EVALUATION OF MINE ILLUMINATION SYSTEMS 

USING NUMERICAL MODELING 

Thomas Novak 

Pittsburgh Mining and Safety Research Center 

Bureau of Mines 

U.S. Department of the Interior 

Pittsburgh, PA 

Robert Goldstein 

Mathematical Applications Group, Inc. 

Elmsford, NY 

ABSTRACT 

The analysis of a machine-luminaire configuration is a timeconsuming process requiring the construction of a machine mockup, 

installation of a designated lighting arrangement, and an extensive 

set of illumination measurements. This entire process, however, is 

well suited to computer analysis. By simulating the machine geometry 

and the characteristics of the desired luminaires, the incident light 

levels can be calculated at the required set of points. This Bureau 

of Mines paper presents a general description of the techniques 

involved in performing this simulation. 

INTRODUCTION 

The Mine Safety and Health Administration (MSHA), U.S. Department 

of Labor, provides a method of evaluating an illumination system prior 

to its installation in an underground coal mine. This method requires 

the construction of a machine mockup that conforms to the shape and 

dimensions of the actual mining machine on which the lighting fixtures 

will be mounted. The designated luminaires are mounted on the mockup 

at their specified locations, with their proper orientations. The 

mockup, with its associated illumination system, is then centered in a 

simulated mine entry, which is a black room that excludes all exterior 

light. This room has movable roof and walls which can be adjusted to 

determine the maximum and minimum dimension of the mine entry in which 

the machine can be operated. 

The illumination levels are determined by dividing the surfaces 

(face, roof, floor, and ribs) into square fields having areas of 4ft2. 

Incident light measurements are taken at the corners of each square by 

orienting the light sensor for a maximum reading., The average illumination for each .square is determined by averaging the readings at its 

corners. The walls and the roof of the simulated entry are adjusted 

until the average illumination of each square field is at least 2fc. 

It is obvious that the method of evaluation is a time-consuming 

process. As a result, the Bureau of Mines awarded a contract to the 
Mathematical Applications Group, Inc. (MAGI) for the development of a 

computer simulation program for evaluating coal mine illumination systems. 

MAGI has previously developed computer techniques for simulating threedimensional geometric structures to analyze geometry-dependent physical 

properties. Therefore, the goal of the project was to incorporate these 

computer techniques into a system for accurately predicting coal mine 

illumination levels. 

A program of this nature must be able to perform the following 

functions : 

a. Process a numerical model of a mining machine which is 

supplied as input. 

b. Accept a specification of the types and locations of 

illumination sources. 

c. Determine which luminaires contribute to the illumination 

at a specified set of points. 

d. Record the indicent illumination levels at each detector 

point in an organized, easily interpreted format. 

MACHINE MODELING TECHNIQUES 

By experimentally determining the candlepower of a light source, 

one can easily predict the unobstructed illumination at a specific 

point by the Lambert cosine law: 

I E = - COS 8 

d * 

This states that the illumination E is directly proportional to the 

candlepower I of the source and the cosine of the angle of incidence 8, 

and inversely proportional to the square of the distance d between the 

source and the point. However, in order to accurately predict the illumination provided by a set of luminaires at any point in a mine entry, one 

must also account for the effects of shadowing due to the machine itself. 

Thus, an accurate representation of the mining machine must be created. 

The mining machine is represented by a numerical model. The model 

is created by a "building block" approach in which basic predefined 

shapes (boxes, cylinders, cones, etc.) are combined according to prescribed rules to form more complicated objectes. In constructing the 

model, each of these basic shapes is assigned specific dimensions and a 

location in a three-dimensional coordinate system. The totality of these 

forms then represents a complete numerical description of the desired 

model. 

As an example, refer to Figure 1 for the construction of a simplified 

continuous miner model. The ripper head of the miner is modeled by a 

cylinder referred to as CYL 1. Its location is first defined by the x, y, 
z coordinates at the center of either base. Thus, if the right base 

of the cylinder is chosen, its location would be defined by the point 

(4,1,1). The dimensions of the cylinder are then given by its axis 

vector and its radius. The axis vector is defined by the x y z coordinates, which give its magnitude and direction from the location point. 

