0,0) and the data can be seen to follow

this line quite closely, with some scatter. Quite amazingly, the data point (38, 47)

for 2005, at the higher speed limit, falls almost exactly on this line, suggesting that

the higher fatalities observed in 2005 were due entirely to the higher number of

crashes and not the increase in the speed limit.

Consider now the best-fit line through the points in Table 3, see Figure 6.

Once again, we see that the data for 2005, when the speed limit was 70

mph, follows the extrapolated best-fit line, and falls just above it. Some

additional comments are relegated to appendix 2.

Figure 6: Graph of the Iowa fatalities-crashes data for 1988-2005, with the best-fit

line y = 0.908x + 8.99, through the data points. The best-fit line has a finite

positive intercept c = 8.99 which means that when crashes x = 0, there is still a

IoKsMTxStudy Page 25 of 60

finite number of fatalities y = 9 (whole number). Also, the slope of the best-line h =

0.908 is less than 1 whereas all observations indicate that the F/C ratio > 1. (This

is also true if we consider data from other states and for the US a whole. The F/C

ratio is always greater than 1.) However, the statistical basis of linear regression

analysis is a very sound one and this suggests that factors other than just the

increased speed limit must be carefully considered to understand the difference

between the two sets of data. In both cases, the increase in the number of crashes

and led to the increase in the number of fatalities but the circumstances

surrounding these crashes, and hence the number of fatalities must also be

considered more carefully. Nonetheless, the effect of increased number of crashes,

as opposed to the speed limit per se, is evident even if we use the best-fit line to

extrapolate to determine the number of fatalities.

Finally, for completeness, the composite graph which includes all the data

from Table 2 and 3, for 1970-2005, is presented in Figures 7 and 8. The

different data symbols represent data for different speed limits. The dashed

line, in Figure 8, with the equation y = 1.25x has a slope h = 1.25, which is

the “average” value of the slope for the two data sets in Tables 2 and 3.

The best-fit line through the data points was also recalculated. The slope h

= 1.200 is higher, see Figure 8, representing the influence of the data from

all the speed limits. More importantly, the intercept c is now very nearly

zero, having just a small positive value of c = 1.02. All the data points, from

all the different speed limits are scattered around this recalculated best-fit

line suggesting no significant effect of the speed limit per se. The number

of fatalities increased because the number of (fatal) crashes increased.

Hence, rather than being distracted by the divisive debate regarding the

speed limit, we should focus on understanding the reasons why a crash,

especially a fatal crash occurs and develop control strategies to either

minimize or eliminate such crashes.

IoKsMTxStudy Page 26 of 60

Figure 7: Composite plot of all the Iowa fatality data for 1970-2005, confirming

the linear law y = hx + c. Different symbols are used to denote data generated

during the years with different speed limits. A significant positive deviation of an

individual data point from the best-fit line, or the line with the ―average‖ slope h

= 1.23, implies that special factors that led to increased fatalities in that year need

more careful investigation. Fewer crashes actually led to more fatalities in that

year, even with the same speed limits prevailing.

This does NOT imply that higher speed limits are of NO consequence and

must be whole heartedly embraced. It only means that we must understand

the underlying reasons why a fatal crash occur, with the high speed limit

being just one of many contributing factors.

IoKsMTxStudy Page 27 of 60

Figure 8: Composite plot of the Iowa fatality data for the years 1970-2005. The

solid line with the slope h = 1.20 is the recalculated best-fit line. This has a very

small positive intercept c = 1.02. The dashed line has the ―average‖ slope h =

1.23 considering both data sets from Tables 2 and 3.

One important factor that continues to be important, in spite of the

strict seat belt laws enacted in practically all states, is the very high

correlation between fatality and the failure to use seat belts.

Perhaps, manufacturers should be required to ensure that seat belts

are automatically deployed and the vehicle made inoperative when

seat belts are not used – not only by the driver but also by every

single passenger – just as we have sensors that tell us when any

single door is not properly secured/closed.

IoKsMTxStudy Page 28 of 60

The Montana No Speed Limit Safety Paradox

http://en.wikipedia.org/wiki/Speed_limits_in_the_United_States#No_speed_limit

http://www.us-highways.com/montana/mtspeed.htm

A typical speed limit sign at the Montana state line from December 1995 to June

1999. On March 10, 1996 a Montana patrolman issued a speeding ticket to a

driver traveling at 85 mph (136 kmph), on a stretch of State Highway 200.

Although the officer gave no opinion as what would have been a reasonable speed

limit, the driver was convicted. He appealed to the Montana Supreme Court. The

court reversed the conviction on December 23, 1998. It held that the law requiring

drivers to drive at a non-numerical ―reasonable and proper‖ speed limit is so

vague that it violates the Due Process Clause … of the Montana Constitution.

Effective May 28, 1999, the Montana Legislature therefore established a speed

limit of 75 mph (121 kmph). Technically speaking, Montana had no speed limit

until June 1999.

http://www.hwysafety.com/hwy_montana_2001.htm

http://www.motorists.org/press/montana-no-speed-limit-safety-paradox

http://www.hwysafety.com/MDT_reply_82001_section3.htm

IoKsMTxStudy Page 29 of 60

http://forums.thecarlounge.com/showthread.php?2553995-Are-Speed-

Limits-Really-Necessary

The data and findings given below, including the highlighted tables, are

extracted verbatim from the article by Chad Dornsife (link above).

Interstates: 4 Lane Divided

1998: No Daytime Speed Limits

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

4 0 2 4 5 1 5 4 0 1 3 2

Jan - June Average Month: 2.7 July - Dec Average Month: 2.5

1999: No Daytime Speed Limits

75 Maximum Speed Limit

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

2 2 4 2 1 0 2 7 4 1 1 4

Jan - May Average Month: 2.2 June - Dec Average Month: 2.7

2000: 75 Maximum Speed Limit

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

4 2 8 5 2 7 7 3 4 1 6 7

Jan - May Average Month: 4.7 June - Dec Average Month: 4.7

Last 12 months/No Daytime Limits

2000: W/Speed Limits Reinstated

27 Fatals / Modern Low 56 Fatals / Modern High

Here is what the Montana data shows (chart below). After all the politically correct

safety programs were in place and fully operational, complete with federal safety

funds, more laws and citations being issued, here are the results.

