Can I Accurately Measure Bike Wheel Radius with a Rotating Sensor?

[Maria Redericki]

I have attached a sensor measuring acceleration to a bicycle wheel. I was hoping to be able to trace out the circle with accurate measurements for the radius of the bike wheel by integrating my data however I have realized that my sensor is of course undergoing centripetal acceleration however as the x and y-axis of the sensor is rotating with the device ( it's a dual axis device) then thre is a problem is I simply plot x measurements against y measurement. Is there a way around this?

 

[mfb]

What do you want to measure? A way around what?

Your sensor will always see centripetal acceleration going in the same direction - let's call that direction "x" (towards the center of the bike). For typical velocities of a bike, this will be by far the largest contribution to the measured accelerations. Smaller contributions come from gravity and accelerations of the bike.

 

[Maria Redericki]

Well I would like to trace out the displacement of sensor and so get a circle by intergrating acceleration twice. But As you say I have rotational acceleration etc is there anyway I can convert this to linear displacement so that I trace out the wheel circle of radius 30 cm? I am using a dual axis device

 

[mfb]

If you can neglect a change in the speed of the bike, centripetal acceleration should be constant and can be subtracted.
Otherwise, you'll have to add some assumptions about your motion I think.

 

[Maria Redericki]

Well I know that it would be subtracted out to then give tangential acceleration, however as the axis are moving with sensor on wheel of bike I am a bit confused how I can get an overall displacement. I am thinking that because these axis move with sensor how can I trace out an overall circle?

 

[Maria Redericki]

To be honest I think i have an idea but I am not sure if there is something I am not considering... This is my steps of my approach that I am thinking to take
a. remove centripedal acceleration
b. Using my frequency (it at some point 3 Hz) of bike turn I am able to work out how much angle it has traveled at any given time.
c. I know that axis travels with object so to the convert to overall axis I convert between my axis and inertial axis

is this correct approach.

 

[mfb]

If you know the rotation frequency and the radius of the wheel, you are done - this gives you the velocity and integrating over that gives the displacement.
Based on the velocity you get, you can also check if the centripet[/color]al acceleration matches the expected value.