Like Pepsi vs Coke, Right vs Left, and South Park vs Family Guy, this is one of those epic debates that seem to defy the constraints of logic, time and space. In the ever-raging war to save a few pennies at the pump, the discussion on A/C vs windows-down seems to have transcended the merely empirical and become a hotbed discussion of sophomore physics classes worldwide. The answer to this particular question is, however, not as quite as pat as you might think.
This one boils down to a question of aerodynamics vs engine drag. On the one hand, turning on your car's air conditioner engages a compressor that draws power from the engine. That power comes from fuel, which impacts bottom-line economy. A/C proponents, though, counter with the fact that rolling a car's windows down disrupts laminar (smooth) airflow over the car's body, effectively increasing frontal area, frontal pressure and, eventually, drag. The question is: at what point do bad aerodynamics counteract the savings from turning the A/C compressor off?
Aerodynamics is a complicated subject, but one of the major concepts in aerodynamics is also the simplest: that power requirements go up with the square of velocity. The rule of squares basically means that you need four times as much power to go twice as fast. So, let's start from there as a base point. The formulas are complex, but in order to calculate aero power requirement for a given speed, we need to know the vehicle weight, its frontal area (the size of the vehicle when viewed from the front) and the coefficient of drag (how "slippery" the vehicle is).
Lets say that a 3,000-pound vehicle has a frontal area of 28 square feet and a coefficient of drag (noted as Cd) of 0.40; these are pretty common for most vehicles. To spare you the complex calculations, that vehicle will need 0.63 horsepower to go 5 mph, 3.05 horsepower to go 20 mph, 15.2 horsepower to go 50 mph, 28.48 horses to go 65 mph and 65.5 horsepower to go 90 mph.
All vehicles are different, and rolling down the windows will have different effects on all of them. We already know that the vehicle's Cd and effective frontal area will go up a bit when you roll the windows down, but any attempt to assign a specific figure would be fairly arbitrary since it varies. So, as a worst-case scenario, we'll recalculate assuming that rolling the windows down fully doubles the car's Cd and FA. Recalculating at 3,000 pounds, a Cd of 0.80 and an FA of 56 square feet, we get the following horsepower requirements: 0.65 at 5 mph, 4.84 at 20 mph, 43.48 at 50 mph, 90 horsepower at 65 and 228 horses at 90 mph.
Now that we've got the principles of power requirements down, let's look at the real world. In reality, rolling down the windows won't result in a set pressure increase on every vehicle since the pressure or drag increase is relative to the car's aerodynamics in the first place. Long story short, rolling the windows down in a Corvette will have more of an effect than doing so in a box truck. In the real world, Cd and effective frontal area go up by a percentage of the vehicle's total, generally no more than 30 percent in most cases. So, let's recalculate using a 30 percent higher Cd and FA.
Recalculating using a Cd of 0.48 and an FA of 34 (a 20 percent increase) we get: 0.63 horsepower at 5 mph, 3.32 horsepower at 20 mph, 19.73 horsepower at 50 mph, 37.86 at 65 mph and 90.39 at 90 mph.
An A/C compressor will use between 5 and 15 horsepower depending on the specific car or truck, so for our example we'll split the difference and call it 10 horsepower. In order for the car to be more efficient with the A/C on it has to use less power to run the A/C than to overcome the power difference between the windows up and windows down.
In our "extreme" example of double Cd and FA, we find that the car uses but 1.79 more horsepower at 20 and a whopping 28.28 more horsepower at 50 mph. Indeed, the car in our extreme example requires the equivalent 10 more horsepower at exactly 28 mph. Below 28 mph, our extreme example car would be more efficient with the windows down than with the air on. The break-point in our real world example, however, comes out to just over 65 mph; below that speed, the car is more efficient with the windows down than the air on.
So, which is more efficient: windows down or A/C on? Well, it first depends on how aerodynamic your vehicle is with the windows up, and second, how much power the A/C compressor draws. But mostly, it depends on how fast you're driving; the slower you drive, the better off you are in killing the A/C and rolling the windows down.
