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Displacement transducer for force balance - Printable Version

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Displacement transducer for force balance - Don H - 12-24-2021

Hi, it is me again, the fellow doing science and engineering experiments with grade 5 kids.  I thought I would share how I am using Phyphox as a displacement transducer within a relatively simple apparatus to measure drag force on models in a wind tunnel (a tabletop fan actually).  The device (picture attached) follows a traditional one-directional force balance design, using load beams made of thin plastic sheet (from some blister packaging) to suspend the model.  Movement of the model under the wind force, hence the drag force, is measured by the magnetic sensor in the phone which is fixed to the base and a magnet on the moving part of the balance.  The device is rather friction-less, as well as rather sensitive to wind fluctuations, so the balance will want to oscillate for long periods of times.  Adding a magnetic damper, consisting of a magnet from a hard drive, an aluminum bar, and the Lentz effect, results in stable movement.  As well, use of gaussmooth in the app is used as extra smoothing, and the app also allows for adding a zero offset.  By setting up the balance to be level, using an old glue stick, it is insensitive to the weight of the model, and gives rather reproducible and discernable results.   As examples, some numbers I got for drag of various standard shapes of same projected area: flat plate - 196, sphere - 105, half sphere into wind direction - 120, pyramid - 137.

I use the balance just to measure relative force numbers, as the experiments to be done are largely to compare drag of different shapes in the air stream.  A rough check using coins and a string setup to apply a side force shows a near linear relationship of magnetic field and force.  I'm not sure, but I would have expected perhaps a parabolic relationship, however perhaps because the displacement is only on the order of 2-3 mm, is it approximately linear.  For larger displacements where non-linearity becomes important, I would expect its possible to correct for this using equations in the app.

Hopefully this proves useful to someone, if not for for making a simple wind tunnel force balance robust enough to bring into a classroom, but any other instrumentation requiring an accurate displacement measurement.