This is a project to build a one-propeller drone, according to some crazy idea I had.
Will it work? No.
(NOTE: The following diagrams are the view of the drone from side on, so up in the diagram is up in real life.)
The first problem with a one-propeller drone is that the angular momentum of the blade when it starts spinning causes the body to begin to spin in the opposite direction:
(Black - propeller, red - fast motor, blue - base)
Conventional quadcopters fix this by having an equal number of blades spinning clockwise as anticlockwise, meaning the total angular momentum is 0. However this isn't possible with only one propeller.
Solution: Let it spin!
Instead of trying to stop the drone from spinning, we will let it spin, but limit the spin by giving the drone...
Wings! The drone will have large wings on its body, which will limit the rotation speed due to their air resistance.
The second problem we face is that we have no way to control the movement of the drone. Our solution to this is to place the battery and electronics (which will act as a sort of weight) in a section at the bottom of the drone, and have this section controlled by a servo such that it can be made to tilt. When the weight is tilted, the angle of the upper body from the vertical will change. How? I'm not entirely sure. But it will probably change somehow, and if we can calculate this, then the drone's speed can be controlled.
Now we have a third problem arising from my solutions to the first and second problems. That is: if the body of the drone is spinning, and the drone's direction is controlled by the weight distribution of the body, then the drone will be doomed to travel in circles forever and ever!
My solution here is a third motor (light blue), separating the lower base (with the servo and electronics) from the upper base (the bit with the wings that spins). A gyroscope sensor in the lower base can be used to control the motor's speed, adjusting so that it spins just fast enough to keep the lower base stationary.
This motor serves an additional function: rotating this motor faster / slower than required will allow the lower base to be rotated (relative to the external reference frame), meaning the drone can change direction.
And so the final result, demonstrating how I anticipate it will move:
This project is currently just an idea - I haven't begun work on it.