Since the cylinder is 8 ft long with its axis parallel to the x axis in 

the negative direction, the axis vector is defined by (-8, 0, 0). The 

radius of the cylinder is 1 ft. 

The cutter boom of the continuous miner is represented by a box, 

which is referred to as Box 2. It can be located by defining any corner 

of the box. If the corner indicated in Figure 1 is selected, its location is defined by the point (2.5, 3.5, 5). Its dimensions are then 

defined by three vectors which originate at the location point and give 

the magnitude and direction of the length, width, and height of the box. 

The length of the box is 2 ft in the negative y direction and 4 ft in 

the negative z direction. Thus, its length is defined by the coordinates (0, -2, -4). Since the box is 5 ft wide in the direction parallel 

to the nagative x axis, its width is defined by the coordinates (-5, 0, 

0). Similarly, the height of the box is defined by (0, -1, 0.5). 

The main frame and the discharge boom of the machine are modeled 

by Box 3 and Box 4, respectively. These boxes are given locations and 

dimensions by the same method used for Box 2. Thus, the entire input to 

the program for the machine model of Figure 1 would consist of the 

following data: 

CYL 1: Location = (4, 1, 1) 

Axis Vector = (-8, 0, 0) 

Radius = 1 

BOX 2: Location = (2.5, 3.5, 5) 

Length = (0, -2, 4) 

Width = (-5, 0, 0) 

Height = (0, -1, Oc5) 

BOX 3: Location = (3, 3.5, 17.5) 

Length= (0, 0, -12.5) 

Height = (0, -3.5, 0) 

BOX 4: Location = (1, 3.5, 23.5) 

Length = (0, 0, -6) 

Width = (-2, 0, 0) 

Height = (0, -1, 0) 

These data are read by the program and stored for the calculation phase. 

The accuracy of the machine model can be verified by generating a line 

drawing of the model on a video display. A detailed model of a continous 

miner, which was generated by the numerical modeling process, is 

illustrated in figure 2. 
LUMINAI RE MEASUREMENTS 

Experimental measurements must be made for a representative sample 

of each type of luminaire. These measurements determine the luminaires1 

isointensity characteristics in order to define an average luminaire for 

each type. The candlepower is determined as a function of the angular 

light distribution of the luminaire. This is accomplished by positioning 

a photometer at a fixed location and varying the orientation of the luminaire by the use of a goniometer. Some luminaires are equipped with a 

protective metal cage. The measurements are taken with the cage in place 

to account for its effects on the variation in light output. Incident 

light measurements (in foot-candles) are made for every 10 degrees of 

orientation, resulting in a spherical, latitude-longitude arrangement. 

These data are then reduced to define the candlepower of the luminaire 

for each angular location by 

where 

E = incident light measurement (fc) 

d = distance from the photometer to the luminaire (ft) 

These data are then stored in a luminaire library. 

LUhIINAIRE LOCATION AND ORIENTATION 

Once the luminaire types are modeled and stored in the luminaire 

library, only the types of the luminaires desired and their locations 

and orientations on the machine need to be specified. Figure 3 shows 

two machine lights (Type 1) and two headlights (Type 2) mounted on the 

model of a continuous miner. The location of a luminaire is defined by 

x y z coordinates, using the same coordinate system utilized in the 

machine modeling process. Thus, the location of the center of luminaire 

1 is defined by the point (-2..5, 3.75, 15.5). Each luminaire is assigned 

an aim and an axis vector which define its orientation on the machine. 

