Aerodynamic drag

Some handy constants.

g = standard gravitational acceleration = 9.80655 m sec⁻²
φ = universal gas constant = 8.31447 J mol⁻¹ K⁻¹
Ts = sea level standard temperature = 288.15 K
L = temperature lapse rate = 0.0065 K m⁻¹
Ps = sea level standard pressure = 101325 N m⁻²
μ = molar mass of dry air = 0.0289644 kg mol⁻¹

The density of ambient air, ρ, assumed to be dry, as a function of altitude, h, in meters.

T = Ts − hL = ambient temperature
ψ = gμ/(φL)
P = Ps (1 − hL/Ts)^ψ = ambient pressure, if air is dry
ρ = Pμ / (φT)

Bullet parameters.

Cd = drag coefficient of bullet
A = cross section area
m = mass of projectile
V0 = muzzle speed

The drag acceleration, ad, as a function of bullet parameters, speed, and the density of the ambient air.

Cb = m / (Cd A) = ballistic coefficient
ad' = −ρ V² /(2 Cb) = magnitude of drag acceleration in dry air

The humidity of air has only a small effect on the air density. Even when you assume that the air is dry, when in fact it is 80% saturated, the relative error in the density is only about 0.0001. To correct the drag acceleration for humidity, do this:

k = percentage (0 to 100) of relative humidity.
Q = 1.08e-6
ad = ad' (1 − kQ) = magnitude of drag acceleration in air at k percent relative humidity

The drag acceleration is directed opposite to the bullet's velocity in the air.