Body Average Density Measurement

[Guest guest]

Well since I've dealt with mass and density for many decades during

my former engineering years, couldn't help but be interested in this

topic. After purusing the internet for a few minutes, I've concluded

that it's much easier to calculate " Body Average Density " than % body

fat. (Apparently a 21% body fat corresponds to a density of 1.05

kg/L.)

From,

http://en.wikipedia.org/wiki/Body_fat_percentage ***

the Brozek and Siri formulas give an estimation of %BF. This

reference also presents at least two simple methods of estimating

body density (mass density/volume) using a large bath tub say or

swimming pool and a simple floatation device such as a one liter

plastic bottle. So today or this evening sometime I'll try to

determine my body density and estimate my % body fat. And I'm

guessing the estimate will be fairly accurate. (JMHO)

a=z

PS I'm also thinking that since average body desity is much easier

to determine than % body fat and should be much more informative than

the just BMI, that this representation of " fatness " should be

universally adopted.

*** http://en.wikipedia.org/wiki/Body_fat_percentage

Body Average Density Measurement

Prior to the adoption of DXA, the most accurate method of estimating

body fat percentage was to measure that person's average density

(total mass divided by total volume) and apply a formula to convert

that to body fat percentage.

Since fat tissue has a lower density than muscles and bones, it is

possible to estimate the fat content. This estimate is distorted by

the fact that muscles and bones have different densities: for a

person with a more-than-average amount of bone tissue, the estimate

will be too low. However, this method gives highly reproducible

results for individual persons (} 1%), unlike the methods discussed

below, which can have an error up to }10%.[6] The body fat

percentage

is commonly calculated from one of two formulas:

Brozek formula: BF = (4.57/ƒÏ & #8722; 4.142) ~ 100

Siri formula is: BF = (4.95/ƒÏ & #8722; 4.50) ~ 100

In these formulas, ƒÏ is the body density in kg/L. For a more

accurate

measurement, the amount of bone tissue must be estimated with a

separate procedure. In either case, the body density must be measured

with a high accuracy. An error of just 0.2% (e.g. 150 mL of trapped

air in the lungs) would make 1% difference in the body fat percentage.

One way to determine body density is by hydrostatic weighing, which

refers to measuring the apparent weight of a subject under water,

with all air expelled from the lungs. This procedure is normally

carried out in laboratories with special equipment.

The weight that is thus found will be equivalent to the body's weight

in air, minus the weight of the volume of water which that object

displaces. The following formula can be used to compute the relative

density of a body: its density relative to the liquid in which it is

immersed, based on its weight in that liquid:

where ƒÏr is relative density, W is the weight of the body, and Wi is

the apparent immersed weight of the body. Absolute density is then

determined from the relative density, and the density of the liquid.

Because the density of water is very close to one, when density is

computed relative to water, for many purposes it may be treated as

absolute density.

Note that it is unnecessary to actually weigh a body under water in

order to determine its volume, density or, for that matter, its

weight under water. Volume can be easily determined by measuring how

much water is displaced by submerging that body.

For a human body, a vertical tank which has a uniform cross-section-

area, such as a cylinder or prism, can be used. As the subject

submerges and expels air from the lungs, the rise in the water level

is measured. The water level rise, together with the interior

dimensions of the tank, determine the displaced volume.

Nevertheless, the equipment to actually weigh people under water

exists, and some organizations, such as universities and major

fitness centers, have it.

It is also possible to obtain an estimate of body density without

directly measuring under water weight, and without directly measuring

water displacement, either. What is required is a swimming pool or

other tank where the subject can be fully immersed. The idea is to

balance the body with a buyoant floatation device of a suitable mass

and volume, such that the body plus floatation device neither sink

nor float. The viability of this method rests in choosing a

floatation device which has some convenient attribute that makes it

possible to determine its volume easily: it is small, regularly

shaped, and perhaps manufactured to a specific volume. From the

volume and mass of the balancing floatation device, and the mass of

the body, the volume and density of the body can be determined.

A person who neither floats nor sinks with empty lungs in water would

have a density of approximately 1 kg/L (the density of water) and an

estimated body fat percentage of 43% (Brozek) or 45% (Siri), which

would be extremely obese. Persons with a lower body fat percentage

would need to hold some kind of floatation device, such as an empty

bottle, in order to keep from sinking. If the floatation device has

mass m and volume v, and the person has a mass M, then his or her

density is

where ƒÏw is the density of water [0.99780 kg/L at 22 ‹C (72 ‹F)].

For

example, a person weighing 80 kg needs to hold a floater with a

volume of 4.5 L and a mass of 0.5 kg has a density of 1.05 kg/L and

hence a body fat percentage of 21%. Note that both the Brozek and

Siri formulas are claimed to give systematically too high body fat

percentages.[7]

A simpler version of the above formula can be derived by making two

assumptions, and one small algebraic change. Firstly, the density of

water can be taken to be 1 kg/L, which is more than accurate enough

for the purposes. Secondly, the mass of light floation device such as

an empty plastic bottle is tiny and so the m / M term is negligible:

if this assumption is invalid, it can easily be compensated for, as

described below. Thirdly, the numerator and denominator can be

multiplied by M, finally yielding

..

Note the similarity of this formula to that given earlier for

relative density, except that masses are substituted for weights. The

v term also represents mass: the mass of water that was displaced by

the floatation device to compensate the weight of the body in the

liquid. That mass is actually ƒÏwv where ƒÏw was taken to be one.

For example, an 80 kg person holding a 4 L floater of negligible mass

has a density of 80/76 or about 1.05. Note that this is the same

result as with the 4.5 L floater weighing 0.5 kg, using the more

complicated formula. The reason is that if the floater has non-

negligible mass, this mass can simply be subtracted from its volume

to obtain an effective volume. An 8 L floater weighing 4 kg provides

the same buyoancy as a 4 L floater of negligible mass. It can be

visualized as a 8 L volume that is half-filled with water. The half

that is filled with water can be removed from consideration.

For the above reasons, a light bottle partially filled with air makes

a convenient floater, since the amount of air in it can be adjusted

yet accurately measured. The measurement begins with a bottle

completely filled with water. Some of the water is poured out into a

collecting container, the bottle is sealed, and the subject is asked

to perform a submersion, air expelled from the lungs, using that

bottle as a floater. If the subject sinks, a small amount of water is

removed from the bottle into the collecting container, and the

experiment is repeated. If the subject floats, some water is returned

from the collecting container to the bottle. When the subject finally

achieves buoyancy equal to his or her weight (neither floats nor

sinks), the amount of air in the bottle is determined by measuring

how much water was poured into the collecting container, and the

formula can be applied, where the variable v is taken to be the

volume of air in the bottle.