1. Introduction

The aim of tunnel lighting is to ensure that traffic, both during daytime and nighttime, can approach, pass through, and exit a tunnel at the designated speed, with a degree of safety and comfort equivalent to that on the adjacent stretches of open road.

This goal is achieved when, firstly, sufficient information is provided about the “run of the road ahead” and the presence of obstacles, including vehicles and their movements. Secondly, drivers should experience the visual confidence as they do on the adjacent stretches of open road. Maintaining this sense of security is critical as drivers approach a tunnel; otherwise, they might suddenly slow down, creating a hazardous situation.

The photometric characteristics of tunnel lighting installation which are considered to be of importance are the luminance level of the road and the lower part of the walls, the uniformity of the luminance distribution on the road, the control of glare, and the avoidance of flicker.

Recommendations given in a guide for luminance levels should be considered as maintained minimum values. To derive non-depreciated values from these maintained values, a maintenance factor appropriate for the prevailing circumstances should be taken into account^[1].

In 1973, CIE published the first edition of its “International Recommendations for Tunnel Lighting” (Publication CIE No 26). Since then it has become clear from practical experience that the 1973 Recommend- ations do not give a satisfactory answer to all problems concerned with tunnel lighting. In 1975, therefore, CIE appointed a subcommittee to study the fundamentals of tunnel lighting. In 1985, a detailed CIE Technial Report, prepared by that subcommittee, was published reviewing fundamental experiments concerning the lighting requirements for drivers approaching the entrance of a tunnel in daytime (Publication CIE No 61-1984-“Tunnel entrance lighting-a survey of fundamentals for determining the luminance in the threshold zone”). That report, together with other information relating to practical experience with different tunnel lighting installations, forms the background of the recommendations given in the Guide at that time.

The terminology and some of the definitions in Publications CIE 88-1990 may be different to those used in Publications CIE no 26/1 and CIE no 61.

The Publications CIE 88-1990 had been prepared by the experts of CIE Committee TC 4-08 in close contact with the working group “Lighting” of the Committee on Road Tunnels of PIARC (Permanent International Association of Road Congresses) and replaces the Publication CIE no 26/1 (1973) International Recommendations for Tunnel Lighting^[2].

The requirements for lighting installation of a tunnel are influenced by several critical factors which determine visibility. These conditions ard eminently variable, and involve characteristics of the driver, including ability, age and personal habits; the physical conditions of the road, access to and the length of the tunnel; atmospheric conditions; traffic density, volume and speed; and type of vehicles in transit. Additional considerations include the contribution of lighting to the architectural aspect of the tunnel opening with regard to visual guidance, comfort and to the overall maintenance of the installation^[3].

The interior zone is the stretch of tunnel following the transition zone. The lighting is generally kept at a constant level over the whole length of the interior zone.

Depending upon vehicle speed, the gradual reduction of luminance in the transition zone may not allow for complete dark adaptation to the lowest illumination level reached in the interior zone.

Therefore, during daylight hours, sufficiently high illumination levels are needed in the interior zone for satisfactory visibility^[4].

The average luminance of the road in the interior zone of the tunnel is given as a function of the stopping distance and the traffic flow. Very long tunnel’s interior zone consists of two different sub zones. The first sub zone corresponds to the length which is covered in 30seconds and should be illuminated with the “long tunnels” levels. The second sub zone corresponds to the remaining length and should be illuminated with the “very long tunnels” levels^[5].

However, this regulation is not yet applied to our tunnel design standards^[6].

Determining the required road surface luminance of the interior zone of a road tunnel requires a decision between the safety of road users and economic feasibility. To date, standards based on experimental results have been applied^{[1, 7]}.

In this paper, the required road surface luminance was theoretically derived from assumed factors necessary for determining the required road surface luminance of a road tunnel. Theoretical equations were derived based on two cases for triggering signals from visual cells to the brain. To verify the feasibility of the results, they were compared with values recommended as standards.

