Introduction

Lighting solutions refers to the use of scientific calculation methods and tools to design a lighting solution for a specific space or scene that meets the requirements of illuminance, energy efficiency, visual comfort and so on. This process usually includes the following key steps: determining lighting requirements (e.g., lighting area, illuminance, uniformity – more about lighting uniformity, and glare limitation), selecting calculation methods (e.g., lumen calculation method, point-by-point method, etc.), optimizing the design (e.g., adjusting the number of fixtures, their locations, and light distribution curves), and evaluating the energy efficiency and cost of the solution. Lighting calculation methods are the core tools in lighting design, of which point-by-point method and lumen calculation method are the two most commonly used. In this paper, we will focus on the basic concepts of these two methods, elaborate the calculation principles and steps of the lumen calculation method, and introduce the practical applications of the lumen calculation method and so on.

What’s point by point method?

The point-by-point method utilizes light intensity distribution data from a light source or luminaire to predict the direct illuminance at each point on a plane. The method calculates the illuminance contribution of each luminaire at a specific point and adds up the total illuminance point by point. The calculation is based on the inverse square law and the law of cosines, and takes into account three key factors: luminous intensity, distance, and orientation of the light source to the surface. The formula for calculating the illuminance of a point source in a given plane is as follows: Illuminance(E)=Intensity(I)/Distance(r)². The inverse square law centers on the fact that as the distance increases, the energy of the light is distributed over a larger area, resulting in a decrease in illuminance. For example, as the distance increases from r to 2r, the energy of the light is spread over four times the area, hence the illuminance decreases to one-quarter the intensity, so we use r² in the formula. If there is a projection angle between the light source and the calculation surface, we need to consider the effect of this angle on the lighting effect, i.e., follow the Cosine Law for lighting calculations. its calculation formula becomes Illuminance(E)= Cosθ×Intensity(I)/Distance(r)², where θ is the angle between the normal of the illuminated surface and the beam. This is because the illuminated area increases when the light is directed obliquely and the illuminance decreases for the same light intensity, so a cosine factor needs to be introduced to correct for this.

What’s Lumen calculation method?

The lumen calculation method is a commonly used lighting design calculation method, which can produce average illuminance by a given number of luminaire or number of luminaires to meet an average illuminance target. Its calculations focused on illuminance on the work plane, and assume light reaches the work plane in two ways include direct light and reflected light. Here work plane height above the floor is usually defined in lES handbook or recommend practice documents. Based the basic relationship that Illuminace(E)=Lumious flux/Area, it also considers the effect of the Utilization Factor (UF) and Maintenance Factor (MF) of the space on the lighting effect. Its final formula is E=FxnxNxUFxMF/A, here F=initial bare lamp luminous flux (lumens), n=number of luminaires, N=number of lamps per luminaire, UF=Utilisation factor, MF=maintenance factor, A= area of the surface (m²). UF can be found in the luminaire’s report, but on closer inspection its value is related to a number of parameters, so it is necessary to check these parameters before finding the UF value. Similarly the value of MF is also complex, so if you are interested you can refer to the article “Maintenance factor in lighting”.

Why go with lumen calculation method?

With the introduction of the previous section, it is not difficult to know why the lumen calculation method is needed, or to know the main applications of the lumen calculation method. One of them is to calculate the effect of lighting (illuminance) when the number of luminaires is known. That is, we can calculate the illuminance of the target area by E=FxnxNxUFxMF/A when the number of lighting fixtures, space types, sizes and characteristics are known. The second is to extrapolate the number of luminaires required when the expected lighting requirements are known. That is, if the lighting requirements of the project are clear, and the type, size and characteristics of the space are also clear, we can calculate the number of luminaires needed for lighting by n = ExA/F /N/UF/MF.

In practice, lighting simulation software can quickly get these results but unfortunately, the lumen method is not directly adopted by the mainstream lighting simulation software. Most of the lighting simulation software, such as Dialux, AGI32 ( More about AGI32 and its application ), Relux, etc., uses the piont-by-piont method, which is a complex method that needs to take into account the illuminance of multiple light sources at a specific point. This method is complex and requires the consideration of multiple light sources for the illumination of a specific point, so it is not convenient for us to use this method to estimate the illumination and the number of lamps. On the contrary, the lumen calculation method is more suitable for beginners and can help us to get the desired results quickly. This fact also tells us that in practice, in addition to focusing on the luminous flux as a parameter, we also need to pay more attention to the impact of light distribution on the lighting results.