Since the axis vector of luminaire 1 is directed toward the face, parallel 

to the z axis in the negative direction, it is defined by the coordinates 

(0 0 -1). Its aim vector is directed toward the roof parallel to the 

positive y axis; therefore, the aim vector is defined by the coordinates 

(0 1, 0) The entire input that defines the locations and orientations 

of the four luminaires illustrated in Figure 3 would consist of the 

f 01 lowing : 

LUM 1: Type = Type 1 

Location = (-2.5, 3.75, 15.5) 

Aim = (0, 1, 0) 

Axis = (0, 0, -1) 

LUM 2 : Type = Type 2 

Location = (-2, 3.75, 7) 

Aim = (0, 0, -1) 

Axis = (0, 0, -1) 
LUM 3: Type = Type 1 

Location = (2.5, 3.75, 15.5) 

Aim = (0, 1, 0) 

Axis = (0, 0, -1) 

LUM 4: Type = Type 2 

Location = (2, 3.75, 7) 

Aim = (0, 0, -1) 

Axis = (0, 0, -1) 

The location of the luminaires can also be defined by an alternate method. 

This requires displaying the machine model on the graphics terminal and 

using movable crosshairs to define the luminaire's position on the model. 

However, the aim and the axis vectors must still be defined. 

Prior to starting the illumination calculations, the program determines the validity of the locations of the luminaires. It tests whether 

any point on the axis of each luminaire lies outside the mine entry or 

inside any geometric shape comprising the machine model. If either case 

occurs, the luminaire has been improperly located, and the program is 

terminated. 

Is should also be noted that high-intensity discharge lamps and 

incandescent lamps can be treated as point emitters owing to their compact 

sources of illumination. However, the point source approximation for 

fluorescent luminaires becomes invalid owing to the length of the arc tube. 

Therefore, the program automatically divides the tube into smaller segments 

and treats such segment as apoint emitter. 

ILLUMINATION CALCULATIONS 

Once the luminaires are positioned on the machine model and the 

dimensions of the mine entry are specified, the illumination calculations 

begin. As an example, assume three luminaires located on a model of a 

continuous miner and a detector point D located on the right rib, as 

illustrated in figure 4a. The calculations proceed in the following 

manner : 

(1) The distance d from luminaire 1 to the detector point D is 

calculated by 

where xl, yl, z1 are the coordinates that define the location of luminaire 1 and x~, y~, ZDare the coordinates that define the location of 

the detector point. The distances d2 and d3 are then determined in a 

similar fashion. 

(2) Since the location of the luminaires with respect to the 

detector point is known, the candlepowers (I1, 12, and I3 of the luminaires are determined from the prestored angular distribution data. 
(3) The program tests whether the candlepower of any luminaire is 

equal to zero; if so, the illumination contribution E of the luminaire 

is assigned the value of zero. If the candlepower of the luminaire is 

greater than zero, the illumination contribution of the luminaire is 

calculated ignoring the cosine correction, by 

Since luminaire 3 is a headlight which is oriented toward the face, the 

detector point D does not lie within the angular distribution pattern of 

the light as shown in figure 4b. Thus, the prestored angular distribution tables would contain the value of zero for luminaire 3 in this 

particular situation. Therefore, E3 is assigned the value of zero. 

Since point D is within the angular distribution patterns of luminaires 

1 and 2, the illumination contribution of each luminaire is calculated 

as follows: 

I1 12 

El = 7- and E2 = -7 

d 7 d? 

(4) To determine the possible effects of machine shadowing, a ray 

tracing is performed for each luminaire whose illumination contribution 

E is greater than zero. A ray is traced from the location point of each 

applicable luminaire to the detector point. If a ray intersects any 

component of the machine model, the contribution of the lumirlaire is 

assigned the value of zero. Thus from figure 4c, El is set equal to 

zero. 

(5) As mentioned earlier, the present method of measurement 

requires the use of a cosine-corrected photometer. These measurements 

are made by orienting the probe in a trial and error fashion until the 

maximum reading is obtained. The reading thus displays the summation of 

the illumination contributions of each luminaire, taking into account 

the cosine of their angles of incidence. 

