Video Projection Formulas

– a Primer by Anthony D. Coppedge, CTS

I’m frequently asked to explain how much ‘horsepower’ (brightness) a projector needs to have in order to make the image on a screen look good. In a moment, I will give some formulas that are very necessary in determining projector brightness and screen size. However, two 'red flags' popped into my head.

First, it's a bit technical, and some will not understand the concept.

Second, while the formulas are not a big secret, they are a necessary part of how I make a living as a consultant. However, I can honestly say that MOST firms that I've run across do not perform all of the math required to make the estimates for screens and projectors as accurate as possible. How do MOST do it? They guess.

Trust me, I'm about to get to the formulas, but this is important.

Most A/V firms 'guess' in that they have done several (if not dozens) of installations. Some of these individuals have developed an 'eye' for guessing approximate values. Some are even very good at this, and, to be honest and try to sound humble, I usually am very close by guessing myself.

But how much money is being invested here? Is that money worth a good 'guess-timate', or is it worth an accurate, calculated proposal? I prefer the latter.

So, here are the basic math formulas necessary:

Determine screen placement
Sightlines are paramount in determining screen location. Make sure everyone (especially those far away) have a clear, unobstructed view of the screen. In some cases, more than one screen is required. I won't go into screen viewing angels, as this has a lot to do with screen gain (or lack thereof) and front vs. rear.

Determine screen orientation (front or rear).
Rear is always best, but requires space behind the screen that is essentially useless for anything EXCEPT the projector (and possibly a mirror).

Determine screen size.
Measure the distance from the screen to the furthest seat that is in line-of-sight to that screen. If the majority of the content is video, divide that number by 8. That is the screen height. Remember that this is just one of many possible formats that will determine which number to achieve the screen height.

The screen height will be the same if the aspect ratio is 4:3 or 16:9 as only the width is different (if done correctly, anyway). Make sure that the closest seat is twice the distance from the screen in comparison to the screen height. Example - 6' tall = 12' away for closest viewer.

Next, measure the distance from the screen to the closest audience seat that is in line-of-sight to that screen. The screen should be no taller than twice that distance. This isn’t always possible, but it is preferable. Remember, the furthest viewers take priority, as it is better for the screen to be “too big” for those close than “too small” for those in the back.

Determine square footage of the screen surface.
Take the screen height (in feet) and multiply it by the screen width (in feet). Ex. 6' x 8' = 48 sq. ft.

Take the number of lumens that is estimated will be needed (this is the ONLY time we'll estimate lumens). Example - 1000 (lumens) divided by 48 (sq. ft.) = 20.83

ANSI specifies that 18 (+ or - 2) is the acceptable number. This is assuming NO light is hitting the screen. Pitch black area. Dark. No light. Nada.

So we now know that 20.83 is our number for this example, and our next measurement is the screen area itself - the amount of foot-candles hitting the screen surface from lights, windows, etc.

Let's assume 8 foot-candles is hitting the screen surface. We now take our number (8) and multiply it by 5 (our next formula). The answer? 40, of course.

THAT (40) is the number we must now reach to have adequate lumens being projected onto the screen surface. In other words, we must project at least 40 lumens per square foot onto the screen.

So, going back to our first example, we have 48 sq. ft. of screen area. If we project 2000 lumens onto the screen surface, and divide that by 48, we get 41.66, which is enough to accomplish our goal.

Therefore, assuming no screen gain, we will need 2,000 lumens projected onto the screen surface from the projector in order to overcome ambient light.

Here’s another item to think about: contrast ratio. In a pitch-black room, lower contrast ratios are not nearly as important. But in a lit room, the better the contrast of the projector, the better the image will be. Contrast, in layman’s terms, is how black the blacks are in comparison to how white the whites are. We call this contrast ratio.

Contrast ratios are normally listed (if at all) in one of two ways on a projector spec sheet: ANSI contrast and ON/OFF contrast. The number to pay attention to is ANSI contrast.

I’ll give another example to help illustrate contrast ratio.

Let’s say you have two projectors: Projector A is 2000 lumens with a 150:1 ANSI contrast ratio. Projector B is a 1400 lumen projector with a 500:1 ANSI contrast ratio. We’ll also say they are using the exact same lenses projected onto the exact same size screens, side by side in a well lit room.

For an easy simulation, let’s also assume the screens are the 4’ x 6’. Now, which image will appear brighter?

If you said Projector A, you’re wrong.

You see, the human eye perceives brightness in comparison to something dark. Therefore, because Projector B had a much greater contrast ratio, the whites would seem brighter next to those blacks. To our eye, Projector B would seem brighter.

Don’t believe me? Try duplicating this test with similarly equipped projectors and see for yourself that this is in fact true.

Beyond this, it gets quite complicated, and I probably have lost 85% of the readers four paragraphs ago anyway. In fact, there's much more to it than what I've typed here. Therefore, I'm wrapping this up.

I do ask this one thing: if it's important enough to do, do it right – the first time - hire a consultant or design/build firm.

To Contact Mr. Coppedge:
Anthony D. Coppedge, CTS
Church Media Consultant
WEB: www.anthonycoppedge.com | EMAIL: anthony@anthonycoppedge.com

PHONE: 817.819.7288 | FAX: 817.887.3700
Copyright 2001-2003 Do not duplicate in any form whatsoever without the written permission from Anthony D. Coppedge.