Steps to run lumen calculation method

Step 1. Determining the utilisation factor

The utilization factor (UF) is the ratio of the total luminous flux received by a surface to the total luminous flux emitted by the luminaire. It depends on the light output efficiency ( What’s lumious efficacy? ) of the luminaire, the light distribution of the luminaire, the geometry of the space, the room reflectivity, etc. Usually, UF tables are prepared for general lighting with regularly arranged luminaires, affected by the three main room surfaces (ceiling cavity, wall and floor cavity or horizontal reference plane). To use a UF table, we must have a few variables determined: room cavity ratio (room index ratio) and surface reflectances (ρ) for ceiling, wall and floor. The surface reflectance of ceiling, wall and floor is the ratio of the light reflected by the surface to the incident light, expressed as a percentage. They are equally important for calculating illumination levels. Typical reflectance values ​​for ceilings are 70%-90% (light colors), for walls are 30%-70% (medium to light colors), and for floors are 10%-30% (dark colors such as wood floors and carpets). For example, in lighting simulation, we generally use the default values, i.e. ρc=0.7, ρw=0.5 and ρf=0.2. Of course, if conditions permit, we can also use a reflectometer to measure the reflectivity. To get surface reflectances (ρ), we can place the measuring head of the reflectometer on the surface to be tested (ceiling, wall or floor), make sure there is no light leakage, press the measurement button and wait for the test results of the equipment (reflectivity values ​​of the ceiling, wall and floor). However, room cavity ratio(RCR) is used to evaluate the impact of indoor cavity (ceiling, floor or wall cavity) on light loss and reflection. RCR=2.5*RCH*P/A. RCR = Room cavity ratio, P=Room perimeter, A=Room area. So RCR=5*H*(L+W)/(LxW). For example: an ordinary office, the illumination value requires 500lx, the space is 50 meters long, 50 meters wide, 6 meters high, the working surface is 0.8 meters, and the lamp is installed at a height of 5.8 meters. We first calculate the room cavity ratio, RCR=2.5*(5.8-0.8)* (50+50)*2/2500=1, KI=5/RCR=5, and then we can get UF=1.1 by looking up the table.

REFLECTANCE
Ceiling	0.8	0.8	0.8	0.7	0.7	0.7	0.5	0.5	0.5	0
Walls	0.7	0.5	0.3	0.7	0.5	0.3	0.7	0.5	0.3	0
Working plane	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0.2	0
ROOM INDEX	UTILIZATION FACTORS(PERCENT)  k(RI) x RCR = 5
k = 0.60	74	66	61	74	66	60	73	65	60	56
0.80	84	76	71	83	75	70	82	75	70	65
1.00	91	83	79	90	83	78	88	83	78	73
1.25	97	90	85	95	89	85	93	88	84	79
1.50	100	94	90	99	93	89	96	92	88	83
2.00	105	99	95	103	98	94	100	96	93	87
2.50	107	102	98	105	101	97	102	98	95	89
3.00	109	105	101	107	103	100	104	100	98	91
4.00	111	108	105	109	106	103	106	103	101	93
5.00	113	110	107	111	110	106	107	104	103	94

Step 2. Determine maintenance factor

Maintenance factor (MF) is defined as the ratio of the maintained illuminance/brightness to the initial illuminance/brightness, i.e., losses for lamp lumen maintenance. In lighting design and simulation, the maintenance factor (MF) is a very important parameter that reflects the attenuation of illuminance during the actual use of the lighting system. This is because in actual use, lamps experience luminous flux attenuation (attenuation of the light source itself and attenuation caused by contamination of the lamp surface), sudden failure of lamps (caused by light source and power failure), room surface contamination and other factors, which will cause the lighting effect (illuminance and brightness) to gradually decrease. In lighting design, the design goal is usually to maintain illuminance/brightness to meet the requirements of the project, rather than the initial illuminance/brightness. The calculation formula of maintenance factor MF=LLMFxLSFxLMFxRSMF, here LLMF means lamp lumen maintenance factor, LSF means lamp survival factor, LMF means luminaire maintenance factor and RSMF means room surface maintenance factor. Due to space limitations, it will not be explained here in detail. Those who are interested in its calculation process and more related knowledge can refer to Maintenance factor in lighting. In many cases, the value of MF is 0.80, 0.85, or 0.90. In this article, we will use 0.80 for calculation.

Step 3. Calculating the number of luminaires needed to achieve a given mean illuminance

For example, your warehouse needs 200 lux illumination, but you don’t know how many lamps you need. Then we can use the formula to calculate the result we want. Through steps 1 and 2, we know that UF=1.1 and MF=0.8, A=2500m2. Moreover, if we choose ZGSM’s 9th generation 100W UFO LED lamp, then F=19000lm and N=1. According to the formula n=ExA/F /N/UF/MF, we can get the result n=200×2500/19000/1/1.1/0.8=29.9, that is, we need 30 pieces ZGSM-HB09-100M UFO LED lamps ( Check to find more about ZGSM Heilos UFO LED lights ) . Below is the suggestion layout of 30 pieces high bay lights.

