I am trying to figure out the air resistance that would act on a rocket that might reach Low Earth Orbit. First off I am only just entering high school so I have an extremely limited math background. I searched around quite a bit for an air resistance formula and eventually found this-
$$Drag \, Force = \frac{c_d \cdot \rho_{air} \cdot A \cdot v^2}{2}$$
Where $c_d$ is the drag coefficient and $A$ is the surface area of the object.
I plugged in my numbers and they essentially told me the drag force would nearly double the original force. Making it clear my rocket wouldn't be able to move. This cannot be. I fiddled with the numbers and found that the only way to squeeze a logical answer out of this formula is to make the surface area the tip of my rocket, something like .0001 meters. I couldn't trust this answer, however, because it varied by several billion newtons. Am I using this formula correctly.
Next, after I decided this formula wasn't helping me I looked further until I eventually came across a lot of talk about linear at quadratic drag. I looked into but I had no idea what it all meant. Is it possible to explain linear or quadratic drag to someone with a background in nothing more than Algebra so that I can calculate the drag on my rocket. If so I would really appreciate an explanation.