# Correcting a mass estimation under acceleration

1. Oct 22, 2015

### Richard Ayers

Hi, I have seed of a project forming but need some help with some physics in it :
What I'm trying to do :
I need to weigh a sample using a load cell, so far so good, but the load cell is on a moving platform, a ship.

I think I know that if the object being weighed and the load cell were moving at the same speed then the data from the load cell would be accurate, I think the analogy is 'a box on a load cell all being lifted by a crane', once the acceleration has stopped and the vertical movement is steady the load cell data will be correct but when lifting starts or stops things like momentum and acceleration come into play.
In the crane scenario you could just wait for the steady movement phase and collect your data then, but on a ship in any sort of wave movement there is no steady phase, you're either going up or down (and sometimes corkscrewing horribly and worrying about the security of your breakfast).

The current thinking is to have 2 load cells, 1 with a known weight as some sort of reference and another with the sample on. I can also insert an accelerometer into the kit and get vertical (or XYZ) acceleration in m/s or G.
I was planning to continuously sample the load cell and accelerometer data, correct the 2 mass values using the accelerometer data, calculate some kind of rolling average over a number of readings looking for a value that has an error within some set bounds and then supply this as the mass of the sample.

Other information - Samples may weigh from 1g up to 45Kg, I'm assuming that momentum is going to cause larger issues at the 45Kg end of the spectrum. Precision wise I need to be at the 0.1g level at the lower end and can live with 5g at the top end, the precision of the data-stream is mostly controlled by the analog to digital convertor that turns the load cell data into machine readable data, perhaps I should use the term accuracy for my 0.1g and 5g limits rather than precision ?

I know from experiments that the movement of the ship does cause variations in the load cell data, and that variation pushes the accuracy of the data outside acceptable limits.

So I guess the actual questions are :
1. Have I missed something obvious...
2. Given a m/s or G value how do I correct a mass

R

2. Oct 22, 2015

### Staff: Mentor

Sounds reasonable.

Things to consider:
* If your mass can move relative to the device in some way, the force might not directly follow acceleration, but show some small time delay. The readout can have a delay, too.
* The accelerometers might have some delay, coming from the electronics and limited readout speed.
* Rotation of the ship leads to small differential accelerations, so accelerometer and test device won't have the same acceleration. I would expect this effect to be small, especially for larger ships. Aligning the accelerometer/test device axis with the length of the ship will reduce it further.
* If your test device is tilted too much, friction with the walls could reduce the force, or the force measurement itself could get unreliable, depending on the setup.

Neglecting weird rolling effects that might act similarly to a centrifuge, it should be possible to get a reasonable estimate simply by integrating over a long time - long enough to average out every motion of the ship, because the net effect averaged over time should be very close to zero.

How to calculate the mass: the force is proportional to mass and proper acceleration, you know force and proper acceleration (this is the direct output of the accelerometer - 1 g at rest, more or less when moving around on a ship), so you get mass by dividing the two values.

3. Oct 23, 2015

### Richard Ayers

mfb : Thank you, its good to get another opinion that I haven't missed the obvious :-)
My time frame for integrating values is quite short, in some weather this will be less than the wave period so I will be measuring mass with acceleration only in 1 direction, meaning I can't use the up/down differences to cancel each other out. Now I know what to do with my g value from the accelerometer I can attempt to correct for acceleration at each data point (looking to sample at 10-25 Hz as a minimum), integrate over an acceptable time period and voila...I will also have my 2nd load cell with a known reference weight on, so, theoretically, I can provide an estimate of the accuracy of the accelerometer corrections. I think I have enough confidence now to give it a go. again, many thanks.