Greets Gentlemen!
rb1957 and sreid are partly correct and partly incorrect on one little detail. cD is indeed a fixed constant in its pure form for a given craft or vehicle, but the change in drag is not influenced by changes in air density alone. Moreover, there is an influence that does effectively vary the cD Factor.
But firstly viscosity, although a very minor factor in gas flow regimes, varies with the constituency of the air and therefore with humidity. This is not directly proportional to density, since there are intermolecular forces of repulsion and attraction at work, which in turn affect the resistance to molecular shearing within the boundary layer.
Secondly, the more significant factor that contributes to this variation irrespective of air density is the flow regime about the craft in question. This flow condition is a boundary layer phenomenon addressed mathematically in fluid dynamics via the Reynolds Equation.
The Reynolds Number is a non-dimensional number distilled from density, viscosity, size, shape and velocity variables (all of which are dimensional - they are values quantified in SI Units.)
A given Reynolds number corresponds to a certain boundary layer flow condition about the craft. At low Reynolds Numbers, the flow is laminar and the influence on the total drag is high, even though the overall drag will be low as a result of the e=mv^2 equation at correspondingly low velocity. In a higher range of Number, the flow condition becomes Laminar Separated and the Reynolds drag factor is lower than in Laminar Flow, even though the total drag obviously increases with the correspondingly higher velocity. In the next higher Number range beginning at around 400,000, the condition is Turbulent Reattached, causing one or more isolated pockets of retro flow within the boundary layer; the Reynolds drag component drops very suddenly to reach its lowest level at about 500,000. The effect on the otherwise exponentiating total drag is very noticeable when this flow condition exists. Clever aerodynamic design aims to optimise the boundary layer flow to create this condition somewhere approaching the craft's peak velocity. A Reynolds Number of +600,000 (if I recall it correctly) predicts a Turbulent Separated flow condition, where the Reynolds drag component begins to increase from its lowest towards a magnitude much greater than that of Laminar Flow. This section of the Reynolds Number curve is more or less exponential, so the total drag witnesses an increase in the rate of exponentiation as a function of velocity.
These different flow conditions influence the volume of air that is carried along by the moving craft and therefore the total drag quite significantly.
I don't recall the mathematical formulae in detail and neither do I have them readily at hand to refer to at present, so I cannot offer more on this aspect of the overall drag equation.
Reynolds Number influences the whole thing in such a way that for convenience, the cD Factor is actually weighted by this phenomenon and is thus seen to vary with velocity.
The complexity of the calculations involved are such that the best methodology is indeed to measure the total drag force practically, exactly as rb1957 suggests.
Measured accurately, you'll discover that the drag curve versus velocity that you get from measuring horsepower and acceleration will not be an exact exponential curve - due to changing flow regimes in the boundary layer as speed increases, even irrespective of horsepower changes with engine rpm.
To get a feel for the relative magnitude of a given component of total drag, be it rolling resistance, profile drag, boundary layer drag, density, viscosity or whatever, the practical test is again recommended, changing one thing at a time only and then running it through the full speed range; or over the 1/4 mile; according to your preference. Then, change the same factor a little more and repeat the performance.
It would unavoidably amount to a hell of a lot of testing!
For boundary layer flow conditions and fairly accurate cD measurement, there is sophisticated wind tunnel simulation software that does it rather well in a virtual environment. It's available from various sources, but is expensive, as is the hire of wind tunnels.
The best way to get your hands on something like a tunnel or the simulation software is to be associated with a university, or be employed by a company at the cutting edge in aero/hydrodynamics.
Regards, Mad Prof.
