Work The Angles

A wider beam lets you cover more area, but with less intensity (if all things are equal).

Please Remember:

The opinions expressed are mine only. These opinions do not necessarily reflect anybody else’s opinions. I do not own, operate, manage, or represent any band, venue, or company that I talk about, unless explicitly noted.

Want to use this image for something else? Great! Click it for the link to a high-res or resolution-independent version.

We’re getting close to a time where I might be able to buy a couple of lighting fixtures. It’s been a while since I’ve updated the illumination at my main gig, and my feet are getting itchy. This functionally means that I spend inordinate amounts of time looking at the same lists of products over and over. Hey, you never know – something might change unexpectedly. (Seeing a vendor get new inventory excites me. Toys are rad. Let’s not pretend that they aren’t.)

Whenever you buy a piece of “tech” gear, you inevitably look at the spec sheet. Spec sheets are a great place for manufacturers to fudge, obfuscate, boast, and otherwise engage in Mark-Twainian truth stretching, but they do have their place. Unless they’re completely falsified, you can use a product’s specifications to get a ballpark estimate of whether or not it will meet your needs.

But you have to know what you’re looking for, and perhaps more importantly, you have to know how various product aspects interact. The interaction is key because it profoundly affects how useful or not useful a given offering is for your application.

One thing that gets both audio and lighting buyers in trouble is to ignore the interaction factor and just focus on a single number. In particular, both audio and lighting humans can become overly fixated on power. That is, the question of how many watts a device can consume. It’s not bad to start by looking at the power, but a place where you can get in trouble is to ignore how that power is used or delivered.

For instance, let’s take a couple of similar, hypothetical loudspeakers that are on a “let’s buy something” shortlist. One can handle 500 watts continuous, and the other can handle 1000 watts continuous. Easy choice, right? Well…what if the 500-watt box is 4 dB more sensitive in the frequency range we need? In that case, the 1000 watt box isn’t actually superior. Sure, it handles more power, but if both boxes are at full tilt it’s actually going to have ever-so-slightly LESS acoustical output than the 500-watt offering. It’s not just the power that matters. It’s what that power ultimately results in that’s useful (or not).

There are, of course, lots of other wrinkles beyond just brute-force output, but I needed a simple example.

Lighting is similar. If you’re dealing with essentially comparable fixtures, then more power equals more light. Where you can get tripped up, though, is when what you THINK are comparable fixtures aren’t actually. If you live in a realm dominated by LED-powered luminaires, you’re in a world where the boundaries are still being poked and prodded. The average output-per-watt next year may well be an improvement over this year, so simply comparing two fixtures’ LED-engine power draws won’t tell you the whole story.

There’s something else, though. Something that can have a dramatic effect on whether or not a fixture is correct for your application. It can be a bit insidious, because it can occur in two fixtures that have the same light source, the same body, the same control features, and basically the same price.

The “it” I’m referring to is the optics involved in the light. Change the optics around and one light will be fine for you, where the other might be a bad choice. It all comes down to angles.


The Lumen Starts Fights, But Lux Finishes Them

The number of lumens produced by a light source (incandescent, LED, fluorescent, whatever) is a measure of how much visible light that thing is emitting. The lumen measurement is thoroughly disinterested in whether or not that energy is actually traveling in a useful direction, or focused into a beam, or anything else. It means only that a certain amount of human-visible radiation is flowing out of an emitter.

A 1000 lumen emitter spits out 1000 lumens whether you’re right next to it, or huddled in a cave on some other planet in another galaxy. The reference frame (the location of the observer vs. the location of the emitter) is essentially irrelevant.

This is different from lux.

Lux is the amount of visible light that is meeting a given surface. For lux, the reference frame matters a lot, and that makes lux much more useful as a measure of whether a light fixture will actually work for a given application. Lux is derived from lumens, in that it describes lumens per square meter. In a certain sense, lux tells you how much of a light’s output is available to do something useful for you after that light has traveled to where you need it.

Yeah, okay, great. Why does this mean that optics matter so much?

Well, look at that description of lux again. If you have the same number of lumens, but you spread them out over a greater area, the lux drops. If you focus 1000 lumens worth of visible radiation into one square meter, you have 1000 lux. If the beam spread changes such that those 1000 lumens are spread over two square meters, you have 500 lux. That’s a significant difference in how much a focus target (a performer, a sweet-looking drumkit, a rad guitar, etc.) is being illuminated.

Let me give you a more concrete example. There’s some math involved, but it’s worthwhile math.

The Difference Between 13 and 26

There’s a certain entry-level “moving head” spotlight available these days that comes in different variants. One variant uses optics that create a 13 degree beam, and the other has optics that produce a 26 degree beam. A person could look at the form factors of the different variants, as well as the rated wattage of their emitters, and conclude that the lights are the same – but that would be incorrect. The lights will not have the same performance, because the optics are different.

I don’t want to assume anything specific about the lumens generated by the fixtures’ light engines, so this might get a little abstract. Even so, the point here is comparison and not exact numbers, to that’s fine.

So, let’s call the lumens generated by the fixtures’ LEDs “Output.” The question is, how much of that output is available to do cool-lookin’ stuff? That question is answered by how much output we get per unit of area, or lux (if we’re using lumens and square meters). The question now is how to figure out the area the light is covering.

The first thing to determine is the shape of the area we’re trying to calculate. To make things easier, let’s just assume that the light hits “dead on.” If the light beam is a cone, then a “dead on” illumination at some point along the beam results in a circular cross-section.



Since the cross-section is a circle, there is only one unknown required to get its area: The radius. The radius is proportional to the beam’s throw-length, because a cone’s absolute radius increases in proportion to the cone’s height. Neat – but how do we figure it all out? Well, if you use your imagination (and squint a bit), you can start to see that a conical light-beam is a sort of “lathed” right-triangle, and that triangle has a base with a length that is, in fact, the radius we need.


If only there were some way to analyze a right-triangle to get the numbers we need.

Trigonometry to the rescue! (We say it “trig-onometry,” but what we really mean is “trigon-ometry.” It’s all about measuring trigons – polygons with three sides. Triangles, in other words.)

Let’s start with something we can arbitrarily define, like the throw-length. Let’s say that our focus target is about five meters from our light (a bit over 15 feet). To find the proportion between the base/ radius length and the height/ throw, with us also knowing the beam angle (13 degrees), the most handy trigonometric function is probably tangent.

There’s a wrinkle, though. The angle we need to use with respect to tangent is NOT 13 degrees. Thirteen degrees in the “full” beam angle, but our triangle cuts the beam in half. What we need to use is the beam angle divided by two.

So, here’s how it all works (by the way – someone should definitely check my math):

Tan(13/2) = 0.114 (The radius is 0.114 X the throw-distance)

0.114 X 5m throw = 0.570m radius

(0.570m radius)^2 X pi = 1.02m squared

So, the 13 degree light has “Output”/1.02 available for doing cool stuff when you’re 5 meters away.

What about the 26 degree light?

Tan(26/2) = 0.231 (The radius is 0.231 X the throw-distance)

0.231 X 5m throw = 1.154m radius

(1.154m radius)^2 X pi = 4.186m squared

At the same distance, the 26 degree light has “Output”/4.186 available for lighting things.

In other words, the 26 degree variant will cover more area, but will also have an apparent brightness that is about one-quarter of the 13 degree light. Again, both lights might look the same. The LED at their hearts might be exactly the same thing.

But they simply will not perform the same way, which means that you might not be able to successfully interchange them in the context of your application.

Read those spec-sheets carefully.

Consider the interactions.

Work the angles.