Projectile of a Trajectory: With and Without Drag

I was inspired to do this after some frustration with the impracticality of disregarding the effects of air resistance that is so prevalent in physics textbook problems. Despite this, I have still made several fundamental assumptions that would not necessarily hold water in real life, so the trajectory with air resistance is still not 100% accurate. It is, however, a far better approximation for a real-world projectile's trajectory than a simple parabola. Here are the assumptions that I have made regarding the trajectory:

1. The graph assumes that the object's orientation is static throughout its flight; that is, that the projectile does not rotate in mid-air.

2. The graph assumes that the horizontal and vertical components of the drag force of the projectile throughout the flight will appropriately match with the corresponding horizontal and vertical components of the velocity of the projectile throughout the flight. This is not the case for three reasons: One reason is that the drag force is squarely proportional to the velocity, not linearly proportional. Therefore, the resultant vector of the horizontal and vertical vector components of the drag force on the projectile will not be consistent with the resultant vector of the horizontal and vertical vector components of the velocity of the projectile. The second reason is that the projected surface area in the x direction and the projected surface area in the y direction will not 'pythagorize' to give the projected surface area in the direction of the velocity of the projectile. The third reason is the same as the second reason, except with the drag coefficient.

3. The graph assumes that no other physical phenomena, such as the Magnus effect, or downforce produced by the aerodynamics of the projectile, are affecting the trajectory of the projectile.

4. The graph assumes that the density of the fluid medium is constant and does not vary with height or horizontal distance. At 1 km of altitude, the atmospheric pressure is about 90% of that at sea level. For non-significant altitudes, the difference in density is negligible.

5. The graph assumes that gravitational force is constant and does not vary with height. At 400 km of altitude, the gravitational force exerted by Earth is about 90% of that at sea level. For non-orbital altitudes, the difference in gravitational force is negligible.

6. The graph assumes that the flow of air behind the projectile is turbulent and not laminar. For objects in the air, this holds true at speeds above ~4 m/s. By extension, the graph assumes that the inertial drag force of the fluid medium is far more significant than the viscous drag force, and the graph assumes that the drag coefficient of an object does not vary with velocity.

7. Finally, the graph assumes that the drag coefficient in the y-direction of the projectile is the same between when the projectile is travelling upward and when the projectile is travelling downward. This is only the case if the projectile's geometry and orientation is such that the projectile has a plane of symmetry on the x-z plane (where the z-axis is sticking out of your computer monitor).