Lighting : Lighting October 2015 - Vol 35 Issue 5
October/November 2015 | LIGHTING MAGAZINE 33 32 LIGHTING MAGAZINE | October/November 2015 TECHNICAL FEATURE The cosine law’s revealing power By Warren Julian One of the enjoyable things about teaching is to see the look of understanding on a student’s face when an idea clicks. This is especially so when a person’s prior experience has left them confused, with little confidence in using maths and in extreme cases a defensive switching off when the subject is mentioned. In this article I will try to explain why directional light can be revealing. It will explore the inverse square and cosine laws of illuminance, hopefully in a way that isn’t terrifying. Figure 1. The left-hand sphere has a radius D and its surface area is 4pD2 whereas the right-hand sphere’s radius is 2D, so its area will be 4p(2D)2 = 16pD2, ie, four times as large. Each has a central light source producing the same lumen output uniformly over the sphere’s surface. It can be seen that the illuminance (lumens divided by area) on the surface of the larger sphere must be a quarter of that on the smaller one’s surface. This also confirms the inverse square law. The lighting set-up for gymnastics. The velodrome from the head- on camera position. Seamlessly mixing residential and commercial space, it’s a model for a healthy urban community. Coinciding with the Games, Toronto also are staging an accompanying amazing 35-day arts and culture festival – Panamania. After doing these events for 18 years, I bump into many colleagues from different parts of the world – the international games event ‘gypsies’ ... many Aussies included. The broadcast lighting is 95% overlay (temporary) by Musco – past masters at such events. And the permanent new legacy installations are ... Musco! One venue, boxing, has LED overlay lighting; the rest are metal halide. The broadcast is all in HDTV with a few super-slow-motion cameras. However, the majority of the sports are not televised by CBC – just 16 out of 48! Of course other countries’ TV networks (16) are here to cover their local heroes. The opening ceremony was a wonderful experience. As with previous Games, my involvement is for the formal protocol elements (not the razzamatazz show) – the athletes’ parade (6000!), speeches, Canadian flag parade and hoisting (complete with legendary Canadian Mounties), the torch flame parade, lighting the cauldron, etc. The 3-hour spectacular show surrounding the protocol parts was created by none other than the world famous Cirque du Soleil! A totally memorable experience. There were some tough challenges to solve. The biggest being aquatics. Water reflects of course. Plus the roof is too low with a myriad suspended acoustic panels installed. Arrrgh!!! Good teamwork from Musco, some outside the box thinking and the right attitude to do the right thing and the TV pictures went to air! As I write this, the last Para events have just ended. Brazil topped the medal list with Canada second edging out arch rival the USA – followed by Mexico, Colombia and 13 of the 41 countries. Last minute tweaks are always expected but you just can’t beat the upfront planning and design well in advance. After Vancouver 2010 winter Olympics, this was my second Canadian major event and a truly enjoyable experience. Next stop ... Rio de Janiero! THE INVERSE SQUARE LAW OF ILLUMINANCE Lighting design often requires the prediction of the illuminance at a point on a surface, using the relationship between the illuminance (E), the distance (D) from the light source and the intensity (I) of the light source in the direction of that point. That relationship is E = I/D2, provided that the light arrives at a right angle (90̊) or normal to the point. The relationship is called the inverse square law of illuminance. In plain English it says that the illuminance decreases very quickly (by the square of the distance) as the distance increases. For example, if you double D to 2D then the illuminance will be a quarter of what it was at D, because in the equation D2 becomes (2D)2 which is 4D2. The reason why the illuminance drops off so rapidly can be seen from Figure 1. Obviously, I cannot see your face as you read this but I hope that you have that look of elation and that the basic Lighting design often requires the prediction of the illuminance at a point on a surface, using the relationship between the illuminance (E), the distance (D) from the light source and the intensity (I) of the light source in the direction of that point.
Lighting August 2015 - Vol 35 Issue 4
Lighting December 2015 - Vol 35 Issue 6