Angles Of View
After we have learned how to select a screen surface and after we have decided to utilize rear or front projection, and after we have established the size and arrangement of our audience, we are left with one unanswered question: How big should the projection screen be? Identifying the type of projection device(s) will yield the aspect ratio of its dimensions, but to determine its absolute magnitude we shall have to explore some criteria for screen
SizingUntil about five years ago the rule of thumb for figuring out the size of a projection screen went like this: Measure the distance from the screen to the Most Distant Viewer (the MDV in Figure 1) and divide by six to get screen width. Thus if the person seated in your contemplated last row was 38 feet back from the screen, you wanted to have the width of that display at least equal to 76 inches (which meant you rounded 76 up to 80 and ordered a 100-inch diagonal).
Today the experts prefer us to do it differently. They want us to begin by calculating for screen height, not width; which means that we divide the distance to the MDV by eight, not six. Since for all 3:4 aspect ratio displays either calculation yields the same result, is there any real significance to this change in emphasis?
There is; and the experts are right. The distinction arises from the advances in technology which have enabled yesterday's video projection to evolve into today's data display. The inexorable improvements in computer speed and software sophistication have impelled projector manufacturers to deliver ever broader bandwidth and continuously finer resolution. Once it was permissible to install a screen big enough for everyone to see; now it is essential that it be made large enough for everyone to read.
If we think about the process of reading for a moment, we will notice that the aspect ratio of a typical display is not 3:4. It is 8.5:11 and it's a page of text (this one, for instance).
If virtually any printed page is taller than it is wide, virtually any projection screen is wider than it is tall. Thus when we go to project a block of text we have to take special care that it's big enough for all the MDVs to read because the page's largest dimension is going to be the screen's smallest (see Figure 2).
When multiple projection sources (either of the same or differing kinds) are being used, figuring out screen height first is particularly useful. Once you've got enough height for all the images to be comfortably read, the screen's overall width can be calculated by plugging that height into the various aspect ratios, solving for their widths, and (more or less) adding them up. Thus two side-by-side video images have a screen aspect ratio of 2.67 (that is, its overall width will be 2.67 times greater than its height). Alternatively, two side-by-side horizontal slide images and a center video overlap require a screen with a width 3 times its height.
In the case of a single video image, combined with a single slide projector, the aspect ratio must be square if (but only if) both vertical and horizontal slides are to be shown. Because video produces much lower resolution than slides, the minimum height for its image must be calculated first. The actual width of the screen then becomes 1.33 times that video height. However, because of the vertical slide requirement, the actual screen height has to be equal to the actual screen width (making a kind of hybrid aspect ratio of 4:4). Note that none of the short dimensions of all three aspect ratios (3:4, 2:3, and 3:2) will ever fill such a screen, although all of the longer dimensions will.
Once we've figured out how big our screen's going to be, our next concern is to decide how far its bottom should be up from the floor. The rule here is plain: get the lower edge of the screen high enough so that the backs of the heads in the front row don't block the view of the heads seated behind them.
Since the nominal distance up from the floor to the eyepoint of a seated adult is 44 inches, we can add about another 4 or 5 nominal inches to get to the top of that person's head. If there are to be multiple rows of seats, we next need to inquire if they are arranged for single-row vision (a viewer can look over the person directly in front of her) or double-row vision (a viewer sees the screen between the heads in front of her). We also want to learn if the floor upon which the chairs are placed is flat or tiered. If the latter, how many risers are there and what is the height of each?
After assessing carefully whatever combination of these factors is relevant to our application, we'll typically end up placing the bottom of our screen somewhere between 36 and 48 inches off the floor.
So now that we know how tall the screen must be and where we need to position it on (or in) its wall, there remain two final sizing questions to consider. What should be the minimum distance from the screen to the front row? And, how wide can that row be?
