Technical Summary of Research into
Unit Power Density and Unit Uplight Density:
Introduction

Table of Contents

Unit Power Density (UPD)

Unit Power Density (UPD) is the ratio of the connected power for a roadway lighting system to the corresponding area of the roadway. UPD directly describes the amount of connected electrical power required by the lighting system, but it also provides information on proportional changes throughout that lighting system. A 10% increase in UPD between systems using the same wattage lamps corresponds to 10% more of most everything except the wiring in the ground (because the project is still as long as it is): lamps, installed lumens, ignitors, ballasts, photocells, luminaires, poles, arms, brackets, foundations, electrical controls, energy use and cost, maintenance requirements and labor, as well as pollutions associated with equipment production, delivery, and installation and of course energy generation and transmission. The proportion may apply even to installation costs and labor, light pollution and mercury from spent lamps going into landfills. Comparisons between systems with different wattage lamps are less directly proportional, because the number of poles and luminaires may be significantly different (because of the significant difference in "coverage" for each pole). Even so such comparisons across wattages can be informative.

UPD is calculated for one "typical" luminaire cycle [1] as:

Eq. 1: UPD = (# of luminaires) * (watts / luminaire) *1.15 / (area of roadway)

The number of luminaires per luminaire cycle is two for staggered (used throughout this work) and opposite patterns and one for single-sided patterns. Watts are the total input watts for each luminaire (shown in Table 2). The factor of 1.15 is included to account for the anticipated spacing reductions in some areas, compared to the "typical" spacing calculated according to [2]. The area of the roadway is the extent of the traveled way, equal to the length of the luminaire cycle times the number of lanes times the width of each lane. Shoulders are not included in the area of the roadway.

Unit Uplight Density (UUD)

Unit Uplight Density (UPD) is the ratio of the upward flux produced by a roadway lighting system to the corresponding area of the roadway. The model assumes that the reflectance of the roadway and surroundings are perfectly diffuse, and treats the uplight from the luminaires in the same manner. The model assumes that the roadway is a repeating cycle, so any flux from one cycle that goes beyond either end of that cycle is exactly matched by flux from the adjacent cycles.

The UUD calculation sums direct uplight and reflected downlight and divides by the roadway area, using values corresponding to the "average LLF" [6]. The downward lumens "LumsDn" and the upward lumens "LumsUp" are calculated from the photometric file and adjusted for any difference between the rated lumens of the photometry and the lamp lumens in the roadway calculation, then multiplied by the average Light Loss Factor (LLFavg). The average LLF is taken as the average of the maintained LLF (LLFmaint) and 1.0, and applied to the upward and downward lumens and also to adjust the illuminance onto the roadway (Eavg) from the maintained value to the average value. The reflected light was calculated as the sum of the roadway reflected light and the off-roadway reflected light. The roadway reflected light was calculated as the roadway reflectance times the roadway lumens, which was calculated as the average illuminance value times the roadway area. The off-roadway reflected light was calculated as the off-roadway reflectance times the off-roadway lumens, equal to the total downlight lumens minus the roadway lumens. The total downlight lumens were calculated as the number of luminaires per cycle times the downlight lumens per luminaire. The resulting value, when lengths are measured in meters, has units of lumens per square meter of roadway.

Eq. 2: UUD = [(#Lum * LumsUp * LLFavg) + (rhoRoad * Eavg * (LLFavg/LLFmaint) * Area) + (rhoOffRoad * {#Lum * LumsDn * LLFavg - Eavg * (LLFavg/LLFmaint) * Area})] / [Area]

Roadway reflectance (rhoRoad) was set at 0.07, the default Q0 value for R3 pavement [2], which is the roadway surface used throughout these calculations. Off-roadway reflectance (rhoOffRoad) was set to 0.18, the "Kodak average reflectance value". Area is the overall roadway width (the number of lanes times the width of each lane) times the LumCycle distance for the staggered layout. All the roadways have staggered layouts, so two luminaires are used when calculating lumens within each luminaire cycle.

The maintained LLF values used in the optimization calculations are shown in Table 2. For MHP, the maintained LLF is 0.50, so the average LLF (LLFavg) is 0.75 for all MHP systems. For HPS, the maintained LLF is 0.70, so the average LLF (LLFavg) is 0.85 for all HPS systems. The UUD values are all calculated using the average LLF, because typical roadway conditions - over both space and time - are midway between initial and maintained, so uplight calculations should be made at that level of maintenance.

The number of luminaires per luminaire cycle is two for staggered (used throughout this work) and opposite patterns and one for single-sided patterns. The area of the roadway is the extent of the traveled way, equal to the length of the luminaire cycle times the number of lanes times the width of each lane. Shoulders are not included in the area of the roadway.

UUD describes the amount of light that the system sends into the space immediately surrounding it. Of course the radiative transfer characteristics of that space significantly effect the amount, direction and even spectral profile of the radiation that reaches the atmosphere and potentially becomes redirected and appears as skyglow. The number of assumptions necessary to make such a model useful is very high, and most of the assumptions would need to vary depending on locality and even the specific project. For UUD, the significant variables can be reliably predicted by lighting designers.

Research Scope

The research discussed here has three steps: preliminary, intermediate and advanced. These three steps correspond roughly to [3, 4, 5]. Each step includes evaluations of luminaire photometric data across a series of appropriate standardized roadways. The calculation procedure optimizes the roadway lighting design for each combination of photometric file and roadway, by determining the system geometry with the maximum distance between luminaires which still meets all the criteria. The optimum system's UPD and UUD values are calculated and evaluated by comparisons between source types, roadways, cutoff classifications, design criteria, rated lumens and Light Loss Factor. In addition, some design constraints - such as "no overhang allowed" - were investigated.