Determining the drag coefficient of an object

When I heard that my mathematics assignment would be in part, about calculating the drag coefficient of an object with and without a parchute, I couldn’t help but extend the assignment a bit further.

Tada! figure figure

I managed to stick a cheap SD card reader with a Teensy 3.1 and Invensense MPU-6050 6-DOF IMU onto a small board, due to size constraints.

figure

Essentially the module fits inside a plastic cylinder with a rounded nose tip. A simple parachute made of a plastic bag is stowed also in the cylinder and only taken out when in use. Unfortunately the object broke after a few 11 m drops from the outside the biology rooms and I threw it in the bin without thinking twice. Moral of story: take photos before you throw something off a building.

I’m not sure whether I’m allowed to post any part of an assignment online, so it’d probably be better if I didn’t, in case they reuse the assignment task in the future. Essentially, you can use numerical integration of acceleration to estimate velocity at any time, t. However, as there’s a lot of error due to the cumulative error of integration acceleration w.r.t time, this is much better as a timing tool to time the drop instead of using a stopwatch. The start of the fall and the landing are easily determined by the magnitude of acceleration.

After calculating the drag coefficient, I found that the parachute decreased the terminal velocity of the object by 89%. Surprising? Not really.