IoKsMTxStudy Page 30 of 60

1. After the new Speed Limits were established, interstates fatal accidents went

up 111%. From a modern low of 27 (11 + 16 for June 1998 –May 1999)

with no daytime limits, to a new high of 56 (28+28 in 2000) fatal accidents

with speed limits.

2. On interstates and federal primary highways combined, Montana went from

a modern low of 101 with no daytime limits, to a new high of 143 fatal

accidents with speed limits.

3. After a 6 year downward trend in the percentage of multiple vehicle

accidents on its 2 lane primary highways, multiple vehicle accident rates

increased again.

4. With the expectation of higher speed when there was no daytime limit,

Montana’s seat belt usage was well above the national average on its

highways without a primary law, lane and road courtesy increased, speeds

remained relatively stable and fatal accidents dropped to a modern low.

After the new limits, fatal accidents climbed to a modern high on these

classifications of highway, road courtesy decreased and flow conflict

accidents rose again.

All the important observations made in original research paper remain very

germane in regards to this doubling of fatal accidents on Montana’s highways.

(February 2000, Montana: No Speed Limit Safety Paradox) The following excerpts

tell the story.

“Research scientists and engineers have long known that there are sometimes

unexpected results from changes in public policies. Ironically, the paradox of no

posted speed limits and low fatal accidents rates is no surprise to the traffic

safety engineering community.” End of verbatim quote from Dornsife.

1996, Officer Steve Wisniewski.

http://www.montanatrooper.com/userfiles/fall2010/fall_2010_cover_story.pdf

IoKsMTxStudy Page 31 of 60

Counterpoint: The tabulated data from Dornsife supports point 1 above.

The same data also permit a different interpretation. Consider the non-

consecutive periods of Jan-June 1998 and June-Dec 1999. Between Jan-

June 1998, when there was no daytime speed limit in Montana, the total

fatalities was 16 and the 6-month average was 2.7 (16/6 ≈ 2.7 ), the same

as the average for the 7-month period (19/7 ≈ 2.7) from June-Dec 1999,

when the 75 mph speed limit was imposed. In other words, there is NO

SIGNIFICANT CHANGE in the monthly average fatalities.

State data from NHTSA: The following data was obtained from the

NHTSA annual reports entitled Traffic Safety Facts. For 1998, Table 106 of

page 160 indicates that there were 30 fatal crashes in rural interstates in

Montana and 0 fatal crashes in urban interstates. The total fatal crashes

and fatalities (Table 104) were 208 and 237, respectively, including all

types of roadways.

Montana Rural and Urban Interstates Fatalities-Crash data

Year Rural

crashes

Urban

crashes

Rural

fatalities

Urban

fatalities

1997 50 1 58 1

1998 30 0 33 0

1999 35 1 41 1

2000 30 4 33 4

2001 35 2 40 2

2002 48 0 59 0

2003 43 0 47 0

2004 37 1 40 1

Source: NHTSA Annual Reports, Chapter 5. Notice the huge contrast with Texas.

For 1997, Table 106 of page 154 states that there were 50 fatal crashes in

rural interstates in Montana and 1 fatal crash in urban interstates. The total

fatal crashes and fatalities (Table 104) were 223 and 265, respectively,

including all types of roadways. The information on fatalities in the rural

and urban interstates was similarly obtained from accompanying tables.

IoKsMTxStudy Page 32 of 60

Notice the big difference in the number of rural interstate fatal

crashes, 50 and 30, for 1997 and 1998, both years for which Montana

had the Reasonable and Prudent speed law. The corresponding

fatalities were 58 and 33. In other words, such large year-to-year

variability, or even month-to-month variability, in the data is expected

and does not necessarily have anything to do with the speed limit.

The jump for 27 to 56 fatalities, between 1999 and 2000, as noted by

Dornsife, is nothing out of the ordinary.

http://www.ibiblio.org/rdu/a-montge.html http://www.ibiblio.org/rdu/dotst-mo.html

Figure 9: Fatalities-Crashes data for Montana (1997-2004) obtained from the

annual NHTSA Traffic Safety Reports (chapter 5). For 1997 and 1998, Montana

had the Reasonable and Prudent (R & P) speed law. The data points (51, 59) and

IoKsMTxStudy Page 33 of 60

(30, 33) for these two years is indicated by the two filled diamonds. The equation

of the straight line joining these two points is y = hx + c = 1.24x – 4.14. All the

other data (solid dots) are with the 75 mph speed limit. The fatalities data after the

introduction of a numerical speed limit follows this straight line (deduced with the

R & P speed law). Fatalities increase as the number of crashes increase. Notice

also the very large change in the number of fatal crashes in the two years with the

R & P speed law.

Figure 10: Montana statewide fatalities-crashes data for the most recent period

1994-2009. The NSML was fully repealed in 1995. Notice that the same universal

relation is revealed. Furthermore the numerical value of the constant h in the

relation y = hx + c also appears to be roughly constant when we consider

IoKsMTxStudy Page 34 of 60

fatalities-crashes data for rural and urban interstates (Figure 9) or all roadways

taken together.

Finally, as seen in Figures 10 and 11, the universal fatalities-crashes law is

also confirmed when we consider the Montana fatalities data for all

roadways for the recent period 1994-2009 (after the repeal of NSML in

1995 and the R&P law in 1999) and also the earlier period 1978-2009, with

NSML. The data for all these periods follows a nice linear trend, suggesting

again that speed limits per se do not affect the number of fatalities. The

number of fatalities only seems to depend on the number of crashes.

Figure 11: The statewide Montana fatality-crash data for the period 1978-2009,

with different speed limits. All data, regardless of the prevailing speed limit follow

the same straight line y = hx = 1.142x where the slope h of the straight line is

taken as the average value of the F/C ratio for all the years taken together.

