Physics Question: Find or estimate person mass using only accelerometer's data?

[adlep]

This will be difficult, but my guess it that it may be doable.

1. It should be possible to estimate an initial force (F) of the jump.
2. It should be possible to estimate upward acceleration (a).
3. It should be possible to estimate the height of the jump (h).
4. We know that the gravity pull of Earth is 9.8 m/sec^2 (g).
5. We know the total time of the jump (t in sec).
6. Assume that the jump is totally vertical so the Force Vectors are acting only among the y axis.

Discuss...
Yes, no, maybe so...

 

[CycloWizard]

If you can estimate the force, then of course it's possible. However, usually one goes about this the opposite way by measuring the mass, then using it to compute the force from the acceleration. Estimating the force and duration of the jump are probably more difficult than you anticipate.

 

[KIAman]

? If you can estimate #1, 2 or 3, then why not just estimate mass and save yourself the trouble ?

 

[adlep]

Originally posted by: KIAman
? If you can estimate #1, 2 or 3, then why not just estimate mass and save yourself the trouble ?

Or I think that I can,
These should be possible to deduce from the instrument - I assume access to a calibrated accelerometer.

Edit: Got a first clue: calculating height (the h):

From here:
http://en.wikipedia.org/wiki/Vertical_jump

(h = g*t2/8), where t = time spent in the air.

Some more data:
http://www.topendsports.com/te...ertical-jump-power.htm

 

[TuxDave]

So how are you estimating the force of the jump without knowing the mass (since that's what you're looking for)

 

[Farmer]

KIAman is on point. The height is irrelevant.

Let's say your jump is modeled as some force F (which you somehow can estimate, it doesn't have to be constant, it can be a function of time) through some constant time deltaT (which you somehow can estimate). If you can estimate acceleration (or velocity, both are equally good if constant F, known deltaT are good assumptions) right after the jump (somehow), that's all that matters, you can compute mass from just that. The difficulty is the jump: instead of a jump, just push the object with a constant force, if you can measure the acceleration via accelerometer, then you're done, high school physics, F=ma.

The following ballistic trajectory after the "jump" stops can't possibly tell you anything about mass, since it is motion in gravitational field only, and acceleration (and hence velocity, position) depends only on mass of Earth.

There are far easier ways, without making as many "it should be possible to estimate" assumptions. For instance, you'd like to measure gravitation force, which does depend on object mass, not gravitational acceleration (which is what you are doing if you want to look at jump height): the solution would then be a scale, which can be as simple as a linear spring hung from the ceiling. Imagine that. There are numerous other, far easier, more accurate ways of computing mass. A "jump" using human muscles is highly nonlinear and difficult to characterize. I mean, this seems somewhat unnecessary.

 

[HolyFire]

As others have said, if you know #1 and #2 you use m=F/a, and if you have a device that measures force, you use m=F/g (where F is the force applied when standing still).

If, however, for some reason what you know is #1,#3,#4,#5,#6, the solution is as follows. If during the jump an average force F is applied for a short time interval t, the total momentum when you leave the ground is Ft. That means your velocity is v=(Ft/m). The height of the jump is given by h=v^2/(2g). So if you know h, you calculate v = sqrt(2gh) and m=Ft/v=Ft/sqrt(2gh).