The Runtastic Libra scale can measure body fat and water percentages, muscle and bone mass, BMI, BMR and AMR (calories burned). That's a lot of measurements done through the skin of the feet from standing?
What's the scientific workings behind these measurements and would the readings be accurate enough for tracking purposes after a few weeks of workouts and physical exercises? I am thinking of getting one.
The "how" is briefly explained in the instructions from page 14 onwards. In essence: Weight is measured; height is entered; BMI is calculated from those; body fat and water percentages, muscle and bone mass are calculated using a tiny electric current; I would guess the metabolic rates are based on average levels using all of the above plus the user's entered age and activity level(s).
It's not going to be entirely accurate, but if you're just using it for the purposes of tracking, I would say that it's "accurate enough". Essentially the values may not be exact for you, but assuming you're taking measurements at the same time of day with similar conditions (e.g. every Sunday morning before breakfast) then you should be able to track a downward trend to the results and see progress.
Also don't forget that numbers aren't the only side to the story. Regular progress pictures are a great way to see how you're progressing. For most people it's really less about the exact number on the scale and more about how they look and feel about the way they look.
The scales have your Weight, Height, Age, and Sex, which is actually enough to approximate all the figures you've listed (+/- 4%), but in addition it takes a BIA (Bioelectrical Impedance Analysis) reading. Essentially the scales incorporate a multimeter, similar to those found in the average electricians toolbox, and it measure by how much a small current is delayed and reduced by being passed up one leg and down the other (Impedance). As different materials have known Impedance values a guess as to the volume of water can be made (+/- 3%), and from your weight, height, age and a few known ratios, and a few formula that approximate how the composition of the body changes with age, a few more numbers can be derived from the estimated water content.
It's worth noting that the formula incorporated into the device have known margins of error, and those margins are based on readings taken on an AVERAGE individual. So the less AVERAGE you are the greater the error is going to be.
A few of the common formula (see Wikipedia for the constants):
BMI = MassKg / (HeightM)^2
BMR (Basal Metabolic Rate) = a + (b * MassKg) + (c * HeightM) - (d * ageYears)
where: a, b, c, and d are constants that vary depending on your sex, and whose version of the equation you use.
LBM (Lean Body Mass) = ( x * massKg ) + ( y * HeightM) - z
where: x, y, and z are constants that vary depending on your sex, and whose variation of the equation you use.
BF (Body Fat) = ((massKg - LBM) / massKg) * 100
or = (e * BMI) + (f * ageYears) - g
where: e, f, and g are constants that vary depending on your sex, and whose variation of the equation you use.
