Re: Rising Obesity in Children Prompts Call to Action

[PF Riley]

On Thu, 28 Aug 2003 07:33:49 -0700, "D. C. Sessions"
> wrote:

>In >, Tsu Dho Nimh wrote:
>
>> Adult formula:
>> BMI = ( Weight in Pounds /(Height in inches squared) x 703
>
>This implies that for constant BMI, you get proportionately
>skinnier as you get taller. That's a good formula for joint
>health, but constant proportion would be height cubed.

Actually, that would be based on the assumption that as one gets
taller, one should also get wider, which isn't necessarily true. And a
more appropriate rough approximation of the humanoid shape is a
cylinder, not a cube. In that case, there is height L and radius R, so
that body mass is proportional to (L*R^2)/2, instead of a cube of
length X where body mass is proportional to X^3. In other words, there
is not just one variable with an exponent of 3.

Even taking this further, biological scaling is rather complex and
does not typically follow simple Euclidean geometry anyway. For
example, many physiologic functions scale to the 3/4 power of body
mass across the spectrum of living things.

PF

[D. C. Sessions]

In >, PF Riley wrote:

> Actually, that would be based on the assumption that as one gets
> taller, one should also get wider, which isn't necessarily true. And a
> more appropriate rough approximation of the humanoid shape is a
> cylinder, not a cube. In that case, there is height L and radius R, so
> that body mass is proportional to (L*R^2)/2, instead of a cube of
> length X where body mass is proportional to X^3. In other words, there
> is not just one variable with an exponent of 3.

Shape doesn't matter as long as the proportions don't change.

> Even taking this further, biological scaling is rather complex and
> does not typically follow simple Euclidean geometry anyway. For
> example, many physiologic functions scale to the 3/4 power of body
> mass across the spectrum of living things.

Yup -- that's thermodynamics. Because of the need to get rid of
heat, metabolic functions go up with surface area (x**2) instead
of mass (x**3) so that even with constant proportion, you get
(m**0.67).

Add the fact that hydrostatic pressure drives added mass towards
horizontal rather than vertical growth, and the mechanics of
joint strength [1] drives bone and joint size to go up faster
than height.

The net result is that an optimized body tends towards a mass
of greater than h**3.

[1] Joint load (second moment) goes up at about h**4, while
joint strength goes up at most as r**3, so joints get
wider somewhat faster than limbs get longer.

--
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end

[al gu]

microsoft children
micro activities making soft kids.


PF Riley > wrote in message
...
> On Thu, 28 Aug 2003 07:33:49 -0700, "D. C. Sessions"
> > wrote:
>
> >In >, Tsu Dho Nimh wrote:
> >
> >> Adult formula:
> >> BMI = ( Weight in Pounds /(Height in inches squared) x 703
> >
> >This implies that for constant BMI, you get proportionately
> >skinnier as you get taller. That's a good formula for joint
> >health, but constant proportion would be height cubed.
>
> Actually, that would be based on the assumption that as one gets
> taller, one should also get wider, which isn't necessarily true. And a
> more appropriate rough approximation of the humanoid shape is a
> cylinder, not a cube. In that case, there is height L and radius R, so
> that body mass is proportional to (L*R^2)/2, instead of a cube of
> length X where body mass is proportional to X^3. In other words, there
> is not just one variable with an exponent of 3.
>
> Even taking this further, biological scaling is rather complex and
> does not typically follow simple Euclidean geometry anyway. For
> example, many physiologic functions scale to the 3/4 power of body
> mass across the spectrum of living things.
>
> PF