To duplicate this procedure, the detector point D is surrounded by 

an imaginary hemisphere which is divided into degress of latitude and 

longitude. Each pair of angles determines a possible orientation of the 

axis of the detector probe. For a given axis direction, the program 

computes the angle of incidence 8 for each luminaire and the following 

quantity: 

ED = C En COS On 

n 

This procedure is repeated for each latitude-longitude pair, which 

results in approximately 200 orientations being tested. Thus, the program scans through a series of angles as shown in figure 4d. For the 

sake of simplicity, the diagram is illustrated in a two-dimensional mode. 

Since luminaire 2 is the only luminaire that contributes to the illumination at the detector point D, the maximum reading is obtained with the 
normal of the probe aimed directly at this luminaire. Therefore, the 

angle of incidence is equal to zero, and the maximum illumination at 

point D is equal to E2. 

After all the detector points on a given entry surface have been 

completed, the averages within each 2-ft by 2-ft square are computed and 

the entire matrix of results is printed. The program then repeats the 

entire process until all five entry surfaces have been covered. The 

output format for a 6-ft-high by 12-ft-wide coal face is illustrated in 

figure 5. Any average illumination level that falls below the required 

level of 2 fc is flagged with an asterisk for easy identification. 

RESULTS 

To verify the accuracy of the illumination calculations, simple 

structures were mocked up, consisting of cardboard boxes placed on the 

floor of a simulated mine entry. Readings were taken on a 2-ft by 2-ft 

grid to coincide with the computer output pattern. The computed results 

from one of these tests are shown in figure 6. The calculations were in 

good agreement with the experimental readings, with differences generally 

less than 8 percent. A few scattered locations, especially those at low 

illumination levels, showed larger differences. Other tests at MSHAts 

Illumination Laboratory produced similar results. 

Experimental measurements for the various types of luminaires have 

shown that their deviations from the average light output can vary as 

much as 10 percent. Thus, the computer simulation provides a more 

standard means of evaluation than present mehtods, since the average 

light output for each type of luminaire is used for the calculations. 

The computer simulation program will significantly decrease the time 

involved with the present method of evaluating mine illumination systems. 

Computer-generated models of mining equipment, with sufficient detail to 

produce accurate results, can be created in approximately 2 hours, as 

opposed to 8 hours for the construction of a less detailed machine mockup. 

The numerical models can be stored indefinitely and retrieved as needed 

for future evaluations, whereas a mockup must be constructed for each 

different evaluation owing to storage and material limitations. Modifications to existing models (the addition or removal of a canopy, etc.) can 

be accomplished without having to recreate a new model. 

CONCLUSION 

The computer simulation program described should be a viable alternative to experimental measurements for evaluating mine illumination systems. 

Once the machine is numerically modeled and the characteristics of the 

desired luminaires are determined, the user need only specify the locations 

and orientations of the luminaires on the model to accurately predict the 

incident light levels on all mine surfaces. The program accounts for the 

effects of shadowing by tracing simulated light rays from each luminaire to 

an array of detector points, and the output of the illumination levels is 

recorded in an organized and easily interpreted format. 
FIGURE 1.--Simplified model of a continuous miner 

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FIGURE 2. 

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--Actual computer genera ted line drawing of a continuous niiner 
FIGURE 3.--Location of luminaires on the machine mockup 
LUM IT LUM 2 p 

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FIGURE 4.--Illumination calculations 
FACE 

0 2 4 6 8 10 12 

1 .O 1.2 2.8 4.8 2.7 1.1 1.1 

Avg . 1.2* 2.1 3.9 3.9 2.0 1.2* 

1.2 1.4 3.0 5.0 2.9 1.4 1.3 

Avg . 1.4* 2.3 4.2 4.2 2.2 1.4* 

1.4 1.5 3.2 5.6 3.1 1.4 1.5 

Avg . 1.3* 2.3 4.2 4.1 2.2 1.3* 

1 .O 1.3 3.0 4.9 2.9 1.3 1.1 

FIGURE 5. --Output format 
0 1 2 3 4 5 6 7 8 9 10 

Upper number is computed (fc) ; lower number is measured (fc) 

FIGURE 6.--Calculated and measured results