# How to estimate a person's mass from a sensor? [closed]

I'm trying to estimate the person's weight from some available sensors and I have an accelerometer, a gyrometer and a magnetometer.

The triaxial accelerometer is fixed in a band in the person's chest, so it can measure the body acceleration. While the person is still in its tiptoes, as the figure below, he's asked to let the body weight fall without resisting. I think this way I can put the knee flexion aside.

I think the movement can be modulated as a mass-spring-damper system so I'll have to calculate the damping coefficient(d), and the spring constant(k).

The accelerometer gives me three accelerations (ax ay az). I remove then the gravity influence from then with an high-pass and compute its projection in the vertical axis.

That is the vertical acceleration.

The image below represents the vertical acceleration while the person's lets the body fall for 4 times. UPDATE:

What if I know the height of the person?

Could it help estimating the mass in the moment of the impact?

UPDATE2:

Assuming this as a mass-spring-damper system, well, now I have to calculate both c (spring constant) and k (viscous damper),

I've calculated this equations,  where e is my coeficient of restitution and fn is my natural frequency.

• What do you mean by "the mass"? And where is the accelerometer located? – fibonatic Feb 5 '14 at 22:09
• @fibonatic I mean the Kg of the person. The accelerometer is located in the chest. – SamuelNLP Feb 5 '14 at 22:18
• Without describing what exactly you're doing or what the setup even looks like, this question has no hope of being answered. – DumpsterDoofus Feb 5 '14 at 23:30
• user9132 says: "There simply isn't enough detail for us or anyone to tell from your picture. If we had access to your program that was used, that would be another matter but no one can say based on the info you have provided." – Brandon Enright Feb 5 '14 at 23:52
• No offense, but I'm still completely confused as to how on Earth you think you can extract a person's weight from this. So what if they fall and their body bounces a little bit when their heels hit the ground? How are you going to extract their mass from that based on accelerometric measurements? Considering that the way they position their feet will hugely impact their damping characteristics, and that fat people jiggle more than skinny people, this seems like an impossible method. – DumpsterDoofus Feb 6 '14 at 2:11

Your question isn't a million miles from the question How can I weigh liquid in a sealed container?. However there's a key component missing that means you can't measure the persons mass.

If you were measuring force as a function of time the problem would be reasonably straightforward. This is because the change of momentum is called impulse and is given by:

$$J = \int F \space dt$$

You can estimate the person's velocity, $v$, if you know how far they fell i.e. how much they raised themselves by standing on tiptoe, and the momentum change is simply $mv$. Then their mass is given by:

$$m = \frac{1}{v} \int F \space dt$$

But ...

You're problem is that you aren't measuring force, you're measuring acceleration, and of course acceleration is force divided by mass so you're factoring out exactly the quantity you want to measure. Once you factor out the mass the equation I gave above turns into:

$$1 = \frac{1}{v} \int a \space dt$$

And all this tells you is that the velocity change is the time integral of acceleration, which is just basic mechanics.

I wouldn't rule out some second order effect I haven't thought of, but basically I think you're stuck! Still, full marks (and an upvote) for trying an interesting experiment.

• Thank you for your explanation, I'll try to find a way around. :) – SamuelNLP Feb 6 '14 at 11:59
• Assuming this system as a mass-spring-damper how could I calculate the natural frequency? I think I would be able to calculate a spring constant range with the masses first (train) and then calculate the mass from new users (test). – SamuelNLP Feb 6 '14 at 18:10
• I suspect your system is too lossy to have a well defined resonant frequency. – John Rennie Feb 7 '14 at 15:13
• Well, could I make an approximation on that? I know it is not well defined. – SamuelNLP Feb 7 '14 at 15:23
• @SamuelNLP: the oscillations your graph shows look as if they have a natural frequency. Just measure the points where the curve crosses y = 0 and you'll get the period of the oscillation. – John Rennie Feb 10 '14 at 12:33

1) Have each subject step onto a scale.

2) Tiptoe fall plus measured impulse on landing.

2) Sandbag on a line (pendulum). Raise to two or thee standard heights, let free fall with modest impact on plate snugged at base of spine, Accelerometer on chest. F = ma after calibration.

All masses free fall at exactly the same rate, for gravitational mass and inertial mass are in constant ratio for all bodies. You must measure something proportional to mass. Energy = mgh.

• Thank you, but I didn't understand the last part of your suggestion. – SamuelNLP Feb 6 '14 at 12:00