IoKsMTxStudy Page 35 of 60

Figure 12: The Montana data for the period 1978-2009 with the best-fit line

superimposed on to the data along with the straight line with a slope equal to the

the “average” value of the fatalities/crashes = F/C ratio. This is called the

“average” slope line. This average slope h = 1.142 is very nearly equal to the ratio

m = ym /xm = 241/211 = 1.142 where xm and ym are the average values of x and y.

Both these lines, the one with the “average” slope and the best-fit line always

passes through the point (xm,ym). The line with average slope (ym/xm) passes

through the origin whereas the best-fit line pivots about the point (xm,ym) and

makes a finite positive or negative intercept on the y-axis. This pivoting of the

best-fit line occurs because, mathematically, the best-fit is an attempt to minimize

the squares of the vertical deviations (y – yb) of each data point from the best-fit

trend line; see also the discussion in appendix 1.

IoKsMTxStudy Page 36 of 60

Additional comments on the Montana data

Montana DOT data: The following information was obtained from the

report by Montana DOT, see link below, which provides the fatalities and

crash data for the 10-yr period 1997-2006. According to the data in Table 1,

the total number of fatalities was exactly the same, 237, in 1997, with R & P

speed law, and also in 2000, when the speed limit was 75 mph.

http://www.co.missoula.mt.us/healthpromo/DUITaskForce/pdfs/2008StateR

eport.pdf

Montana’s scenery. Photo of Butte, MT provided by driving enthusiast John

Watne, Montanabahn vs Autobahn http://home.comcast.net/~jwatne/autobahn.htm

The higher fatality number for 2000 given here is because fatalities in all

roadways is included, not just the fatalities on the Interstates. There were

208 fatal crashes in 1997 and 203 fatal crashes in 2000 but the 5 fewer

crashes in 2000 still produced the same total fatalities.

IoKsMTxStudy Page 37 of 60

Also, from Table 3 of this report, we see that the fatality rate (per 100 M

VMT) was actually higher in 1997 (2.84) and 1998 (2.50), with no numerical

speed limit, compared to 2000 (2.40) suggesting a beneficial effect of the

speed limit.

http://lubbockonline.com/news/021597/in.htm

The above, from 1997 Lubbock Avalanche-Journal, includes brief

comments following the debate in the Montana legislature on the speed

limit. One lawmaker argued that a limit is need because traffic deaths on

Montana's interstates doubled from 1995 to 1996: from 16 to 32. Added

Attorney General Joe Mazurek: ''I'm glad the Senate debated it, but I can't

help but ask: How many people have to die before we need a speed limit?''

http://www.deseretnews.com/article/466857/MONTANA-TROOPER-SAYS-

DRIVERS-ARE-MISTAKEN-ABOUT-SPEED-LIMIT.html

http://books.google.com/books?id=u_kSIrzxxKQC&pg=PA316&dq=montan

a+1997+interstate+fatalities&hl=en&ei=HLjpTYCdIuru0gGAn5WgAQ&sa=X

&oi=book_result&ct=result&resnum=2&ved=0CD4Q6AEwAQ#v=onepage&

q=montana%201997%20interstate%20fatalities&f=false

Montana: The Great Experiment by Kevin Atkinson. The second link above

gives the % of drivers exceeding various speeds when there was no

numerical speed limit is Montana. In Urban Interstates, only 5% exceeded

75 mph and none exceeded 80 mph. In rural interstates, 8% exceeded 75

mph and less than 3% exceeded 80 mph and under 1% exceeded 85 mph.

http://leg.mt.gov/content/Publications/Audit/Report/98l-11.pdf

http://nakedlaw.avvo.com/2011/05/would-highways-be-safer-with-no-

speed-limits/

http://www.ipenz.org.nz/ipenztg/papers/2002/11_Patterson.pdf

http://www.us-highways.com/montana/mtspeed.htm

IoKsMTxStudy Page 38 of 60

The Texas Interstate Traffic Fatalities-Crashes

Letter: Don't reward lawbreakers with higher speed limits Posted April 15, 2011 at 5:51 p.m

http://www.reporternews.com/news/2011/apr/15/dont-reward-lawbreakers-with-higher-speed-limits/

Why on earth are we raising our speed limits in Texas?

It is a proven fact that lower speed limits at around 55 mph make most cars get better gas

mileage. We should be lowering them, not raising them………………

******************************************************************************

As we see from Table 1A and Table 1B, urban fatalities in Texas are

significantly higher than rural fatalities. Is this due to the much publicized

higher speed limits in Texas?

However, if we look at the pattern so far, this may be simply be due to the

higher number of urban crashes in Texas. The linear law, y = hx + c,

relating crashes and fatalities applies for both sets of data, see Figure 13.

Also, and interestingly also, extrapolating to higher number of crashes

using the rural best-fit line, it is clear that the number of urban fatalities in

Texas is indeed significantly lower. Alternatively, extrapolating from the

urban best-fit line shows that the number of rural fatalities is significantly

higher. This suggests a more careful study of the nature of crashes in these

sections of the Texas interstates and also the emergency responses

available to crash victims.

IoKsMTxStudy Page 39 of 60

Figure 13: Graph of fatal crashes versus fatalities in rural and urban Interstates

in Texas. The data reveals a very high positive correlation between crashes, x, and

fatalities, y, with a high +ve value of the correlation coefficient r2.

Texas Motor Vehicle Crash Statistics – 2009 http://www.txdot.gov/txdot_library/drivers_vehicles/publications/crash_statistics/default.htm

2009 l 2008 l 2007 l 2006 l 2005 l 2004 l 2003

Furthermore, and even more significantly, we see that the best-fit line has a

negative intercept c for both rural and urban data. Theoretically speaking,

when the number of crashes goes to zero (x = 0), the number of fatalities

must also go to zero (y = 0). Hence, the ideal value of the constant c = 0

IoKsMTxStudy Page 40 of 60

and the best-fit line must pass through the origin. However, as we see

here, in the real world the intercept c is sometimes positive (as in the data

for Iowa, this means higher fatalities than should be theoretically achieved,

for the number of crashes) and sometimes negative, as we see here for

Texas.

