# Hand-to-hand room lighting calculation

• Tutorial
I’ll try to very briefly and simply outline the method of manual calculation of lighting in rooms, which I was taught on the course “Lighting Calculation” of the LiDS lighting design school.

What should be the illumination?
When planning lighting, first of all, it is necessary to determine the target illumination that meets the standards and calculate the total luminous flux that the lamps should give in the room.
It is easy to determine the standards - either we look for our type of room in the tables SanPiN 2.21 / 2.1.1 / 1278-03 "Hygienic requirements for natural, artificial and combined lighting of residential and public buildings" and SP 52.13330.2011 "Natural and artificial lighting", or we agree with the basic requirement for illumination of residential premises - 150 lx or office premises with computers - 400 lx.

A rough estimate of the required luminous flux
By default, the calculation of illumination is done in the Dialux program . But the result, at least approximately, needs to be known in advance in order to compare the data with the “by eye” assessment.
As written even on Wikipedia, the average surface illumination is the ratio of the light flux incident on it to the area. But in a real room, part of the luminous flux of the lamp does not reach the working planes, disappearing on the walls. Illumination in the room is the ratio of the total luminous flux of the lamps to the area of ​​the room with a correction factor of "η".

The fraction of light "η" that reaches the working surfaces can be estimated by eye. In the most general approximation, for some very average room with some kind of fixtures, about half of the light reaches the working surfaces, which means that for a very rough estimate, you can use the coefficient η = 0.5.
For example, in a room with an area of ​​20 m 2, a lamp with a luminous flux of 700 lm (the equivalent of an incandescent lamp of 60 W ) will create illumination E = 0.5 × 700 lm / 20 m 2 = 18 lx. And this means that to achieve the standard of 150 lx, you need F = 700 lm × (150 lx / 18 lx) = 5800 lm, or the equivalent of 8 60W incandescent bulbs!
(Half a kilowatt of incandescent lamps on a small room! It is clear why the lighting standards for residential premises are much lower than for institutions, and why nobody has been lighting incandescent lamps for a long time.)

A more accurate method of manual calculation
But since the rooms come with different walls, different forms, with high or low ceilings, the correction factor is not necessarily equal to 0.5 and for each case its own: in practice, from 0.1 to 0.9. Despite the fact that the difference between η = 0.3 and η = 0.6 already means a double run of the results.
The exact value of η must be taken from the tables of the coefficient of utilization of the light flux developed back in the USSR. In full view with explanations of the table I quote in a separate document. Here we use an excerpt from the tables for the most popular case. For a standard bright room with reflection coefficients of the ceiling of the walls and floor in 70%, 50%, 30%. And for ceiling mounted luminaires that shine for themselves and a little to the side (that is, they have a standard, so-called “cosine” light intensity curve).

Tab. 1 Luminous flux utilization factors for ceiling lamps with a cosine diagram in a room with reflection coefficients of the ceiling, walls and floor - 70%, 50% and 30%, respectively.

In the left column of the table the index of the room is indicated, which is calculated by the formula:

where S is the area of ​​the room in m 2 , A and B are the length and width of the room, h is the distance between the lamp and the horizontal surface on which we calculate the illumination.
If we are interested in the average illumination of working surfaces (tables) in a room of 20m 2 with walls of 4m and 5m, and the height of the lamp suspension above the tables of 2m, the room index will be i = 20m 2 / ((4m + 5m) × 2.0m) = 1.1. Having made sure that the room and the lamps correspond to those indicated in the signature to the table, we obtain the light flux utilization factor - 46%. The factor η = 0.46 is very close to the expected offhand η = 0.5. The average illumination of working surfaces with a total luminous flux of 700lm will be 16lx, and to achieve the target 150lx, you need F = 700lm × (150lx / 16lx) = 6500lm.
But if the ceilings in the room were half a meter higher, and the room was not “bright”, but a “standard” room with reflection coefficients of the ceiling, walls, and floor of 50%, 30%, and 10%, the coefficient of light flux η would be (see . expanded version of the table ) η = 0.23, and the illumination would be exactly half as much!

We check the calculations in dialux.
We will build in the dialux room a 4 × 5m room, 2.8m high, with a working surface height of 0.8m and the same reflection coefficients as with manual calculation. And we’ll hang 9pcs of small fixtures with a classic cosine diagram of 720lm each (6480lm per circle).

Fig. 1 Taken as an example, the Philips BWG201 lamp with a luminous flux of 720lm, and its classic "cosine" light distribution

Will we get an average illumination of work surfaces of 150 lx, as we estimated manually? Yes, the calculation result in Dialux is 143 lx (see Fig. 2), and in an empty room without furniture and a human figure - 149 lx. In lighting engineering, values ​​that differ by less than 10% are considered coincident.

Fig. 2 The result of the calculation in dialux - the average illumination of the working surface (with a safety factor of 1.0) was 143 lux, which corresponds to the target value of 150 lux.

Fig. 3 Beautiful pictures that people believe in.

Conclusion:
A rough estimate using the primitive method according to the formula E = 0.5 × F / S will take 1 minute, to refine the utilization rate according to the tables - another 3 minutes, for a project in Dialux after some training - about 20 minutes and another 20 minutes if you want to beauty. " Dialux produces very beautiful pictures (see. Fig. 3), which are worth the work spent, because people believe in them. But according to the ratio of efficiency and labor costs, the assessment of illumination by hand is out of competition. Hand counting is simple, reliable and effective as a sapper blade, gives confidence and understanding.