I am introducing the DDR (Diameter to Distance Ratio) as a quick guide in this LdG-4 (Lighting Design Guide-4)

## Introduction

A lot of beam angles for luminaire/lamps are available for architectural lighting, we can find a lot the terms Narrow Spot spot , super spot , flood , wide flood ,narrow horizontal flood, vertical flood …etc but how can easily use the right beam angle ?

lets find out more about the proposed DDR and how helpful could be for selecting quickly the right beam angle.

## Beam Angle

Before looking at the application of the beam angle, let’s see what dose beam angle mean? and how it is calculation

The beam angle is the **degree of width** that light **emits from a light source**. In other terms this is the angle between the two points on the beam axis where the intensity drops to 50% of its maximum.

but why the beam angle is using the angle of light where intensity of light drops to 50% only.

Because after I_{max } the light will fade and will not be part of the highlight, the light after the I_{max }is spill light. and the human eye will see mainly the beam angle.

## Beam Angles

there are many different beam angles with different names, the most common angles are

5°,10°,15°,24°,35°,45°

while some manufacturer call the 5° Narrow spot some other call the 15° Narrow spot, as there is no standard for the name I am going to use the ERCO beam angles name in this tutorial which are as follows

Narrow Spot 7°

Spot 14°

Flood 28°

wide flood >45°

this system is easy to remember as it start form the 7° then 2×7=14° , then 2×14 =28°

what is good about this system that is unique in ERCO range indoor or outdoor, if you select any lumianire in Narrow Spot it will be 7°±2,Spot will always be 14°±2 and flood will be 28°±2

## The Cone Diagram

the cone Diagram is very helpful and provide useful data for designers

the cone diagram is provided by the manufacture of generated by lighting design software like DIALux , relux , AGI32 …etc when you use the photometric file e.g IES or Eulumdat

some manufacture provide table not the cone like the one bellow but it has similar information

## The relation between Diameter , Angle and Distance.

The closer the beam angle to a surface the smaller the diameter is and the higher the lux is.

if two spotlight with same lumen but with different beam angle are used at the same distance to the surface then the bigger angle will have bigger diameter and less lux.

the cone diagram is a good tool to see the relation between beam angle , diameter of light and distance, however during the design to avoid looking at many data there should be an quicker way.

## The Magical Number 0.018

to know the diameter of light without getting back to the cone diagram there is a quick formula

**Diameter of light = 0.018 × beam angle × the distance**

for example if you need the diameter of light for a spotlight of 14° @ 3 meter distance then

Diameter=0.018×14×3=0.756

this formula is correct for beam angle up to 50°

## DDR(Diameter to Distance Ratio)

the 0.018 is quite handy but I am using more handy way which I would like to share with you.

I am proposing the DDR (Diameter to Distance Ratio)

this DDR simple relation between different angle and diameter of light for famous angles

from the above chart if you want to use narrow spot beam with 6° @ 7 meter the diameter will be =0.1×7 = 0.7 meter.

## The useful 4 DDR

the one tenth , quarter, half and 1 are very useful to select the right beam angle very quickly.

if you want to highlight an object with *one*–*tenth* (¹/10) the distance then use

DDR_{1 }=0.1→ beam angle Narrow Spot around 6°

in dont really require the exact beam angle, ±2° should be fine

¹/10 the distance →Narrow spot 7°±2

¼ the distance →Spot 14°±2

½ the distance →Flood 28°±2

full the distance →wide flood >45°

## Indoor Application of the DDR

lets say you want to highlight a flower vase on a table in a room height of 3 meter

the distance between the spotlight on the ceiling and the flower on a table 2.25 meter

then the 0.1 will give a diameter of 0.22 meter which should be good, of course the lighting will fade out and will not stop at 0.22

¹/10 the distance →Narrow spot 7°±2 for this flower vase

Another example if there is a niche in the wall with 1 meter and you have small item lets say 30 cm and the light to this item is 0.6 meter then you need diameter that is half of the distance

because 30 cm is half of the distance then you need ½ the distance beam angle which is flood.

½ the distance →Flood 28°±2

these 4 DDR are useful to know the Diameter of a beam angle @ certain distance in a very quick way .

after selecting the closest beam angle then you need to select the required lumen and intensity of light, for good accent lighting , it would be advisable to use minimum 5 times the general lighting e.g if you have 200 lux as general lighting then 1000 lux or higher would be appropriate to have good contrast between the highlighted object and the background.

## Outdoor Application of the DDR

if a crown of a palm tree with 10 meter height need to be highlighted by using two uplight , lets say the crown is 2 meter wide then each uplight will have to cover half of the crown which is 1 meter @ a distance of 10 meter then DDR=0.1 would be suitable for this application

¹/10 the distance →Narrow spot 7°±2

anther example if you are highlightng a tree where the part of crown to be highlighted is half of the distance then ½ the distance →Flood 28°±2

## Notes

- The DDR works well when the light is perpendicular to the surface, once there is a tilt then the beam will changed especially when the tilt is @steep angle, but would be useful in general.

- It is always good to check the final results with a design software like DIALux.
- The design examples are not necessarily the best option for design, they are only examples and a designer should not be limited by by ideas.
- these DDR mainly for accent lighting for other type of lighting like general lighting there is an industry standard which is called the SHR (Space to hight Ratio)
- these 4 DDR are the most common but there are many other beam like oval beam.

if you want to see more applications of thses beam angles then you would probably be interested if you see the LdG-2

# Lighting design LdG + LdC Page

if you are interested to learn lighting design software DIALux evo then visit DIALux evo Tutorials DLX-T page

شكرا باشمهندس لقد أمتنا كثيرا وربنا يزيد من فضله وعلمه

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Thanks

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Good article Ezzat, as always!

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Thanks

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Thanks

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thanks

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Very good and helpful explanation, waiting to see more from your side.

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Thanks Khalid

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Very informative and useful.

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Thanks Michael

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Your job and dedication makes me learn and grow up. Thank you so much fro Guatemala

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Great work, keep it up

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Very informative thanks a lot

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WOW! WOW! WOW! This is exactly the article I have been searching .

My company is a LED lighting fixture manufacturer selling mostly to interior designers. We do provide complete photometric data and IES file for each of our lighting fixtures. Still, the most common question they have is how to position and space the lights.

Most small retail and residential interior design projects do not have the budget to hire lighting designers, but the interior designers should at least know how to use DDR cone diagrams.

With your permission, I like to translate this article into Chinese and use the photos to make a youtube video in Chinese and English.

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thank you so much for your nice Explanation

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