Weight Loss and Body Fat

Two weeks without losing any additional weight (using Apidexin) %&$#@*? ... as noted here.
So we're trying something else: PGX

We blame our bathroom scale (among other things), so we bought a new scale on eBay
... but the digital readout was missing the last digit.

I was tempted to invent my own digit (like a zero), but the Missus wouldn't let me cheat -- so we bought yet another scale.

It's a Weight-Watchers Scale, made by Conair and it looks like this:
However, it ain't no simple-minded scale. In addition to weight it measures:
Body Fat (BF, in pounds or kilograms), Body Fat %, Body Water %, Bone Mass % and Bone Mass Index (BMI).

'course, it first asks a bunch of question, like your age, height and sex.
Armed with this info it provides all of the above data every time you step on the scale.

>You're kidding, right? It can calculate all them things -- just knowing your age, height and if you have sex?
For "Sex" I chose "Male". However, it'll keep track of my wife's weight too, so she picked "Female".
Each time you step on you tell it that you're person#1 or person#2 etc. (else you get your weight but nothing else).
Then you get your weight and a succession of other stuff like BF.
And, as far as measuring all other that stuff ... that's what I'd like to investigate.

For one thing, there are these two magic formulas for measuring Body Fat (BF) where D is the density of the person's body.
MethodD = Density in gm/cc (Water has D = 1.0 gm/cc.)
Brozek BF = 4.57 / D - 4.142
Siri BF = 4.95 / D - 4.50

>So how do you measure Density? Since Density = Weight / Volume ... finding Volume ain't so easy, eh?
I can stick you in a vat completely full of water and measure the volume of water that spills out.
Archimedes did something like that.

>And how does your scale measure density.
I give up.

Figure 1
>From Figure 1, it seems that if you're much heavier than water you got less BS.
That's BF.
Also, your density will depend upon whether you inhale or exhale.
If you inhale, you are less dense and float in water. In fact, the average human density is about 1.02 so ...

>So the average human is dense ...
Dense enough to sink.
However, remember that it's essential that humans have some fat.

Essential Fat10-12%2-4%

  • Suppose you're 180 pounds with 25% Body Fat. (That's in the "acceptable range".)
  • That's 25% of 180 or 45 pounds of BF.
  • The remaining body mass, namely 180 - 45 = 135 lbs. contains "essential" BF (and bones and organs, etc.).
  • Suppose you want to lose 20 lbs.
  • If you actually succeed in losing 20 lbs, your BF, originally 45 lbs, is now reduced to 25 lbs.
  • With BF = 25 lbs and your weight now at 160 lbs that's 25/160 or 15.6% BF.

>And you've become a female athlete!
Only if you started as a female.

Let's do that again:
  • Suppose you're W pounds with BF = p. (p = 0.25 means 25%)
  • That's a fraction p of W or pW pounds of BF.
  • The remaining body mass, namely W - pW contains "essential" BF (and bones and organs, etc.).
  • Suppose you want to lose X lbs.
  • If you actually succeed in losing X lbs, your BF, originally pW lbs, is now reduced to pW-X lbs.
  • With BF = pW-X lbs and your weight now at W-X lbs that's a new BF of (pW-X)/(W-X).
Sex? = Male=1, Female=2
Current Weight = lbs (or kg)
Current BF = %
You want to lose lbs (or kg)
Your new BF = %
[A]           new BF = (pW-X) / (W-X) where
                W = your current Weight, p = your current BF, X = the weight you want to lose.
>Are the weights in pounds or kilograms?
It doesn't matter. The final BF percentage would be the same regardless of what units you use for weights.
Here are some pictures showing how your "new" BF will depend upon your Current Weight and how much you want to lose.

Of course, you can lose too much weight and your BF% will go negative and ...
>And you're dead.
I'd say so.
>Suppose I'd like to reduce my BF% from its current value to some lower value? What then?
You can use this:
[B]           X = Weight Loss = W (p - newBF) / (1 - newBF) where
                W = your current Weight, p = your current BF, newBF = the BF you'd like to achieve.
W = 180 kg, p = 0.25 (that's 25%), newBF = 0.156 (that's 15.6%) then X = 180 (0.25 - 0.16) / (1 - 0.16) = 20 kg.
Did I mention that, for weights, you can use pounds, kilograms, tons, ounces, stones ... whatever

Also, with the calculators, I wouldn't believe the comments you get. What do I know ?!

Sex? = Male=1, Female=2
Your current Weight: W = lbs (or kg)
Your current Body Fat %: p = %
What would you like your BF to be?: newBF = %
You should lose lbs (or kg)
>So you trust your sexy new scale to measure density and generate a BF number and ...
Actually, it doesn't measure density at all. It sends an electrical current up one leg and down t'other and measures the resistance.
It's called the Bioelectrical Impedance Analysis (BIA) and it varies with the amount of water, blood, muscle etc. ... and fat.
They all have different resistance to the current. Fat has a larger resistance than water and would tend to give high impedance values.
Together with a person's age, height and sex it generates a BF value.
As you might imagine, the BF value it generates will also depend upon body hydration, body temperature, time of day and the phases of the moon.


Another measure of Body Fat is the Body Mass Index or BMI.
There's a very simple formula, namely:
[C]       BMI = k Weight / Height2 where
          k = 1 if you measure Weight in kilograms and Height in metres
          k = 703 if you measure Weight in pounds and Height in inches

It you use pounds and inches, the factor k = 703 takes care of the conversion to kilograms and metres..
That is, the ranges for underweight/overweight are the same.

As you might imagine, BMI gives a very rough determination of fatness or thinness.
It'll depend upon your age (children have different "proportions"), gender, ethnicity, etc.

BMI < 18.5Underweight
18.5 < BMI < 25Normal
25 < BMI < 30Overweight
BMI > 30Obese
BMI > 40Mamma mia !

Your Weight: pounds
Your Height:
Your BMI is
Your Weight: kilograms
Your Height: metres
Your BMI is
Some interesting things to note:

  • Your body Volume should be proportional to Height3 ... assuming all "proportions" remain the same.
  • Your Weight should be proportional to your Volume, so Weight = C Height3 where C is some constant.
  • Then BMI = k Weight / Height2 = k C Height should be proportional to Height.
  • However, taller persons usually have thinner builds, so their "proportions" do not remain the same and their BMI (according to the above formula) will be too large.
  • It has been suggested that the BMI formula be revised to something like BMI = k Weight / HeightR where 2.3 < R < 2.7.

Strain Gauge Scales

Another interesting thing is how these electronic scales actually measure weight.

>What? Along with BF and BMI and all that ... they actually measure weight?
Pay attention.
Remember when I said they calculate Body Fat by measuring resistance to a current? Well they also measure weight that way.
If you stretch a piece of wire, it's resistance will change. There's some wire inside the scale that'll stretch when you step on the scale.
You make connections to the ends of the wire and measure the resistance and it'll vary with the amount of stretching and ..
>And the stretching depends upon how heavy you are, right?
Yes, and the wire is attached to the top of a lever that bends when you step on the scale.
>Aah ... the lever bends and the top of the lever stretches.
You got it.

Strain gauge is measuring
your weight in a scale.

A mechanical strain gauge
is measuring change in crack width.

Many strain gauges are
measuring stress in a wing.

See also losing weight