# Understanding accelerometer data

1. Aug 23, 2013

### HalcyonicBlues

I'm having trouble understanding what accelerometers really measure. In observing a simple gravity pendulum, the accelerometer recorded this data (jpeg image attached) which is acceleration in the vertical direction (supposedly).

Now I've been told all sorts of things, like that the accelerometer measures g-forces, not acceleration (and what's the difference? My physics teacher told me there was no difference - let's hope she doesn't find this post!).

If the accelerometer measures acceleration due to gravity (which I thought it would, since it's a gravity-driven pendulum), then shouldn't the data be flat-lined at 9.8?

Looking at the textbook pendulum formula

$T = 2 \pi \sqrt{\frac{l}{g}}$

If the acceleration (g) changes within a period, then wouldn't the period value you calculate be different depending on what value you used? (if that made any sense)

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2. Aug 23, 2013

### voko

The "pendulum formula" gives you the period, which is a static property of a pendulum. The accelerometer measures the acceleration as a function of time. Do you know any formula that describes the oscillations of a pendulum as a function of time?

Edit: it is probably better to say the period is "time-invariant", rather than "static".

Last edited: Aug 23, 2013
3. Aug 23, 2013

### Basic_Physics

The pendulum bob accelerates as it swings to-and-fro. It is moving in a circular arc, but not at a constant speed. In order to execute that motion the string needs to supply a centripetal force. This causes a tension in the string at the bottom. The accelerometer measures the acceleration of the bob as it swings to-and-fro, which changes as the graph shows. Where in the motion would the acceleration be a maximum, zero, minimum (as the graph shows that the acceleration is changing periodically as the pendulum swings)? What are you basing your argument on?

4. Aug 23, 2013

### rcgldr

An accelerometer measures the force on an internal mass and translates this into a rate of acceleration. If the accelerometer is in free fall, it measures 0 acceleration. Assuming this is a one axis accelerometer, and it was attached to the pendulum, then "vertical" was in the direction of the pivot point.

5. Aug 23, 2013

### D H

Staff Emeritus
I've never liked that term. The "g" is short for gravity, and that's the one force accelerometers cannot measure.

Relativistic explanation: Accelerometers measure proper acceleration, acceleration relative to a co-moving, freefalling object. Newtonian explanation: Accelerometers measure acceleration due to the net non-gravitational force acting on the accelerometer.

6. Aug 23, 2013

### HalcyonicBlues

Does that mean that figures taken off the graph can't be stated as merely vertical acceleration (as one component of the resultant vector quantity)? So is the acceleration measured...centripetal...?

7. Aug 23, 2013

### D H

Staff Emeritus
The acceleration measured is that due to non-gravitational forces, and only the component along the direction to which that single axis accelerometer is sensitive. Look at the output when the pendulum has come to rest. The pendulum isn't accelerating, yet it's registering an acceleration of +9.81 m/s2. Calling that centripetal acceleration is a bit dubious because if you put that same accelerometer at rest on the ground and oriented so it can sense vertical acceleration, it will still report an acceleration of about 9.81 m/s2, directed upwards.

8. Aug 23, 2013

### Basic_Physics

So no acceleration gives a numerical output of 9,8. That means to get the real acceleration you need to subtract 9,8 from the displayed values.

9. Aug 23, 2013

### HalcyonicBlues

Thanks for the replies everyone :) I understand now.

10. Aug 24, 2013

### rude man

An accelerometer does measure gravity.

Hold an accelerometer with its sensitive axis pointed up and it will register g.

Accelerate the accelerometer upwards and it will register g plus the upward spatial acceleration. Drop it and it will measure g + downard spatial acceleration = 0.

Accelerometers measure "specific force".

Last edited by a moderator: Aug 24, 2013
11. Aug 25, 2013

### D H

Staff Emeritus
No, they don't. That accelerometers cannot measure gravity is the reason why inertial navigation systems for aircraft, spacecraft and other flying devices need an onboard model of Earth's gravity field.

OK. Is the accelerometer accelerating at 1g from a Newtonian perspective? More importantly, is the accelerometer accelerating at 1g *upwards*? That is what the accelerometer reports. It reports this upwards acceleration because that upwards acceleration results from the normal force. The accelerometer is sensitive to this force. If an accelerometer was also sensitive to gravitation, it would report a much, much smaller acceleration. It doesn't. It reports 1g upwards.

You have just proved my point, that accelerometers do not sense gravity. If an accelerometer did sense gravity, why would it report zero acceleration in free fall?

12. Aug 25, 2013

### rude man

It reports zero because it measures the sum of g and the negative spatial acceleration. They add to zero.

You have just proven my point. The accelerometer, when held, measures gravity = 9.81 ms^(-2). And if I took it to Mars it would similarly measure gravity there.

Same idea as if I hold a voltmeter in my hand and measure voltage. Pretty simple, really.

13. Aug 25, 2013

### rude man

Exactly. The accel outputs have to be corrected for gravity because the accel outputs include the (undesired) effects of gravity.

14. Aug 25, 2013

### D H

Staff Emeritus
Nonsense. Think of an object at rest on the surface. g points downwards, yet an accelerometer registers about 9.81 m/s2 upwards.

It is measuring the normal force, which is approximately equal in magnitude to the gravitational force. Note: I said approximately. The Earth is spinning about it's axis and it is orbiting the Sun. If an accelerometer could sense gravitation (which it can't), an accelerometer at rest on the surface of the Earth at the equator would register a downward acceleration of about 3.39 cm/s2 plus a sunward acceleration of about 0.59 cm/s2. The accelerometer instead registers an acceleration of about 9.8 m/s2 upwards.

From a Newtonian perspective, an accelerometer is insensitive to gravitation because gravitation is nearly uniform across the tiny spacial extent of the accelerometer. If the accelerometer was in free fall, the acceleration of the test mass due to gravitation is going to be almost exactly equal to the acceleration of the accelerometer as a whole due to gravitation. The accelerometer registers zero because the accelerometer does not sense gravitation.

From a relativistic perspective, it's even easier. Accelerometers are only sensitive to real forces. An accelerometer is insensitive to gravitation because gravitation is not a real force.

15. Oct 6, 2016

### Naman S Kumar

16. Oct 26, 2016