It's all coming together!
I just mocked up an idea of what I would want my proposing sign to look like if I did it on a 15x20' tarp. I found a font that is simple and quite legible at small sizes, and filled up the canvas as best I can. Then I scaled it down to about 3/8" the long way on my monitor and determined that it was quite legible at a yard. That means given a good enough resolution, I would be able to read it if it were 1/8" and I were a foot away from it.
My next question was how high would that be equivalent to viewing a 20' sign from? A little simple math solves that. Consider the triangle with my eye as one corner, and the sign as the opposite side. As long as the angle of the corner where my eye is remains constant, the perceived size will remain the same. Sparing the mathematical proof, that means that the distance from the viewer is directly proportional to the size required to get the same perceived size. Since I know it's visible at 1" when it is 1/8", and I know that it will be 20' or 240" when done, I can solve for how far away I could see it at full size.
1/8" / 12" = 20' / X
1/96 = 20' / X
X/96 = 20'
X = 20' * 96
X = 1920'
That means my 15'x20' sign would could be barely read at around 2000 feet, which means it should be easily read at 1000 feet or 500 feet.
Now I just need to make the silly thing.
My next question was how high would that be equivalent to viewing a 20' sign from? A little simple math solves that. Consider the triangle with my eye as one corner, and the sign as the opposite side. As long as the angle of the corner where my eye is remains constant, the perceived size will remain the same. Sparing the mathematical proof, that means that the distance from the viewer is directly proportional to the size required to get the same perceived size. Since I know it's visible at 1" when it is 1/8", and I know that it will be 20' or 240" when done, I can solve for how far away I could see it at full size.
1/8" / 12" = 20' / X
1/96 = 20' / X
X/96 = 20'
X = 20' * 96
X = 1920'
That means my 15'x20' sign would could be barely read at around 2000 feet, which means it should be easily read at 1000 feet or 500 feet.
Now I just need to make the silly thing.