Sean Breheny <shb7@cornell.edu> wrote:
> On Tue, Mar 4, 2008 at 12:05 PM, Dave Tweed <pic@dtweed.com> wrote:
> > Sean Breheny <shb7@cornell.edu> wrote:
> >  > Thanks! I do wish they had discussed more of the physics, though.
> >  > There are a lot of misconceptions out there about what accelerometers
> >  > can and cannot do (for example, as you said, you need to know
> >  > something about the way it is moving or not moving in order to extract
> >  > tilt information from the measured accelerations. Actually, what I'd
> >  > like to see is a general app note on inertial navigation, covering,
> >  > for example:
> >
> >  That's not an app note, that's a whole shelf full of books!
> 
> I'd contend that a basic, practical-level intro to it would not be.
> You're not going to be good enough to build ICBMs with it, but you can
> start playing with INS for robotics-type applications with this level
> of knowledge.

OK, I'm confused. Why are we having this conversation?

On one hand, you seem to already have sources for the level of knowledge
you seek. It sounds like you could quickly put together such an app note
yourself.

> If you have an accelerometer in free-fall in a vacuum, accelerating
> under the influence of gravity, it measures zero. If you then set it
> on a table so that the sum of the forces on it is zero, but there is 1
> newton of gravity and 1 newton worth of normal force acting back from
> the table, it will measure ONLY the force from the table (1 newton).
> This EQUALS gravity because you know that it is sitting on a table and
> not being allowed to accelerate. It is only under this assumption
> (that it is not accelerating) that you can relate its measurement to
> gravity.

On the other hand, you seem to be a bit confused about gravity and
acceleration.

First of all, gravity does not have units of Newtons. It is indeed, an
acceleration field, with its magnitude measured in units of length per
time squared.

Yes, any real accelerometer measures its own acceleration *relative* to
the local gravity field. As Einstein showed, there are no *absolute*
references. Gravity in one frame of reference is in no way distinguishable
from a constant linear acceleration in another, so I'm not sure what point
you're trying to make. Perhaps we're in violent agreement.

When I set my accelerometer on a table, it reports that it is accelerating
at 9.8 m/s^2 upward. It is my interpretation, based on the lack of motion
in my larger external reference frame, that attributes this acceleration
to the gravity field and not to actual movement. If I lift it up, the
reading momentarily increases, and if I lower it, the reading decreases.
The accelerometer cannot by itself separate which part of the reading is
due to gravity and which is due to my movements. It's a fundamental system
startup issue -- actual movement is indistinguishable from sensor bias and
scale factor errors. An independent source of information is always needed.

-- Dave Tweed
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