I need to calculate how big a 4' X 8' sign would appear from 400ft. Bonus: Size lettering would be readable?

Answer 1

First, make a model of what is going on ( a model on paper ). Draw a long skinny right triangle. The base and the leg are the dimensions you already know, 4 feet and 400 feet respectively.

Second set them up as a ratio ( right triangles and trigonometry all work off of ratios ), in this case, 4 / 400. Using fractions simplify this fraction to 1 / 100. This means it would look the same as a 1 foot by 2 foot sign at 100 feet. If you are heading for a standard distance, why not 20 feet? Divide 100 by 5 and you get 20; so if you divide 1 by 5 you get 1/5 or .2 feet.

Third, multiply .2 feet by 12 inches and you get 2.4 inches. This means a 4x8 sheet of plywood looks 2.4 x 4.8 inches at 20 feet (close enough to 2 1/2 x 5 inches). To get a visual, take a 3x5 card and cut one inch off of the long side (whoops! I meant 1/2 inch off the long side), then tape it to the wall at eye height and measure 20 feet from the wall as the place to stand (small isn't it?).

We divided the ratio by 4 and then by 5, so we divided in total by 20 (n/4/5 = n/20). When you find out how big to write on your card to be visible, measure how tall the letters are and multiply the height by 20 to get the full size lettering height.

Answer 2

I made one of those out of bedsheets and 3/4" pvc pipe for the ESPN CollegeGameday show. But my distance was much less than 400 feet. My sign was visible from about 100 feet away, and very readable on the narrow field-of-view "head" shots of Corso and Herbstriet.

I used 11" letters (sheets of 8.5 x 11 paper for stencils) You won't be able to get more than 4 lines of text on a 4x 8 with 11 inch letters. With 17" to 23" letters you'll get 2 lines of text (11 x 17 paper).

At 400 feet, eye-readable (without optics), you'll definitely need those 23" letters, or even larger (one line of text).

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Answer 3

Hi. Two hints. Trig and optical resolution.