Mechanism
As seen this design uses a Z-axis which will push the motor up and disengage the motor from the central axle. This thus eliminates our back e.m.f problem without the use of gears.
When we want to carry out our experiments, we will activate the Z-axis which will connect the motor to the central axle. This will allow the shaft to spin. The cylinder will be mounted onto our shaft and will act as our surface (meaning it has the riblets milled onto the cylinder). Air will pass over the cylinder at the speed at which the cylinder will be spinning.
Since our motor is spinning at a maximum of 12,000 RPM, this means that our cylinder (with a 7cm diameter) will be able to spin at a speed of ~40 m/s. This will enable us to test air movement over our cylinder up to a speed 40m/s.
In order to measure drag, we will use the deceleration method. We will use a tachometer to measure the RPM that the central cylinder is spinning at. We will plot a graph of how the RPM changes with time – from the start where we power up the motor to when it stops. The percentage for the RPM to decrease by a certain amount will be used as a proxy to measure a change in drag.
Drag measurement
We decided to measure drag by graphing the deceleration of the cylinder after it hits a constant RPM. By considering the forces acting on the cylinder, we can obtain a differential equation describing the RPM over time.
RPM is a measurement of angular velocity. As such, we can relate the decrease of RPM to the torque acting on the cylinder. The two main forces acting on the cylinder are the Frictional force and the Drag force. This gives rise to the following equation, where the first term denotes the contribution of Drag and the second term denotes the contribution of Friction.
To relate this to the RPM, we need to solve the above differential equation. The general solution to the above is of the form:
By attempting to fit our data to the above equation, we can derive the constants that allow us to quantify the forces acting upon our cylinder. This allows us to ascertain the drag reduction properties of different surfaces.
From the graph above, it can be seen how the curves are fitted with the red line. The app Origin was used. Each red line has an equation taking the form of the above general solution to the differential equation. The coefficients can be obtained to quantify any difference in drag! The table below shows some of the runs we have made so far. Unfortunately, our motor clutch broke before more runs could be completed. No worries though, the clutch can easily be re-printed!
