# Calculating a calibration factor for velocity between Volts and m/s

1. Nov 7, 2009

### CaspianTiger

1. The problem statement, all variables and given/known data

Hi, i have to calculate a calibration factor to change a measurement for velocity in volts from a vibration test rig into a measurement of velocity in m/s.

2. Relevant equations

I have data for velocity in volts and i am using the equation v=x'=awcos(wt) to calculate the velocity in m/s... however I can't find a CF for these two values...

3. The attempt at a solution

I tried some simple ideas... like the difference between them, however this is not constant over time. I tried the ratio between them but again this is not constant as the time changes. I tried both of these multiplied and divided by time...

Has anyone got any ideas or is there a general concept for calculating a calibration factor i have overlooked?

2. Nov 18, 2009

### rdt24

I have EXACTLY the same problem. I am given a dataset (A) of velocities in volts. I also have a dataset of displacements at time intervals of 1ms over a time period of 2s, giving 2000 readings.

Since:
x=asin(wt)
v=x'=awcos(wt)

I thought that I could use the fact that

x * (w/tan(wt)) = awcos(wt) = v

to generate a dataset (B) of velocities in m/s, then I should be able to find the calibration factor, CF using:

CF = (Dataset B)/(Dataset A)

HOWEVER, when I plot the velocities in m/s against time in s, the graph I get is a tan wave, but it should be a sin wave. This is extremely frustrating! Someone please help!

3. Nov 19, 2009

### CaspianTiger

I have since solved my problem this is what i used.

The recorded velocity was given in volts and the velocity needs to be in m/s, a calibration factor can be determined to change the velocity from volts into m/s. The velocity in volts and in m/s has the same frequency, same sinusoidal wave but a different amplitude, so the calibration factor can be determined using equation 7.
Calibration Factor=aωcosωt/(V_max cosωt) (7)
This can be simplified to equation 8.
Calibration Factor=aω/V_max (8)

Multiplying a value of velocity recorded in voltage by this calibration factor will return a velocity in m/s.