2. Luminance level equation

A Theoretical Equation for the Road Surface Luminance in the Interior Zone of a Road Tunnel

2.2 Theoretical Equations

When the vehicle stops, the acceleration is -am/s², the object identification start distance is Sm, and the design speed is v km/h(=v/3.6 m/s). The time to reach the object identification distance without braking is t_s(=3.6S/v) sec and the braking time is t_b(=v/3.6a)sec. Therefore, the recognition time trsec is calculated by the following equation.

(1)

$t_{r}= t_{s}- t_{b}=\dfrac{3.6 S}{v}-\dfrac{v}{3.6 a}=\dfrac{3.6^{2}a S - v^{2}}{3.6 a v}$

The acceleration a when the vehicle stops is mainly determined by the vehicle's braking ability and the condition of the road surface. When analyzing the design speed and braking distance specified in the currently applied regulations, a was found to be 1.5 ~ 2.5 m/s^2[11]. In this paper, assuming an optimal braking state, a was set to 2.5 m/s².

The distance S was assumed to be 500 m based on the calculation under the condition of an obstacle with a size of 0.15 m×0.15 m and a reflectivity of 0.2, which is commonly used in road tunnel tests^[12], assuming that a human eye with 1.0 vision can perceive a visual difference of 1'^[13].

Based on assumption 3.(1), when the product of the log value of the average road surface luminance Lr cd/m² and the recognition time tr reaches a certain amount Cr1(=log Lr×tr) cd․s/m², the brain recognizes the object and send a braking command to the muscles. Therefore the average road surface luminance is determined by the following equation.

(2)

$L_{r}=10^{\dfrac{C_{r1}}{t_{r}}}=10^{\dfrac{3.6C_{r1}av}{3.6^{2}a S-v^{2}}}$

The critical accumulated light quantity Cr1, which is the product of the log value of the average road surface luminance and the recognition time, was used as 6.57 cd․s/m² by using the standard of Lr=9 cd/m² when the tunnel transmittance is 50% and v is 100 km/h^[14]. Using the above assumed constants, (Equation 2) is organized as follows.

(3)

$L_{r}=10^{\dfrac{60v}{16200-v^{2}}}$

Based on assumption 3.(2), when the product of the average road surface luminance Lrcd/m² and the recognition time tr reaches a certain amount Cr2(=Lr×tr)cd․s/m², the brain recognizes the object and gives a braking command to the muscles, so the average road surface luminance is determined by the following equation.

(4)

$L_{r}=\dfrac{C_{r2}}{t_{r}}=\dfrac{3.6C_{r2}av}{3.6^{2}a S-v^{2}}$

The standard of Lr is 9 cd/m² when v is 100 km/h. Assuming that the transmittance within the currently used tunnel is 50%, Cr2 was assumed to be 62 cd․s/m^2[14].

Based on the assumed constants above, (Equation 4) can be summarized as follows.

(5)

$L_{r}=\dfrac{560v}{16200-v^{2}}$

Fig. 1. Concept diagram from seeing and recognizing an obstacle to stopping

2.3 Verification

Comparisons of the theoretical calculation results of (Equation 3) and (Equation 5) with the currently used standards derived experimentally are shown in Table 1^[6]. For assumption 3.(1), the results were similar at the design speeds of 100 and 40 km/h, but the calculated values were 31 and 17% lower than the standards at 80 and 60 km/h respectively.

Under assumption 3.(2), the results were almost identical, except for a 17% higher than the standard at 60 km/h.

Based on the results above, (Equation 5) was in good agreement with the experimentally derived criteria, so (Case 2) of Assumption 3 was more valid.

Table 1. Calculated and standard values of average luminance level of a road according to design speed.

3. Conclusion

This paper proposes a theoretical equation for the average road surface luminance in road tunnels and validates its feasibility by comparing the results with current standard.

The threshold of photoreceptor cells that detect obstacles and send signals to the brain does not follow the Weber-Fechner's law, but is determined by the product of the surface luminance and time.

In the case of design speeds of 110 and 120 km/h, which have not yet been presented as standards, the predicted values of the road surface luminance of road tunnels are 14.8 and 36.3 cd/m², respectively, according to the results of this paper.

Further research should explore object recognition by distinguishing between rods and cones.