Say you just finished drawing your latest muscle babe, and you want to include her measurements in a story about her. How do you do this? It's not easy to go into the drawing and wrap a tape measure around her arm or leg, so there needs to an alternative. Here's one that should do the trick.
This method involves geometry, namely elliptical circumference, so it may be good to be familiar with the subject before trying this approach. It would also help to have a spreadsheet editor to enter the values into (notepad + calculator will work, but it's harder to organize).
What you do is, first, assign a height to this amazon. Next decide which direction/angle the body part you want to measure is facing the "camera". Lastly, you take the on-screen measurement of the part, with the on-screen total body height, and figure the elliptical circumference with the ratios and formulas given below.
1. You need to set the height, all measurements will depend on this number. This sets the overall scale of the amazon, and the rest is a matter of ratio and formula.
2. Second, is the very import matter of deciding the orientation of the body part. A straight-ahead front, back or side view of the limb is easiest, but for in-between angles, you can approximate how far between the straight-ahead directions your angle is, and using ratios given below to help calculate the depth and width.
Also, it would help to explain which is "depth" and which is which is "width" for each part. Let's assume a body is standing straight, facing forward, with their arms perpendicular to the ground, palms facing their body. "Width" would be the distance left-to-right, across any body part, and "depth" is distance front-to-back. For example, a bicep's depth is it's "peak" height.
I approximated the following ratios off of a few big female bodybuilders, like Tina Lockwood, Gina Davis, and Conny Brandt. Ratios are given in r=width/depth, I used a sample set of 4 women for each part.
-- Bicep --
Low: 0.85
High: 0.92
Average: 0.88
Std dev: 0.03
Recommended range: 0.85 <-> 0.95
Comments: "Off-season" (ie softer) arms tend to be wider, but the depth is always significantly greater than the width.
-- Thigh
Low: 0.73
High: 0.81
Average: 0.77
Std Dev: 0.04
Recommended range: 0.7 <-> 0.85
Comments: Upper legs are surprisingly deep. The front may look more impressive and "bumpy", but the side is sometimes close to 40% bigger. The ratio depends largely on hamstring development. It doesn't seem to change much from ripped to soft condition.
-- Calf --
Low: 0.94
High: 1.13
Average: 1.03
Std dev: 0.08
Recommended range: 0.95 <-> 1.15
Comments: Some calves grow more sideways than backwards. Choose the ratio that seems more fitted to your creation's shape. I'd imagine softness has little effect on the ratios.
3. Now comes measuring and calculating of circumference. Measuring should be easy if you have an imaging program with a pixel measuring tool (like GIMP). If not, you can do a rectangular selection, between the two points you are measuring. All you have to do is read the rectangle's width and height dimensions from the status bar (or wherever it is displayed), and use the Pythagorean equation of d=sqrt(x^2+y^2) to get the pixel distance between points.
The pixel height of the character should be easy to get if the character is standing (or lying) relatively straight. Otherwise, you will have to add head, neck, torso, pelvis, femur, and shin distances together to get an approximate pixel height. After getting the pixel height, divide it by the real height you gave the character in step 1.
Once you have the height, measure the diameter of the limb you want to measure, approximately where you would put the measuring tape, if she were taken off the canvas into life. You want a straight line distance, even if the tape would be curved if projected onto your canvas. This is a diameter through the limb, not distance around (we're getting to that shortly).
Now you have the diameter of the measured area. This is your starting point for the final equation. If the width or depth dimension of the part is pretty much facing the "lens" of your drawing directly, then this should be simpler. If not, no worry. Say width is 0 degrees and depth is 90 degrees, and your body part is facing somewhere in between. Well, approximate the angle at which it is facing, between width and depth, and use this formula:
Let A be angle the part is facing the "lens", between 0 (width) and 90 (depth).
Let r be the width/depth ratio for the chosen body part.
Let m be the measured distance.
t will be a value between r and 1.
d will be the body part's depth.
w will be the body part's width.
t=r+(A/90)*(1-r)
d=m/t
w=d*r
Now comes the actual elliptical circumference calculation. With the width and height found, getting a set of elliptical radii is a simple matter of dividing both the width and height by two:
a=w/2
b=d/2
Now there are many ways to calculate elliptical circumference, with varying degrees of precision. I will only cover the most simple method, as we're just going for a loose estimate here (besides it works quite well when the radii are nearly equal). That method would be:
C=pi*(a+b)
where C is the approximated elliptical circumference.
Now that you have this formula, you can claim your 6-foot muscle mistress has 20" biceps with a greater degree of accuracy
