[Lingster]

I love this thread.

[trilliwig]

Heh, sure, what's not to like?  We get to apply our analytical skills to one of our favorite aesthetic subjects!

[John]

Hi MuskelGrothe.  Many thanks for creating this useful tool!  I've been trying to apply it to a commissioned piece of artwork, and run into a couple issues for which I have questions.  ???

First, the example spreadsheet entries for the chest appear to use a width greater than the length (75 pixels versus 45 pixels).  Your diagram shows chest width as the measurement from collarbone to abdomen, while the chest length is the measurement across from side-to-side, so by the diagram, length should be greater than width.  Which is correct, or does it matter?

I messed up on that entry.  But since cylindrical volume simplifies to =(1/4)*pi*w*h*d, it doesn't matter which dimension is which, due to the commutative law.

Second, your ratios width/depth for thighs, biceps, and calves don't give guidance for a normal, non-muscular woman.  I tend to use the ratios closest to 1 in that case.

For volume, I think it the ratios are a little less important, especially for longer bones (limbs). 

Third, the weight sheet contains an input for Target weight in pounds.  Isn't that what we're trying to calculate?  So what purpose does that serve?  For now I've been putting in something that approximates 0.036 lb/in^3, erring on the low side for less muscular women and on the high side for more muscular women.

Target weight doesn't affect the computed weight at all.  I just included it to help adjust the formula if needed.  The idea was to compare a known weight of an individual with the computed result.  The constant PoundsPerCubicInch and PPCIDev (PoundsPerCubicInch random deviation range) are used with the volume, calculated skeleton weight, and constant adult head weight to get the result.  If you want to change the PoundsPerCubicInch or PPCIDev values, just type them in on the constant page.  I got PoundsPerCubicInch by averaging out a sample set, and PPCIDev was the standard deviation of that set.

Also, I've put in a row for elliptical circumference using Ramanujan's approximation, which is

pi*[3(a+b) – sqrt((3a+b)(a+3b))]

where a and b are the major and minor radii.  This seems to work out pretty well.  An example formula is

=PI*(1.5*(C8+C9)-0.5*SQRT((3*C8+C9)*(3*C9+C8)))*$B18/$B17

which gives a circumference in inches.

I'll put a circumference measurement on the spreadsheet soon.  Biceps, Forearms, Thighs, Calves, Waist, and Chest should be on it. 

[trilliwig]

I messed up on that entry.  But since cylindrical volume simplifies to =(1/4)*pi*w*h*d, it doesn't matter which dimension is which, due to the commutative law.

Ah, good to know.  It does, however, matter for chest measurements like circumference.  And I don't know what a typical depth to width or depth to height ratio for the chest would be, and I was hoping you'd have some advice there.

For volume, I think it the ratios are a little less important, especially for longer bones (limbs). 

Great, I'll not worry about it overmuch then.  It seems to me though that for my Lina commission I got some rather large circumferences for her normal form,  20" thighs and 18" calves, before her little growth spurt.  Looking things up, that seems on the high side for a normal woman.  But perhaps she really did have thundrous thighs. 😀  Or maybe ellipses aren't the greatest model of a cross-sectional leg.

Target weight doesn't affect the computed weight at all.

Ah, then I'm guessing it was just the random element of the computation that was fooling me.  Thanks for confirming that.

I'll put a circumference measurement on the spreadsheet soon.  Biceps, Forearms, Thighs, Calves, Waist, and Chest should be on it. 

That would be great!  Thanks again for setting this up!

[John]

I posted the updated sheet last night.  Measurements for thigh, calf, bicep, forearm, chest, and waist are calculated.  Others like neck can be added easily by copying and pasting a cell.

For chest, here is an alternate approximation to the one on the sheet:
=HTRat*AVERAGE((2*I7+I9*(PI-2));2*(I7+I9))

The first one
2*I7+I9*(PI-2)
is the circumference of a circle with diameter=depth, plus 2*(height-depth).  I forget what it's called (I'm sure there's a name for it) but it's the shape formed by the rectangle (h-d)x(d) placed between the two halves of the circle diameter=depth. (a form of a rounded rectangle)

The second parameter
2*(I7+I9)
is just the perimeter of the rectangle d x h

For really busty women, it may be good to figure in the boobs & pecs separately.

[Author]

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