This actually means that the number of fatalities in both rural and

urban interstates is less than what might be observed if c = 0. The

data for Montana reveals the nearly ideal situation (c ≈ 0), with the

intercept c having a very small positive value. However, the Texas

data shows that even further reductions in fatalities are responsible.

Additional discussion of the significance of the constant c in the linear law,

y = hx + c, relating crashes and fatalities, is relegated to appendix 1.

Selection of Iowa statewide crash-fatality data

at various speed limits

Year Speed limit,

mph Fatal Crashes, x Fatalities, y

1970 75 752 912 1973 75 682 813 1975 55 578 674 1976 55 663 785 1986 55 388 441 1989 65 452 515 1993 65 399 457 1995 65 446 527 1997 65 411 468 2005 70 399 451 2006 70 386 439 2009 70 337 370

Average 491 571 Source:http://www.iowadot.gov/crashanalysis/pdfs/historicaltravelcrashesfatalitiesrates_1970-2009_20100706.pdf

IoKsMTxStudy Page 41 of 60

Iowa Statewide Crash Data and Changing Speed Limits

Finally, to illustrate the effect of both the speed limit and the efficacy of the

(fatal) crash-fatalities analysis emphasized here, consider the following

statewide data for Iowa. The historical data from 1970-2009 has been

compiled by the Iowa Department of Transportation and made be found at

the link given below.

http://www.iowadot.gov/crashanalysis/pdfs/historicaltravelcrashesfatalitiesrates_1

970-2009_20100706.pdf

Figure 14: Graph of the statewide Iowa fatal crashes-fatality data which covers the

40-year period 1970-2009 when Iowa had four different speed limits: 75 mph (data

indicated by filled triangles) in 1970-1973, dropping to 55 mph (filled diamonds)

IoKsMTxStudy Page 42 of 60

on Jan 1, 1974. The speed limit was raised to 65 mph (filled squares) on rural

interstates on May 12, 1987. In 1996, the speed limit was raised to 65 mph in rural

4 lane highways and on July 1, 2005 the speed limit was raised to 70 mph (filled

circles) on rural interstates. The open circle near the center of the graph is the mean

point (xm, ym). The best-fit line passes through this mean point. The data reveals a

near-perfect positive correlation with a regression coefficient r2 = 0.999. Perfect

correlation would be indicted by r2 = +1.000. The crash-fatality data at different

speed limits simply follow this best-fit line.

Although only a small selection of the data, extracted in the table here, has

been considered, the statewide observations reveal a remarkable trend

with near-perfect correlation between the number of fatal crashes and

fatalities, even with changing speed limits. The higher the number of fatal

crashes, x, the higher is the number of fatalities, y. It appears that exactly

the same number of crashes and fatalities might have been observed if

there had been no change in the speed limit.

However, it must be pointed out that the 40-year data considered here

does indicate that the two of the highest crash numbers were observed at

the highest speed limit of 75 mph (the two triangles near the top of the

graph). Also, the three lowest crash numbers occurred at 70 mph (the filled

circles near the bottom of the graph), after the most recent change in the

speed limit in July 2005. The 55 mph and 65 mph data fall in the middle.

Hence, it appears that instead of entering into a futile debate on the speed

limits, greater attention must be paid by traffic researchers and safety

experts to understand the conditions and factors that

Lead to a crash in the first place.

Promote survival of the vehicle occupants in the event of a crash

and/or minimize their injuries. (Sometimes, unfortunately, third

parties, such as pedestrians, bicyclists, etc. are killed in a motor

vehicle crash, especially in other third world countries, where a

motorist has to combat a variety of other transportation methods.)

In addition to the speed limit, and the urgent need to “Texas Proof” vehicles

of the future by various manufacturers as speed limits continue to rise,

IoKsMTxStudy Page 43 of 60

ultimately it is the interaction of the following that determines the type of

vehicle that will be offered to the consumer in the future.

First, there can be no doubt that a lower speed offers more control and

ability to avoid a crash in an emergency situation, or when road hazards

are encountered unexpectedly (could even something as simple as a sharp

bend on the road, which led to a fatal crash recently with a photograph of

the crashed vehicle, as highlighted in the earlier report).

Second, a manufacturer must consider the interaction of the following:

Speed → Crash → Safety → Weight → Fuel economy

All these factors must be taken together to arrive at a societal compromise

which dictates vehicle design and engineering and what is offered to the

consumer. The higher the vehicle weight, the lower the fuel economy,

although such a heavier vehicle would probably be more crashworthy and

promote safety of its occupants in a crash. Safety and crashworthiness are

tied to speed which determines the energy that must be absorbed by the

vehicle infrastructure.

There is also the legal ramification of how much any vehicle manufacturer

should be expected to do in terms of vehicle design and engineering to

keep a driver in Texas safe, in a crash at 90 mph or 100 mph. Just like

CAFÉ standards and emission standards led to the development of all

electric (GM‟s EV) and hybrids, rising speed limits will force manufacturers

to either rebel and force back such laws, or innovate! There was never a

better time to be a materials scientist in charge of developed advanced,

high strength and lightweight materials that could be manufactured at a

cost lower than dirt.

Lighter than air (not quite!) – Stronger than steel - Cheaper than dirt!

Does the need to meet CAFÉ standards conflict, from a purely technical

standpoint, with the need to keep vehicle occupants safe in Texas?

Indeed, the discussion of exactly these factors was the topic of a workshop

IoKsMTxStudy Page 44 of 60

sponsored recently (on Feb 25, 2011) by NHTSA (details included as

appendix 2 with links to presentations by various experts).

http://www.nhtsa.gov/Laws+&+Regulations/CAFE+-

+Fuel+Economy/NHTSA+Workshop+on+Vehicle+Mass-Size-Safety

Even in Montana, when the law only specified a “reasonable and prudent”

speed, motorists, especially out-of-state motorists, found themselves being

ticketed for speeding and failing to obey the reasonable and prudent

standard. One such driver challenged his ticket (although convicted) and

went to Montana Supreme Court which then agreed that the Montana law

was so vague as to be unconstitutional. Lawmakers were therefore forced

to adopt the numerical 75 mph speed limit. 80 mph or 90 mph or even 100

mph might seem safe, or reasonable, or even prudent to a few (perhaps,

the 15% who always seem to be traveling above the posted speed limit, if

one accept the 85th percentile rule to fix the speed limit). However, they still

have to share the road with the remaining 85% whose lives cannot be

threatened and who must not be put in a dangerous situation to avoid a

collision with the happy speedster!

