How to predict the flight states of a paper airplane?

Question

Mathematics

Hello.
The condition of the problem is that a paper airplane flies. There is a flight state data set. You need to predict the parameters for 3 seconds and 30 seconds. And when it hits the ground.
I don't quite understand which way to go. In theory, there are a number of parameters, such as speed, heading, altitude, vertical speed. And also - acceleration / deceleration for all speeds - roughly speaking, horizontal, vertical and angular speeds. These are the parameters of the aircraft itself. And there are also parameters of the external environment - wind speed and direction, land relief (the height of the airplane itself is taken from sea level or barometric height).
How to predict - I do not understand yet. The script needs to be written in Python.
I will be glad for any help.

Answer 1

You need only 2 formulas (possibly probabilistic):
- influence of vertical and horizontal speeds on vertical acceleration (lift force)
- influence of vertical and horizontal speeds on horizontal acceleration (air resistance)
All components affect the object by a linear composition. Accordingly, the entire flight is described by a set of differential equations of the 2nd order, which can be modeled instead of being solved analytically.
I propose to obtain the formulas described above empirically - by video recording of the flight of a real paper plane.
Here I modeled "on my knee" flight against a sinusoidal wind:

Answer 2

As I understand it, you need to make a physics engine and calculate the parameters in it. This will be the "prediction"
Please specify what kind of flight state data set? Where does it come from?

Answer 3

>But the task is purely academic, it has nothing to do with the real flight of the airplane
. Then we imagine that the airplane is the core, and we calculate it according to the formula for throwing a projectile. 5th grade, right?