I'm trying to model a rocket's position with air resistance as a factor. The rocket is fairly low-powered (Estes A8-3, 9.7N of thrust for 0.7 seconds), and I estimate it won't be going faster than 50 metres per second.
Should I be using linear or quadratic air resistance for this?
I found online that linear air resistance is used for relatively low velocities. How low is 'low velocity'?
The quantity to check is the Reynolds number $$Re = \frac{\rho v L}{\mu}$$ where $\rho$ is the density of air, $v$ is the relative velocity, $L$ the typical dimension of the rocket and $\mu$ the (dynamic) viscosity.
For small Reynolds numbers, i.e. $Re\ll 1$, viscous forces dominate and you have laminar flow. In this regime, the drag force is proportional to the velocity. For large Reynolds numbers, drag is dominated by turbulences and is proportional to the velocity squared.
Plugging in some numbers: $\rho \approx 1~\textrm{kg}~\textrm{m}^{-3}$, $\mu\approx 2~ 10^{-5}~\textrm{kg}~\textrm{m}^{-1}\textrm{s}^{-1}$, $v\approx 20~\textrm{m}~\textrm{s}^{-1}$, $L\approx 1~\textrm{m}$, you get a Reynolds number on the order of a million, which is much larger than 1. This suggests (as expected) that you are in the turbulent regime and should use the force proportional to the velocity squared.
Use quadratic resistance, i.e. the square of velocity. I do not know what the unlinked and unnamed source on the net meant with low velocity having linear resistance, but any velocity involved in model rockets is not low for sure. (It might be about Stokes law, applicable to such thigs as sedimentation of sand in water, where velocity is indeed linearly linked to resistance, but this is in the realms of Re<1, think grains of sand in water, dust-motes in air etc)
The cw value that is used in that equation, as well as the constant for air density, are not as 'constant' as their name might imply. cw is dependent on the Mach number (though with a top speed of 50m/s you won't have much effect from that), and air density on height, so you might have to solve for several stages of flight, or approximate the dependencies of cw and density as functions of speed for your specific case, and then plug those approxiamtions directly into the resistance equation.
