Of course, it wasn't very symmetrical, and it didn't fly in a steady way, so I made another (this took about 10 minutes total, if you exclude the time I took to take the photos), and I took videos of it.
Step 1: Marking the circle
I then divided the quarter circle approximately into thirds. This I then used to make 12 markings on the cup.
The same was repeated for the bottom of the cup. (Pictures not included)
Step 2: Drawing the lines
Step 3: Cutting along the lines
After cutting along all 12 lines, I alternately cut along the top of the card to make the 'blades'
Step 4: Folding back
Step 5: Launching it
A sharp twist of the wrist, while throwing it upwards is usually enough. Feel free to try other methods.
To see if it could be launched bottom up, I found that it worked quite well.
And of course, the control.
To prove that this design actually converts a coffee cup into a flying object, I tried using the same hand motion on an uncut coffee cup