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# Projection, Math, and You

Projection might seem intimidating with the math involved in its engineering; however, there are some simple equations that can make your life easier as a projectionist. There are three main factors that are required when engineering projection:

Throw Distance – the distance between the projector’s lens and the projected image.

Image Width – the width of the projected image. This is typically a projection screen, but can be anything from a blank wall to projecting on the outside of a building.

Throw Ratio - the relation between the throw distance and image width. The ratio can either be fixed, like a fixed lens (0.8) or a ranged ratio found on a zoom lens (1.4-1.8). As you can imagine, these numbers aren’t all fixed and sometimes they are unknown. The most common factor you should always know from the start is your screen size and width.

Here are two easy equations to help you figure out the rest:

Calculating Throw Distance If you’re a tech on site know the size of your screen (image width) and what lens you were sent (throw ratio), all you have to do to figure out projection placement is the following: THROW DISTANCE = IMAGE WIDTH x THROW RATIO An example of this would be: You have a 7’ x 12’ projection screen with a 0.67 lens for your projection. 12 x 0.67 = 8.04, so you would need just over 8FT of throw. When you have a zoom lens, you have more wiggle room for your projector placement. Take the previous scenario but swap out the lens for a 1.4-1.8 zoom lens. Ideally you place the projector right at the center of that range and your throw distance would now be 19FT, but you can get as close as 16.8FT before falling out of throw range. Example of throw distance with a zoom lens.

Now if you’re engineering a show and need to figure out what lens to use (throw ratio), you’ll need to know the image width and the throw distance.

THROW RATIO = THROW DISTANCE/IMAGE WIDTH

So if you’re projector is 45FT away from your 7’ x 12’ screen, you would need to be in the 3.75 lens ratio (2.6-4.1 lens). 45/12=3.75.

With this information and a handy calculator, you should be on your way to becoming a competent projectionist.

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