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Publication Number: FHWA-RD-03-082
Date: December 2003

Minimum Retroreflectivity Levels for Overhead Guide Signs and Street-Name Signs

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CHAPTER 4. MR MODEL

MODEL DESCRIPTION

To develop MR recommendations, the researchers developed a computational model that considers the relationships between the headlamps (source), sign (target), and the geometric relationship between these and the driver (receptor). The TTI model is a combination of ideas from other models such as CARTS and Exact Roadway Geometry Output (ERGO), with refinements to address shortcomings in the previously developed models. The elements (source, target, receptor, and vehicle) of the model were addressed in the following manner:

  • Headlamps: External databases are used to accommodate different headlamp profiles such as CARTS50 or others, such as those published by the University of Michigan Transportation Research Institute (UMTRI).
  • Sheeting: The model includes external retroreflectivity matrices for all types of sheeting. The data were obtained from the ERGO model with the permission of the model developer. The researchers conducted goniometer evaluations (on the TxDOT goniometer) of several materials to confirm the accuracy of the ERGO data and found it to be accurate.
  • Driver: The model does not incorporate any human factor elements for driver considerations beyond the minimum luminance needed to read a sign at a specific distance. For this research, a field study (described in chapter 5) was conducted to determine the minimum luminance needed to read overhead guide signs and street-name signs.
  • Vehicle: External databases are used to allow various vehicle designs to be studied. The database includes information about the location of the headlamps and the driver's eyes.
Once the driving scenario is defined by the user in Cartesian coordinates, the TTI model makes transformations in order to take advantage of vector algebra. Once unit vectors have been defined, the model determines the exact magnitude and direction of the vectors needed to fully define the three-dimensional retroreflective space. These calculations are made separately for each headlamp. Multipoint quadratic lookup features are then applied to the headlamp and retroreflectivity data files to obtain accurate values for the headlamp intensity and the retroreflective properties of the sign material. The luminance from each headlamp is then determined and totaled to arrive at the total luminance.

Up to this point, the TTI model performs similarly to ERGO. However, after ERGO outputs sign luminance, its usefulness in terms of establishing MR levels has ended. This is where the TTI model expands the current state-of-the-art by being able to determine the retroreflectivity needed to provide a user-defined threshold luminance.

The concept used to determine MR is provided below. The terminology introduced will be used throughout the remainder of this report.

  Click to view alternative text (1)

where,

Minimum RA           =          MR at standard measurement geometry (alpha symbol = 0.2°, beta symbol= -4.0°) needed to produce assumed threshold luminance, cd/lx/m2

New RA,SG                  =          Averaged retroreflectivity of new sheeting at standard geometry, cd/lx/m2

Demand RA,NSG        =          Retroreflectivity needed to produce the minimum luminance at the nonstandard geometry (backcalculated and determined for each scenario), cd/lx/m2

Supply RA,NSG         =          Retroreflectivity of new sheeting at nonstandard geometry (determined for each scenario), cd/lx/m2

If the Demand RA,NSG > New RA,NSG, then the material cannot provide the threshold luminance for the given scenario. As shown below, the Demand RA,NSG is determined from the illuminance falling on the sign, the viewing geometry, and the assumed threshold luminance needed for legibility.

Click to view alternative text                                             (2)

The Supply RA,NSG is found through a lookup table for each type of material. Nu is the viewing angle for the sign, using the driver as the observation point. The lookup tables contain almost 200,000 retroreflectivity values, depending on the applications system's four angles that are used to fully describe the performance of the retroreflective sheeting.

Appendix B provides additional information pertaining to the details of the development of the MR levels. A step-by-step example is provided for additional clarification.

MODEL ASSUMPTIONS

Several assumptions are associated with this methodology. For instance, this methodology assumes that the retroreflective characteristics for each type of sheeting degrade uniformly as the sheeting weathers. Figure 2 shows an illustrative example of this concept. The concept of uniform degradation for beaded materials (i.e., types I, II, and III) is a reasonable assumption. However, for microprismatic sheeting (i.e., types VII, VIII, and IX), the researchers acknowledge that this assumption has not been validated. For these microprismatic materials, the weathering may cause the microprisms to change shape, which may produce different retroreflectivity characteristics. Some sheeting may actually get brighter with age, but only to a point, and even then, the change may not be consistent along the full dynamic range. However, no data currently exist in the public domain that can be used to develop weathered curves that illustrate how microprismatic sheeting characteristics change over time. Efforts are currently underway at FHWA to measure the retroreflectivity of weathered microprismatic sheeting to determine the validity of this assumption and to make changes if needed.

Figure 2. Weathering Degradation of Retroreflective Sheeting

Click to view alternative text

The modeling methodology also assumes that the retroreflectivity of new sheeting at the standard measurement geometry can be generalized with one value per ASTM type of material (even though there are several manufacturers of certain types of sheeting). The values shown in table 14 were determined by averaging the retroreflectivity values for each type of material at alpha symbol = 0.2°, beta symbol = -4.0°, epsilon symbol = +180° to -180° in 15° intervals and omega symbol = +180° to -180° in 15° intervals. The sheeting data from the ERGO model were combined with measurements made by the researchers to develop the values shown in table 14.

A final modeling assumption is that the photometric relationships used in the model provide accurate estimates of the illuminance falling on a sign and the returned luminance directed toward the driver's eyes. Real-world factors such as pavement glare and ambient lighting are not considered in the model, or in any other available model. However, atmospheric and windshield transmissivity are considered.

Table 14. Average RA of New White Sheeting

ASTM Type

Retroreflectivity
(cd/lx/m2)

I

100

II

175

III

315

VII

1100

III

800

IX

450

RA values at alpha symbol = 0.2° and beta symbol = -4.0°

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