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Publication Number: FHWA-HRT-04-142
Date: December 2005

Enhanced Night Visibility Series, Volume XI: Phase II—Cost-Benefit Analysis

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CHAPTER 2—LITERATURE REVIEW AND METHODOLOGY

As a benchmark, the 1998 report A Safety Evaluation of UVA Vehicle Headlights, by Nitzburg, Seifert, Knoblauch, & Turner and published by the Federal Highway Administration, is useful for comparison with the findings of this study.(1) Nitzburg et al. used engineering estimates and a limited body of relevant literature to estimate the steady-state cost of maintaining a UV–A headlamp technology and a fluorescent pavement marking technology after implementation. Nitzburg et al. created a file that is a weighted combination of 1988–1991 Crashworthiness Data System (CDS) files and 1982–1986 National Accident Sampling System (NASS) files. Adding details from the CDS files to the personal injury statistics from the NASS files provided a more accurate injury cost estimate. Nitzburg et al. used the General Estimated System (GES) to estimate crash costs from this hybrid CDS/NASS file and tabulate the crash cost estimates in six categories defined by the crash geometry:

  • Pedestrian crashes.
  • Single-vehicle road departure.
  • Opposite-direction crashes.
  • On/off ramp.
  • Work zone crashes.
  • Sideswipe.
  • All crashes, including the six categories above.

Nitzburg et al. then calculated what percentage of these estimated crash costs the UV–A headlights and fluorescent pavement markings would need to prevent to cover their estimated cost.(1) The report states that a 9.6 percent reduction in nighttime crashes involving pedestrians or a 3 percent reduction in all relevant nighttime crashes would make the UV–A and fluorescent technologies cost effective.

By ignoring the possible startup costs as well as the possible lag between the incurrence of costs and the realization of benefits during the period of implementation, the FHWA analysis subjected the UV–A and fluorescent technologies to a reasonable, but weak, assessment of cost-effectiveness. If this test had generated a cost-benefit ratio close to unity, then a less favorable dynamic analysis might be a matter of interest because it would have been possible that slow acceptance, in the presence of a nonlinear relationship between the percentage of implementation achieved and the percentage of potential benefits realized, might prove to be a barrier to an otherwise promising technology.

MODELING THE BENEFITS OF ENHANCED NIGHT VISIBILITY

The fundamental effect of an enhanced night visibility (ENV) system is to increase the driver’s sight distance. The relationship between the sight distance to a point on the highway and the crash rate in the vicinity of that point is the hinge on which any crash reduction estimate hangs. Although some other quantities such as the horizontal curvature or the posted speed limit have been found to account for more of the statistical variance in total day and night crashes than sight distance, sight distance alone does have explanatory power.

Stopping Distance

The safe stopping sight distance depends on the condition of the pavement surface and the characteristics of the driver.(2,3) The equation in figure 1 is a typical model of stopping distance.(3)

Equation. Stopping distance model. Click here for more detail.

Figure 1. Equation. Stopping distance model.

In the equation, S equals the required distance in feet, u equals the velocity in miles per hour, t equals the time in seconds between perception and reaction, f equals the coefficient of friction between the tires and the road, and G equals the grade of the incline or decline, if any. A model such as this likely would be applicable in analyzing the effect of ENV on certain crash geometries.

Crash Rate to Sight Distance Relationship

Based on the findings of studies published between 1973 and 1980, a 1994 paper by Choueiri et al. contains a nomograph that quantifies the relationship between the crash rate in the neighborhood of an intersection and the sight distance for drivers approaching that intersection, holding other factors constant.(4) It should be noted that this relationship is between the average crash rate in all conditions of weather and lighting and the daytime sight distance that the geometrics of the highway permit. Table 1 shows five points on the nomograph by Choueiri et al. over the range of sight distances from 100 to 600 m (328 to 1,969 ft).

Table 1. The relationship between sight distance and crash rate.
Crash Rate per 100,000
Vehicle Kilometers Traveled
Sight Distance
(m (ft))
3.20 106.68 (350)
2.60 213.36 (700)
2.40 290.47 (953)
2.25 396.24 (1,300)
2.10 609.60 (2,000)

The relationship between the sight distance and the crash rate is nonlinear; the elasticity of the crash rate with respect to sight distance ranges from −0.30 at the lower end of the sight distance range to −0.16 at the upper end.(4) This model, too, might be applicable in analyzing the effect of ENV on certain categories of crashes.

Crash Cause Interactions

Lum and Reagan(5) discuss a paper by Rumar(6) that classifies all causes of crashes as (1) driver characteristics, (2) roadway characteristics, or (3) vehicle characteristics. Rumar concludes that driver characteristics accounted for 57 percent of crashes, roadway characteristics for 3 percent, and vehicle characteristics for 2 percent. Rumar further concludes that the interaction of driver and roadway characteristics accounted for 27 percent of crashes and that the other possible two- and three-way interactions accounted collectively for 10 percent (1 percent was lost in rounding). Driver characteristics include variables such as age and blood alcohol level; roadway characteristics include curvature, pavement surface condition, and ambient light; and vehicle characteristics include vehicle type, tire type, and other equipment. With this classification of causes, installation of a new VES or pavement marking cannot be interpreted as a change in driver characteristics. This breakdown of crashes would imply that a new vision enhancement technology or a new pavement marking technology could affect at most 43 percent of potential crashes, while the other 57 percent would depend statistically on driver characteristics being unaffected. Under the assumptions (1) that changes in the fraction of crashes that depend statistically on roadway or vehicle characteristics would respond with an elasticity of exactly −1 to the changes in sight distance caused by the experimental technology, and (2) that this effect is restricted to the 43 percent of crashes that depend statistically on roadway or vehicle characteristics or both, the elasticity of the crash rate with respect to sight distance would equal −0.43. The applicability of this result is open to question; nonetheless, it is interesting to compare the elasticity derived from Lum and Reagan(5) with the elasticity derived above from Choueiri et al.(4)

Crash Modification Factors

The crash modification factor (CMF) is an established means of quantifying the effect of a safety improvement.(7,8) In principle, the crash rates implied by an equation or a nomograph, such as those noted above, make it possible to associate a specific CMF with any change from one system to another, provided the change in sight distance is known. The proportion between the predicted crash rate CR1 for one sight distance and the predicted crash rate CR2 for another, longer site distance is a forecast of the proportion by which the number of crashes would change if a night vision system were replaced with a night vision system that yields a longer sight distance. Figure 2 shows the equation for this CMF.

Equation. Crash modification factor. Click here for more detail.

Figure 2. Equation. Crash modification factor.

DISCUSSION

Although models that relate sight distance to crash rates exist and fit certain specific crash geometries, it is doubtful that any one model would provide valid results for all of the types of crashes in which VESs might have an effect. The approach of computing implementation costs, crash costs, and break-even crash reduction rates, while remaining agnostic about the precise relationship between sight distance and crash rates, has the virtue of allowing each reader to look at the measured effect of VESs on sight distance. This permits each reader to draw his or her own conclusions about the potential for crash reduction. For this study, the approach has the further advantage of permitting ready comparison between the new findings and the previous findings of Nitzburg et al., who used this approach.(1)

 

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