Texas Legislator Pete Gallego unveiling a new 80 mph speed limit sign on

Interstate 10 near Fort Stockton, Texas.

IoKsMTxStudy Page 45 of 60

Kansas Speeding-related Crashes-Fatalities

Year 1990 1991 1992 1993 1994 1995 1996 1997

Crashes, x 123 103 93 93 91 105 112 99 Fatalities, y 142 118 106 105 101 116 122 109 Speed limit 65 65 65 65 65 65 70 70

Year 1998 1999 2000 2000 2001 2002 2003 2004 2005

Crashes, x 113 108 108 106 111 119 112 94 100 Fatalities, y 123 129 119 113 134 140 127 114 118 Speed limit 70 70 70 70 70 70 70 70 70

Year 2006 2007 2008 2009 2010 2011 2012 2013 2014

Crashes, x 111 89 87 n/a n/a Fatalities, y 118 99 97 n/a n/a Speed limit 70 70 70 70 70 75 75 75 75

http://www.marc.org/Transportation/safety/pdf/2000%20Kansas_Traffic_Accident

_Facts_Book.pdf Data for 1990-2000

http://www.ksdot.org/burTransPlan/prodinfo/accista.asp Click on speed to get data

for 1998-2008

******************************************************************

The Kansas legislature recently approved an increase in the speed limit to

75 mph, as reported in the Wichita Eagle on April 4, 2011 (see link below).

http://www.kansas.com/2011/04/10/1801633/will-higher-speed-limit-mean-

more.html

An officer of the Kansas Highway Patrol thinks this means drivers will be

doing 80 or 85 mph. Does it necessarily mean more accidents or more

deaths? The data compiled here, however, yields conflicting interpretations.

Considering only the speeding-related crashes in Kansas, there were

exactly 111 crashes in 2001 and again in 2006 but with 134 fatalities in

IoKsMTxStudy Page 46 of 60

2001 as opposed to only 118 in 2006. The speed limit was the same in

both years. On the other hand, 103 crashes in 1991, when the speed limit

was 65 mph resulted in 118 fatalities. The same fatalities were reached

with just 100 crashes in 2005 when the speed limit was raised to 70 mph.

The crashes-fatalities graphs, presented in Figures 15 and 16 again reveal

no significant effect of the speed limit. The data for both speed limits clearly

overlap and follow the best-fit equation relating crashes x and fatalities y

deduced by considering the data for the 70 mph era.

Figure 15: The data for speeding related crashes are readily obtained from the

Kansas Department of Transportation website (see links given). As seen here,

when the number of crashes x increases, the number of fatalities y increases and

seems to follow the predictions based on classical linear regression analysis. The

IoKsMTxStudy Page 47 of 60

linear regression coefficient r2 = 0.698 is quite high. As included is straight line

the ―average‖ slope which passes through the mean point (xm, ym). The best-fit line

also passes through this point but pivots to either a higher or lower slope

depending on the ―scatter‖ in the data. The slope of the best-fit line is determined

to minimize the sum of the squares of the vertical deviations of each (x, y) pair in

the data set from the best-fit line.

Figure 16: The speeding-related fatalities-crashes data for 1990-1995, indicated

by the black solid dots, are superimposed here to the graph in Figure 15. These

data are intermingled with the 70 mph data and follow the best-fit line deduced

earlier suggesting no statistically significant effect of the increased speed limit on

the Kansas speeding-related fatalities, after the repeal of the NSML in 1995.

IoKsMTxStudy Page 48 of 60

Finally, the following comments, posted on the internet by readers of the

above news item (on increasing the speed limit in Kansas to 75 mph), are

revealing. It starts with the sad statement from the parent of a young 18

year old who was killed in an accident when he was driving at 65 mph. He

was not speeding. The current speed limit in Kansas is 70 mph.

The Clutter Cutter

My 18 year old son was going 65 mph (NOT

speeding) when he crashed on the turnpike and

yet speed impacted the severity of his crash (he

was killed). When the speed limit is legally raised, I

will NOT be driving that fast. All you have to do is

see what a 65 mph crash does to a car and a loved-

one’s body, and you will never go that fast again.

04/10/2011 02:56 PM

TyrannyResponseTeam

Sorry to hear about your loss but you are unsafe at

any speed in a car. Even sitting at a light.

04/11/2011 03:13 PM

in reply to The Clutter Cutter

ShaneVendrell

Reasonable and prudent...Where can I find some of these huuuuuge tracts of land?

04/10/2011 02:53 PM

Effect of high speeds

Narrowed field of vision (tunnel vision)

Less effective safety cushion of maneuvering space

o Greater stopping distances

Reduced ability to safely negotiate curves,

Reduced ability to react to other motorists encroaching on their lane of travel, and avoid a collision.

Source:

http://www.policechiefmagazine.or

g/magazine/index.cfm?fuseaction=d

isplay_arch&article_id=1001&issue_i

d=92006

IoKsMTxStudy Page 49 of 60

cafanter

Montana was like that in the 90s.

You could set your cruise around

90-100 if you had a newer car. At

night it dropped to 65 and

Montana would warn you at

70mph.

04/10/2011 03:19 PM

milehighks

Yea.. this is good news. Although

this will cutdown on the laughing

at the Colorado drivers who

forget to slow down after they

cross the border.

Tippycanoe

BAD POINTS

1. Cost of signs

2. Fuel Consumption

3. So with the new limit some will

drive between 85 - 90

4. When the turnpike first opened

they would check your speed with

the time stamp on your turnpike

ticket. They found a goodly

number of drivers were running at

triple digits.

National Motorists Association

NMA Position On Speed Limits

Speed limits should be based on sound traffic

engineering principles that consider the actual travel

speeds of responsible motorists.

