What do accelerometers actually measure?

[jprecinos]

I am a bit confused about what accelerometers actually measure and hopefully somebody can help me resolve the following scenario:

Say we have a vehicle with mass m, fixed CG location and subject to
gravity. The vehicle is traveling at constant speed in the X
direction heading to a cliff. When it reaches the edge it loses
grip, rolls over, goes into free fall and hits the ground. With enough information we could calculate the acceleration vector of the CG of the vehicle at all times. I understand that in theory we would have zero acceleration during the straight line,-1G magnitude during free fall and depending on the impact velocity and duration of impact a very large deceleration vector when the vehicle hits the ground.

Now here is the question: We have the exact same scenario but we
decide to attach a 3 axis accelerometer at the CG of the vehicle,
oriented in the same way as the vehicle coordinate system.

As the vehicle travels to the cliff at constant speed what would the
accelerometer read? Would it read 1G or -1G?

What about during the free fall, would we have a reading in any direction?

Finally at impact would the acceleration of scenario 1 and scenario 2
differ only by the addition of another vector in the -1G global
direction? Do accelerometers care about what is going on outside their reference frame?

thanks for the help. JP

 

[zhermes]

Accelerometers do not care what's going on outside their reference frame.

A 3-axis accelerometer measures all three components of the acceleration instead of just the magnitude. This means that it knows the direction of the acceleration as-well.

In the first case, you would know the acceleration was zero, then g, then big---you wouldn't know that the drop had a 'negative' acceleration.

In the second case, it would be exactly the same, except the accelerometer would know the acceleration was 'down' during the fall, and 'up' during the impact.

 

[A.T.]

I am a bit confused about what accelerometers actually measure

They measure proper acceleration, which is a frame independent quantity.

With enough information we could calculate the acceleration vector of the CG of the vehicle at all times. I understand that in theory we would have zero acceleration during the straight line,-1G magnitude during free fall

That is the frame dependent coordiante acceleration (dv/dt) in the frame of the earth.

As the vehicle travels to the cliff at constant speed what would the
accelerometer read?

1G (upwards)

What about during the free fall, would we have a reading in any direction?

Zero G , if we ignore air drag.

Do accelerometers care about what is going on outside their reference frame?

There is no such thing as the "outside" of reference frames. Reference frames assign coordinate accelerations to objects. The proper acceleration measured by the accelerometer is the coordinate acceleration of the accelerometer in an inertial frame.

In other words: If you have an accelerometer A that shows X Gs, and a second accelerometer B that shows zero Gs, then the coordinate acceleration (dv/dt) of A relative to B is also X.

 

[jprecinos]

thanks for the quick replies. So one last question to clear my mind of any doubts :)
Say a person is watching the all scenario at the bottom of the cliff and from his reference he can calculate the deceleration of the vehicle after impact. The value that he will calculate in the global system will probably be short compared to what the accelerometer will read right? The reading of the accelerometer at impact could be much higher because you will have to add the -1G vector in the gobal Z direction, right?

What tromps me is that we use the accelerometers to measure what the passengers of vehicles feel but is hard to visualize the +1G reading when we are sitting at the stop light (I guess that is what our buns felt when we got behind the wheel lol)

 

[Drakkith]

,-1G magnitude during free fall

Negative, you would not read an acceleration in free fall until you reached terminal velocity, at which point it would read 1g.

See here: http://en.wikipedia.org/wiki/Accelerometer

What tromps me is that we use the accelerometers to measure what the passengers of vehicles feel but is hard to visualize the +1G reading when we are sitting at the stop light (I guess that is what our buns felt when we got behind the wheel lol)

Exactly. An accelerometer cannot tell the difference between acceleration due to gravity and due to change in velocity. If you were on a spaceship accelerating in space at 1g, you could stand on the floor and it would feel exactly like you were standing on the ground here on earth.