I worked on a drawing on a regular 8 1/2 by 11 inch sheet of paper. I’ve drawn a person there and her eye line is 9 inches from the bottom of the paper. I figure that in the picture she is 1/4 life size. Here is how I come up with that. I assume in this case that the height I am working with for a woman is 5’6". Also an average for a woman for the proportion of head to figure height is about 9/70, or if you consider it from the inverse she is 7 and 7/9 heads tall. If her head is level then the eye line is 20/39 of the height of her head . or at least that is close to the mean for attractive faces that I have studied.. If you multiply the two numbers times each other then you get 6/91. Thus 6/91 is the proportion of the figure from the eyeline to the chin. If you multiply 6/91 times 66" you get 4 and 32/91 inches, which is what this distance would be at life size. I measured the distance from the eye line to the chin in the picture and I get 1 and 3/32 inches. That is 1/4 of life size.
If the woman if 5’6" then her eye line would be at a height of 61 and 28/65 inches, but I only show the part of her down to where her fingertips are when she is standing. On the paper that is a distance of 9 inches from the eye line. That times 4 for the scale gives us 36 inches. So how far away is she? The standard angle of view is the arc tangent of 1/4, or a distance proportion of 1 to 4. For instance if the horizon is at an altitude of 5 feet then the ground is not in sharp focus until it is 20 feet away. Again, here, I place the horizon at her eye line, 61 and 28/65 inches, which would place her about 20 and 1/2 feet away if we saw the ground at her feet, but she is a little closer than that. The distance from her eye line to the bottom edge of the picture is 36 inches, and taking in the angle of view we would say 4 times 36 inches, and that (144 inches) divided by twelve, to give us feet, is 12 feet even, and so that is how far away she is from our window
Now I want to draw a lion standing behind her and so the question is what scale should he be? So then I have to place the lion farther away than 12 feet if he is to be at the correct scale and be behind her. If her scale is 1/4 life size then what scale should the lion’s scale be if, for instance, I want him to be 14 feet away?. Here is where I saw the pattern. The denominator is the distance, if 3 is the numerator, in other words, 3/3 = 1 (life size), 3/12 = 1/4 (where the woman is), and so for the lion to be 14 feet away he needs to be on a scale of 3/14 or smaller. In a photo I have of a lion I estimate that his scale is about 36/161 of life. which is equal to 3 divided by 13 and 5/12. That would put the lion 1 foot and 5 inches behind her. That’s pretty close, but OK because I know that my lion won’t hurt anyone.
I hope the picture comes through. I haven’t seen it yet so I will try again.
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