Typically, this should result in speed limits set at the

85th percentile speed of free-flowing traffic (the

speed below which 85 percent of traffic is

traveling).

These limits should be periodically adjusted to

reflect changes in actual traffic speeds.

http://www.motorists.org/speed-limits/position

Motorists have rights. We've

been protecting them since 1982.

IoKsMTxStudy Page 50 of 60

Summary and Conclusions

1) There is clearly an overwhelming public sentiment in favor of

increasing speed limits, as indicated by the willingness of various

state legislatures (since the full repeal of the National Maximum

Speed Limit of 55 mph in 1995) to increase the speed limits to as

high as 75 mph with Texas being in the forefront, willing to push to

85 mph. Nonetheless, it is also clear, and borne out by indisputable

facts that accidents, or crashes as they are called by traffic safety

researchers, when do they occur at such high speeds (even at 65

mph, when one is not speeding), or even in zones where the posted

speed limit is less than 35 mph, can be tragic and fatal. There is no

escaping the laws of physics and the increasingly higher amounts of

energy that must be absorbed by the vehicle infrastructure to prevent

death and/or serious injuries to the occupant(s).

2) When this study was initiated recently [prompted mainly be the news

about Texas going to 85 mph, and started reviewing fatalities and

fatal crashes data from states like Iowa (with its speed limit

increases) and Montana (with no numerical speed limit) and Texas

(with its highest in the nation speed limit)], the author was fully

expecting an outcome that showed fatalities and crashes going up

significantly after each increase in the speed limit, although he was

aware that fatality rates, based on VMT, have been going down. This

led to the decision to more carefully study the relation between fatal

crashes (C) and fatalities (F) under relatively well controlled

conditions – such as the available data for rural and interstates

crashes or the data for speeding-related crashes.

3) We do not fully understand all the factors that lead to a crash,

especially a fatal crash, and how they are affected by the posted

speed limits. This is actually a futile debate that would never end.

However, we do know that by definition, a fatal crash means at least

one person has been killed. In some fatal crashes more than one

IoKsMTxStudy Page 51 of 60

person is killed. In spite of the many variables and the unknown

variabilities that affect this phenomenon, the data overwhelmingly

shows that fatalities, F, increase as the number of fatal crashes C

increase, in a very statistically predictable manner. A simple linear

law, of the type y = hx + c, seems to describe the relation between

the number of fatal crashes, x, and the number of fatalities, y. Fatal

crashes, rather than total crashes (i.e., we exclude crashes resulting

only in injuries and/or property damage), provides a much better

correlation. Unlike the VMT based fatality rate, which is subject to

the criticism of VMT inflation (VMT is an estimated quantity, not a

measured quantity), both the number of crashes C and the number

of fatalities F can be more reliably measured. (Dr. Leonard Evans, a

leading traffic safety expert and author of a leading book entitled

Traffic Safety, cautions that even something like the number of

fatalities is sometimes difficult to estimate, as in the case of the

sinking of the Titanic, natural disasters, or the deaths due to the 9/11

terrorist attack, and so on. However, traffic fatalities are a bit different

and a more accurate count is certainly possible, although, as noted,

some of these deaths could even be suicides! Thankfully also,

homicides using motor vehicles are rare.)

4) The linear law y = hx + c can be tested under various conditions to

reveal the effects of significant variables such as speeding, alcohol

impaired driving, rural versus urban, interstates versus other

roadways, etc. (provided high quality data is available to sort each

such variable of interest), to determine if there is a significant change

in the numerical values of either the constant h or the constant c.

5) The Iowa data on the number of fatalities and fatal crashes shows

very clearly that there is NO statistically significant effect of the

changing speed limit under which these crashes/fatalities occurred.

The data follows the same straight line with higher crashes simply

leading to higher fatalities. This is also confirmed by nationwide data

(discussed briefly in the earlier report) and the data from other

states, such as Montana, Texas, and Kansas.

IoKsMTxStudy Page 52 of 60

6) The significance of the numerical values of the constants h and c, in

the universal law y = hx + c, must be appreciated. Ideally, the slope

h = 1 and the constant c = 0 since a single crash must produce at

least one fatality, 2 crashes 2 fatalities, and so on, and the number of

fatalities y must go to zero as the number of crashes x goes to zero.

In the real world, h > 1 and the greater the deviation from 1, the

higher the rate at which fatalities increase due to a variety of factors

(speed limits, road conditions including weather, type of roadway,

vehicle infrastructure, driver behavior, and so on). Likewise, if the

intercept c has a high positive value, fatalities are too high for a

given set of conditions. A large negative value of the intercept c, as

we see for Texas, is definitely desired. The significance of these

constants will become more obvious once traffic safety researchers

accept this simple law and study its implications more carefully to

isolate various crash factors and their effect, with higher-quality data.

7) The relation of the constants h and c to the corresponding constants

in Einstein‟s famous photoelectric law is also obvious and must be

explored by traffic safety researchers.

8) The study here points to the urgent need to improve the quality of

data collection, as it pertains to both fatalities F and crashes C, to

reveal the effect of important factors that most researchers accept as

being important. For example, to study the effect of a change in the

speed limit, it is best to look at F and C values for rural and urban

interstates ONLY, not statewide crash and fatality data.

Unfortunately, with few exceptions, such data is not currently

available for all states. Also, historical data, at least at the state level,

going back to the 1950s or 1960s, are not readily available and

should be compiled and researched thoroughly. Nearly 40,000

people die each year in traffic related accidents and more teenagers

die each year in traffic related crashes than many other events that

grab national or international events (as duly noted by Evans).

IoKsMTxStudy Page 53 of 60

9) The complex interaction of vehicle speed, vehicle weight, fuel

economy, safety and crashworthiness, and other economic

ramifications (insurance costs, medical costs) will ultimately decide

what type of vehicles will be on the road and what speed limits are

indeed reasonable and prudent. We must not forget that in the 1950s

and the 1960s, there was a virtual “epidemic” of traffic related deaths

(highlighted in the earlier report by the author) which prompted the

highly publicized Congressional hearings and the subsequent traffic

safety laws that were enacted. Seat belts and airbags, although

originally resisted by manufacturers due to the costs imposed, are

now common place. Mandatory seat belt laws have also been

enacted in practically all states. Yet, even today, the failure to use

seat belts is still one of the most common reasons cited by law

enforcement for a traffic fatality. (Perhaps, legislators who

champion an increase in the speed limits should be persuaded

to write into such laws the mandatory deployment of seat belts,

by vehicle design, before it can be operated!)