Step 4. Calculating illuminance available at the work plane

For example, your workshop now needs to replace a batch of lamps, the number is 24, and you are going to use ZGSM’s 200W UFO lamps. You don’t know how much illumination you can achieve, so we can also use the formula to calculate the result we want. Through steps 1 and 2, we know that UF=0.9 and MF=0.8, A=2500m2, the luminous flux of ZGSM’s 9th generation 200W UFO lamp is F=38000lm, and N=1. According to the formula E=FxnxNxUFxMF/A, we can get the result E=38000x24x1x1.1×0.8x/2500=321lux, which can meet the lighting requirements of ordinary assembly workshops according to the corresponding standard EN12464-1 ( EN12464-1 standard refers to workshop and warehouse lighting ). However, if it is a fine assembly workshop with an illumination requirement of 500lux, the current solution cannot meet the requirements. We either increase the wattage of the lamps or increase the number of lamps to achieve higher illumination.

Lighting result comparison – lumen calculation method vs Dialux

Lumen calculation method vs Dialux

In Dialux, we tried to carry out lighting simulation by following information. The lighting space was set as follows: it’s 50 meters long, 50 meters wide, and 6 meters high, the working surface height is 0.8 meters, and the lamp installation height is 5.8 meters. After selecting and inserting the IES file of ZGSM-HB09-100M, according to the information in the previous section, the field arrangement method (5×6 layout, a total of 30 lamps) was adopted. After completing all the above operations, the calculation result was obtained, and the illumination was 196lux, which was very close to the result calculated by the lumen calculation method, further confirming the reliability of this method.

Lumen calculation method which is not suitable for outdoor lighting

The lumen calculation method can be used to calculate the illuminance of indoor lighting and the number of lamps required. So, can this method be applied to outdoor lighting simulation ( Get more details about ZGSM lighting simulation )? Unfortunately, it is not applicable. ZGSM believes that there are two main reasons: First, there are no walls and ceilings in the outdoor lighting environment, so it is impossible to calculate the situation where the light emitted by the lamp is reflected from these surfaces to the target area. Second, the illumination distance of outdoor lighting simulation is far, and the attenuation and scattering of light are very obvious, but the lumen calculation method does not involve calculations in this regard. Both factors will lead to deviations in the calculation results (usually the calculation results by lumen calculation method are too large). According to ZGSM’s experience, if you must use the formula E=F×n×N×UF×MF/A to calculate the illuminance, you need to add a coefficient η, which is generally 0.7, that is, E=η×F×n×N×UF×MF/A. If it is an indoor stadium lighting (as picture shown above, such as a multiple sports venue), we do not need to multiply this coefficient. And when you have an outdoor lighting project, ZGSM recommends using software for simulation. Most of this type of software uses point illuminance method, ray tracing method and radiosity method, and the calculation of the results is more accurate. If you are interested in the application of Dialux in lighting design, you can refer to the following applications with Dialux.

Summary

Lighting calculation method includes point by point method and lumen calculation method. This paper first introduces the point by point method, its principle and its application in lighting simulation software. Then it focuses on the lumen method, which is a basic lighting design method used to determine the number of luminaires needed to achieve the corresponding illuminance level in a space. It can also be used to calculate the average illuminance, which is very simple and effective. This article outlines the key steps of the lumen calculation method, including determining the utilization factor (light distribution efficiency), the maintenance factor (which takes into account light loss over time), calculating the number of luminaires required, and verifying the illuminance at the work plane. This article also compares the lumen calculation method to the advanced lighting simulation software Dialux, emphasizing that while Dialux provides greater accuracy and detail for complex designs, the lumen method provides a faster, simpler solution for initial estimation. ZGSM believes that in practice we can use the lumen method to initially identify the number of luminaires required for lighting or the lighting effect that can be achieved by applying these luminaires, and then use a tool such as Dialux to provide the client with a more intuitive simulation. At the same time we need to remember the limitations of the lumen calculation method as it is mostly used for indoor lighting, whereas for outdoor lighting such as sports venue, parking lots, roadways, etc., we would recommend the use of a simulation software in order to get the right lighting solution faster, including the number of fixtures, wattage, lenses ( more about symmetric or asymmetric lightdistribution ) and layout of fixtures etc.

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