The answer to both these questions is derived by ascertaining how much geometric distortion can be tolerated within a projected image. By geometric distortion we mean the apparent deformation that occurs when our viewing angle to some portion of a display is anything other than 0o .
Figure 3 demonstrates that for a viewer positioned perpendicular to one edge of a screen a circle (or the letter "O") will appear less and less circular as the viewing angle from which it is perceived is enlarged. As the "O" becomes increasingly elliptical, the ease with which it may be recognized as a circle diminishes. It turns out that the maximum acceptable viewing angle is 45o . Beyond that the character or other image element risks becoming undecipherable.
Since it is quite typical to see alphanumeric text displayed in 80 character lines, we now understand that we must be sure that a viewer positioned perpendicular to the first character in the line be able reliably to read the 80th. And if the angle formed between that viewer's eyepoint and the 80th character mustn't exceed 45o , then some simple trigonometry discloses everything we want to know about the front row.
Figure 4 illustrates a screen of width W. Lines drawn at 45o from each edge of the screen intersect at a distance from the screen which is one-half of W. By definition, then, no one can sit closer to the screen than half its width and accurately read text at both its edges.
Beyond the .5W distance the lines diverge and form an ever expanding cone which can, the further back we go, accommodate an ever widening first row. Some useful proportions to remember are that at a distance back from the display equal to 1.5 of its widths, you can have a front row that is twice as wide as the screen (See Figure 4). At 2W back, the first row can be 3W wide. And so on.
What happens when sizing for the back row conflicts with sizing for the front row? What happens when we can't get the screen high enough for the back row or we can't get the front row back enough for the screen? We have to compromise. And the most sensible way to do that is to identify which of all the viewing positions is occupied by what is called the Least Favored Viewer (the LFV).
The concept of the LFV really describes the proverbial "worst seat in the house." In a conference or boardroom we are likely to encounter the LFV seated much too close to the screen and way too far off to the side. In an auditorium he's probably to be found way out at the edge of the back row where, of course, he's not only the LFV but the MDV as well.
In either case, once identified, the compromise in screen size should be made to his advantage which would mean that the boardroom screen size might shrink a little or that the auditorium screen might get a little too wide for its front row.
Regrettably all of these guidelines are rendered ineffectual if proper attention has not been given to the proportions of the data points to be projected. If the chosen font size for the displayed material is too small and if the character or line count is too large, then all our efforts properly to size the screen will be to no avail. Fortunately there exist well established legibility standards which can keep us out of trouble.
Since we want everybody in our audience to read our display, clearly we must ensure that all of our projected symbols and characters are legible by the MDV. Whether he's also the LFV here doesn't matter; viewers seated close to the screen will always be able to decipher a single character (even if its bigger, for them, than it needs to be) but the fellow seated farthest away has to have the text be of a minimum size or he simply won't, even with 20-20 vision, be able to make it out.
How big is that minimum size? Research has shown that for any viewing distance the smallest symbol to be discriminated needs to subtend at least 9 minutes of arc. That limit, incidentally, describes the body height of a lower case character.
A quick and useful way to calculate this minimum font height is to take the distance to the MDV, convert it to inches, and multiply by .0026 (the tangent of .15o ). This will yield a symbol height that increases ź-inch for every additional eight feet of viewing distance.
Since graphical information will often include lines or other non-alphanumeric elements of the sort generated by CAD programs, etc., the dimensions of the minimum "character cell" become dependent on the smallest element of the drawing you will expect an MDV to read. Common sense would encourage the diagonal (or diameter) of that minimum area to subtend at least 15 arc minutes. And that standard may be satisfactory only for high resolution displays (e.g. 1024 x 1280). Lower pixel counts will require larger "cells" if there is not to be information loss within them.
Summing up, it's easy to see that projectors and computers will inevitably go on improving their abilities to display information. What won't be so easy to see is the contents of that information because our eyes regrettably are not going to get better at reading it. When we look at screen sizing decisions for today, then, what we really must see is reading requirements for tomorrow.