10) The 20th century ushered a new era in personal transportation, with

the introduction of affordable automobiles for the masses. Much more

than the need to improve vehicle occupant safety (which certainly

yielded seat belts and airbags), the demand for improvement in fuel

economy, following the energy crisis (triggered by the Arab oil

embargo in 1973, which highlighted US vulnerabilities to foreign oil),

and the need to improve emission standards, ultimately lead to the

development of modern electric and hybrid vehicles. Likewise, a new

era of higher speed limits, can spur innovations in commercialization

of high-strength, light-weight materials. Such advanced materials are

indeed available but are not cost-competitive at this time. The 21st

century can still become a century of innovations, led again by the

automobile and other type of high speed mass transportation. The

automobile and the vast stretches of open highways, with reasonable

and prudent speed laws, or better yet, no posted speed limits at all,

still beckon many a driving enthusiast. Montanabahn or the

Autobahn! We can, and need to, “Texas Proof” our vehicles!

IoKsMTxStudy Page 54 of 60

Heavier Vehicles Are Dangerous and Kill

http://www.slate.com/id/2297796/

Your Big Car Is Killing Me

American cars are getting heavier and heavier. Is that dangerous? By Annie Lowrey Posted Monday, June 27, 2011, at 6:26 PM ET

Like Americans themselves, American cars are getting heavier and heavier every year.

We pay a hidden cost for our fat cars. They may be sucking up less gas, slowing the degradation of the

environment and the warming of the planet. But they have other "negative externalities"….

A working paper released this month by two economists from the University of California, Berkeley,

Maximilian Auffhammer and Michael Anderson, tackles the first question, attempting to put a price tag

on the fatalities associated with big cars. They studied accident data from eight states, identifying the

type and weight of vehicles involved in collisions by their VIN numbers. The researchers confirm that the

heavy cars kill.

Data understate bus deaths

By Alan Levin, USA TODAY June 29, 2011

http://www.usatoday.com/NEWS/usaedition/2011-06-29-bus-

crashesART0_ST_U.htm

NHTSA's failure to track all the accidents has given Congress and the public a false impression that buses

are safer than they are and has thwarted efforts at tougher regulation, safety advocates say. "By

underreporting crashes and fatalities, it has given the industry the political cover they want to go to

(Capitol) Hill and say, 'We are really safe,'" says Jacqueline Gillan, vice president of the non-profit

Advocates for Highway and Auto Safety.

USA TODAY found at least 42 deaths of motor coach occupants and drivers were not reported using

NHTSA's standard definition of a motor coach from 1995 to 2009, the most current year for which data

are available. Since 2003, 32 fatalities were not included.

IoKsMTxStudy Page 55 of 60

Appendix 1

Significance of the intercept c of the best-fit line

Legendre’s Best-fit Line and Einstein’s Work Function

The rather small value of the slope, less than the F/C ratio observed in all

Iowa fatalities-crashes data, is worthy of further discussion. Let us first

recall two important points here regarding the best-fit line.

1. The best-fit line always passes through the point (xm, ym), the

average point of the data set, in our case, the point (26, 32), see

Table 2. The slope of the line through this “average point” is the same

as the “average slope” 1.273 determined here.

2. The best-fit line, also sometimes known as the least squares line,

pivots around the “average point” depending on the “scatter” in the

data. The extent of this pivoting determines the slope of the best-fit

line. How should the slope be determined?

Some data points will lie above the best-fit line and some will lie below it.

The deviation of any single point (y – yb) is either positive or negative,

where yb is the value on the best-fit line. The sum of all deviations ∑(y – yb)

is exactly ZERO. But the square of each deviation, (y – yb)2 will always be

positive and the sum of all the squares ∑ (y – yb)2 will also be positive.

Mathematically speaking, linear regression analysis fixes the slope of the

best line by minimizing the squares of such deviations; hence the term

least squares method. But, as noted by Legendre, in his famous 1805

paper, when he proposed this method (which was immediately adopted,

one of the most rapid acceptances of any statistical method in the entire

history of statistics, see Stigler, link below), the best-fit line, or least

squares line, is just one of many lines that can one legitimately fit

through the “average point”. Each situation, where one observes a “scatter”

merits its own analysis. The best-fit, or least squares, slope happens to be

the easiest to calculate mathematically.

IoKsMTxStudy Page 56 of 60

However, other “real world” or “physical” considerations cannot be

overlooked. Perhaps, the Iowa fatality-crash data (with a slope less than 1,

which is theoretically impossible, since the F/C ratio must be greater than

1, by definition) is a case in point.

This discussion also points us about the fundamental significance of the

numerical value of the constant “c” determined using the best-fit method.

Intuitively, and considering the Iowa data, the constant “c” appears to be

related to the nature and circumstances of the crashes that led to the

fatalities. This must be more fully investigated. To use a phrase from

physics, the constant “c” is like the “work function” introduced by Einstein to

explain the photoelectric effect.

The mathematical equation proposed by Einstein to explain the puzzling

aspects of photoelectricity is also a simple linear equation, of the type y =

hx + c. Very briefly, when light shines on the surface of a metal, electrons

which are normally bound to the atoms of the metal, are ejected. Modern

photocells, widely used in many applications (garage door openers,

security systems, motion sensing applications such as paper towel

dispensers, toilet flushes, etc.) are based on this principle. The electrons

then flow through an electric circuit to make the device work.

