CALCULATION AND CONSTRUCTION OF CURVES OF EQUAL HORIZONTAL ILLUMINANCE VALUES USING THE MINSK-32 COMPUTER

V. A. VEKLENKO, A. V. MOSKALEV, V. A. FEDORENKO

In designing lighting with the use of both floodlights and various luminaires, isolux diagrams are widely used; these are given in lighting-engineering handbooks, in the “Instructional Guidelines” of the Tyazhpromelektroproekt Institute, and in other materials on lighting design.

In connection with the ever-increasing volume of design work and the introduction of new lighting devices, the expenditure of working time on such a cumbersome and labor-intensive process as constructing isolux curves of horizontal illuminance, which are required in large numbers, increases considerably. Therefore there arises the need to reduce the time spent on auxiliary calculations. The use of computers in this field provides such a possibility.

In the journal Svetotekhnika in recent years a number of articles have been published in which calculations using computers are presented. The work of M. S. Elinson and N. N. Firsanov [1] is of undoubted interest. For example, computers of the BESM-4 type and the Nairi-S electronic digital computer were used. But in some works only conventional isolux curves are calculated [2], while in others assumptions are introduced that limit the application of the program [3]. In all cases the result is issued in the form of a table with numerical illuminance values, from which the isolux curves must then be drawn.

On the basis of all the foregoing, the authors consider the proposed program the most acceptable for calculating isolux curves of horizontal illuminance.

The calculation method is valid for those lighting devices whose luminous-intensity curves in different longitudinal planes are similar, since in this case, for constructing isolux curves, the values of luminous intensity in only the horizontal and vertical planes are sufficient [4, 5].

The well-known formula for determining the horizontal illuminance at the calculation point \(A\) [6] was adopted as the basis of the calculation:

\[ E_{\mathrm{r}} = \frac{I_A \cos^3 \alpha}{h_p^2}, \]

where \(I_A\) is the luminous intensity in the direction toward the calculation point \(A\) (Fig. 1);

\(\alpha\) is the angle between the direction of the luminous intensity toward the calculation point and the normal to the illuminated surface;

\(h_p\) is the mounting height of the lighting device above the calculation plane \(P\).

From the geometry (Fig. 1) we obtain

\[ I_A = I_{\alpha В}\cdot \frac{I_{\alpha Г}}{I_0}; \]

where \(I_{\alpha В}\) and \(I_{\alpha Г}\) are the luminous-intensity values in the vertical and horizontal planes;

\(I_0\) is the value of the axial luminous intensity;

Fig. 1. On the construction of isolux curves of horizontal illuminance

\[ \frac{I_{\alpha Г}}{I_0} \]
is the similarity coefficient.

\[ \cos \alpha = \frac{h_p}{\sqrt{x^2+y^2+h_p^2}}, \]

where \(x\) and \(y\) are the coordinates of point \(A\) on the calculation plane \(P\).

From [1], [2], and [3] it follows that

\[ E_\Gamma = \frac{I_{\alpha В}\cdot I_{\alpha Г}\cdot h_p} {K_3\cdot I_0\left(\sqrt{x^2+y^2+h_p^2}\right)^3}, \]

where \(K_3\) is the maintenance factor.

\[ \left. \begin{aligned} \alpha_{\mathrm{В}} &= \operatorname{mod}\left[ \operatorname{arctg}\left( \frac{x-h_p\operatorname{ctg}\Theta} {h_p-x\operatorname{ctg}\Theta} \right) \right],\\ \alpha_{\Gamma} &= \operatorname{arctg}\left( \frac{y}{\sqrt{x^2+h_p^2}} \right), \end{aligned} \right\} \]

where \(\alpha_{\mathrm{В}}\) and \(\alpha_{\Gamma}\) are the values of the angles in the vertical and horizontal planes.

The illuminance is calculated along the \(X\)-axis and along the \(y\)-axis from 0 to 500 meters with a step of 5 m. From the data obtained, isolux curves are plotted for the following series of illuminance values: 0.15; 0.2; 0.3; 0.4; 0.5; 0.7; 1.0; 1.2; 1.5; 2.0; 2.5; 3.0; 4.5; 5.0; 7.0; 15.0; 20.0; 30.0; 40.0; 50.0; 65.0; 80.0.

The initial data for the calculation are the mounting height \(h_p\) of the luminaire above the calculation plane, the angle of inclination of the luminaire relative to the calculation plane \(\Theta\), the scale \(M\) in which it is desired to obtain the isolux curves, the maintenance factor \(K_3\), the number of specified luminous-intensity values in the vertical and horizontal planes, respectively \(n_{\mathrm{В}}\) and \(n_{\Gamma}\), and the values themselves.

The result is issued in the form of ready-made isolux graphs (Fig. 2). In addition, numerical illuminance values are printed on the ATsPU.

The program for calculating and plotting the isolux curves “RIZOL” was written in the languages FORTRAN and YaSK for the Minsk-32 computer. The graphical part is performed on the drafting device “Digigraph p/m 32,” manufactured in the CSSR.

Fig. 2. Graph of isolux curves of horizontal illuminance obtained on the Minsk-32 computer

The assembled program occupies 42 sheets of machine memory.
Computation time: 10 minutes.

Conclusions

1. Practical application of the “RIZOL” program makes it possible to reduce labor expenditures to a considerable extent, and also to shorten the time required for calculating and plotting isolux curves of horizontal illuminance.

2. The proposed program may find wide application in the design of lighting installations.

REFERENCES

1. M. S. Elinson, N. N. Firsanov. Calculation of illuminance from floodlights on a computer. Svetotekhnika, 1974, No. 2, pp. 13–14.

2. N. A. Vanshtein. Use of a computer for constructing conditional isolux curves of lighting fixtures. Svetotekhnika, 1975, No. 6, pp. 18–21.

3. M. S. Elinson, N. N. Firsanov. Calculation of isolux curves of floodlights on a computer. Svetotekhnika, 1973, No. 2, p. 14.

4. G. M. Knorring. Calculation of illuminance from lighting fixtures with a sharply asymmetric light distribution. Svetotekhnika, 1970, No. 8, pp. 8–10.

5. G. M. Knorring. Lighting-engineering calculations in artificial-lighting installations. Moscow, Energiya, 1973, pp. 22–27.

6. V. V. Meshkov, M. M. Epaneshnikov. Lighting installations. Moscow, Energiya, 1972, pp. 147–151.