The maximum energy of the electron must be less than the energy of the

photon (a particle of light) that is used to eject the electron. The energy of

the photon is hf, where f is the frequency of light and h is the famous

Planck constant. The idea that light can be thought of as being made up of

particles, each with a fixed “bundle of energy” was a revolutionary one back

in 1905 when Einstein proposed this idea. The idea of light being made of

particles, that obey of laws that he had discovered, had been proposed by

none other than Newton himself. However, this particle idea of light had

been rejected by physicists, in favor of the idea of light being a type of

wave motion. Later, Maxwell, proposed the idea of light being a type of

electromagnetic wave - similar to other electromagnetic waves like X-rays,

gamma rays, microwaves, radiation of all types, and all “waves” that are

now widely used to make our cellphones, GPS systems, and other radio

and modern communications work. Here Einstein was actually extending

IoKsMTxStudy Page 57 of 60

and borrowing an important idea introduced by Max Planck to develop

quantum physics, in December 1900.

After discussing some other important aspects of physics, to justify the idea

of a photon, Einstein went on to postulate that the maximum energy E will

be less than the photon energy hf since some “work” must be done by the

photon to eject the electron. This will vary from one metal to another and is

a very complicated matter. To simply the whole problem, Einstein

introduced the concept of a work function W which must be determined

from actual experimental observations. It cannot be predicted theoretically

but the slope h is predicted theoretically, and must be the value that is

consistent with other types of observation on radiation (which Planck had

been studying back in 1900). The photoelectric equation is therefore,

E = hf - W or y = hx + c

Here W is the work function of Einstein. In this equation y = E, the

maximum energy of the electron and x = f, the frequency of light. The

intercept c = - W.

The problem of the relation between fatalities and crashes that we are

considering here is also a very complex one. The analogy between the

constant “c” and Einstein‟s work function W might well be quite appropriate

and bears further study and investigation by traffic fatality researchers.

Complex problems sometimes indeed have simple solutions.

IoKsMTxStudy Page 58 of 60

Appendix 2

NHTSA Workshop on Vehicle Mass-Size-Safety

NHTSA hosted a workshop on the effects of light-duty vehicle mass and

size on vehicle safety on February 25, 2011. Our purpose was to bring

together experts in the field to discuss some of the overarching questions

that NHTSA must grapple with in our upcoming CAFE rulemaking.

Panelists discussed how statistical analysis can help the agency evaluate

the effect of vehicle mass and size on safety, and how consideration of

vehicle structural crashworthiness, occupant safety, and advanced vehicle

design can help inform the agency‟s understanding of what levels of mass

reduction might be appropriate to consider for CAFE rulemaking.

A number of research projects currently are ongoing at NHTSA and other

agencies and in the private sector to help to answer these questions.

NHTSA held the workshop to help kick off the dialogue process between

the agency and stakeholders and to set a good baseline for further

discussions.

The workshop was at NHTSA headquarters. Due to space constraints,

NHTSA offered a streaming live webinar to expand participation. A

recording of the webinar is accessible below, as are printable versions of all

the presentations.

Workshop materials

Webinar recording

Official transcript NHTSA Deputy Administrator Ron Medford Opening Speech

Panel 1: Statistical Evidence of the Roles of Mass and Size on Safety

Kahane, NHTSA, “Relationships Between Fatality Risk, Mass, and Footprint” Wenzel, LBNL, “Analyzing Casualty Risk Using State Data on Police-Reported

Crashes”

IoKsMTxStudy Page 59 of 60

Van Auken, DRI, “Updated Analysis of the Effects of Passenger Vehicle Size and Weight on Safety”

Lund, IIHS, “The Relative Safety of Large and Small Passenger Vehicles” Padmanaban, JP Research Green, University of Michigan Transportation Research Institute

Panel 2: Engineering Realities – Structural Crashworthiness, Occupant Injury and Advanced Vehicle Design

Summers, NHTSA, “Finite Element Modeling in Fleet Safety Studies” Peterson, Lotus, “The Design and Impact Performance of a Low Mass Body in

White Structure” Kamiji, Honda, “Honda‟s Thinking about Size, Weight and Safety” German, ICCT, “Lightweight Materials and Safety” Schmidt, Alliance of Automobile Manufacturers Nusholtz, Chrysler, “Mass Change, Complexity and Fleet Impact Response” Field, MIT, “Innovative Automobile Materials Technologies: „Feasibility‟ as an

Emergent Systems Property” Jim Tamm, NHTSA Fuel Economy Division Chief, Concluding Remarks

How do I comment on the workshop proceedings?

NHTSA strongly encourages interested parties to submit written comment

on the workshop proceedings to the mass-safety docket. We suggest that

you submit your comments by March 30 to ensure that the agency will have

time to consider fully in the upcoming CAFE NPRM.

However, we will leave the docket open throughout the rulemaking period

and encourage you to check back as we will upload new studies and

information as it becomes available. The docket can be accessed at

http://www.regulations.gov; you can input the docket number NHTSA-2010-

0152 at that website and upload comments electronically, or you can

contact Rebecca Yoon (202-366-2992) at NHTSA for assistance with

submitting comments.

IoKsMTxStudy Page 60 of 60

About the author

The author obtained his Master’s (S. M.) and Doctoral (Sc. D.) degrees in

Materials Engineering from the Massachusetts Institute of Technology,

Cambridge, USA. He then spent his entire professional career at leading US

research institutions (MIT, NASA, Case Western Reserve University, and General

Motors R & D Center, in Warren, MI). He holds four patents in advanced

materials processing, has co-authored two books, and has published several

scientific papers in leading peer-reviewed international journals. His expertise

includes developing simple mathematical models to explain the behavior of

complex systems. He can be reached by email at vlaxmanan@hotmail.com

Acknowledgements

The author is grateful for encouraging comments and helpful feedback

provided by friends and colleagues with whom these documents were

shared prior to uploading as public documents.

Disclosure

This document is being uploaded as a public document and available for

using by anyone interested. The author is not currently affiliated with

anyone in the automotive industry and has no personal conflicting interest

in the debate on the benefits of raising or lowering the speed limits. (Just

drive safely and go from Point A to B, has been his philosophy.) This

research was done entirely on the author‟s personal time. He does not

grant the right to use labels such as “Texas Proof”, or anything remotely

resembling it, in any ad campaigns in the future for any commercial

purpose. Permission for such use is, however, freely granted for

noncommercial uses.