Atmospheric Effects on Aerodynamic Drag

 We’ve all read or heard about the fact that colder air increases aerodynamic drag due to its increased density, reducing your BEV range or ICEV fuel economy in winter. What most people don’t know is how much aerodynamic drag increases with dropping temperature, or how much benefit there is on a hot day. Is it significant? Let’s figure it out.

Yes, we have a reindeer farm in central Illinois. Merry freakin' Christmas.

Standard Atmosphere Model
 
To do that, we first need an appropriate model of atmospheric parameters such as temperature, pressure, and density, and how they change with altitude.
 
In the Aerospace Engineering program I'm about to complete, we use the 1962 International Standard Atmosphere (ISA). This model was derived from decades of atmospheric measurements, from which a set of equations were developed that adequately reproduce variations in temperature, pressure, and density as altitude changes. Up to 36,089 ft, a thermocline (temperature gradient) of approximately -3.6°F per 1,000 ft altitude reduces temperature (and speed of sound); above 36,089 ft temperature is approximately constant. If you’ve ever wondered why commercial aircraft fly at around 30,000 ft, this is why. Density goes down as you go up, requiring more air speed for the same lift—but as you go up, your Mach number increases for a given air speed. Couple this with engine performance (which is dependent on temperature and pressure at the inlet and exhaust, and with strict design limitations due mainly to the compressor), and you get a "sweet spot" altitude at around 30,000 ft where commercial planes can fly at transonic speeds with minimum total drag for the required lift.
 
The ISA model defines a "standard" day as 59°F at sea level, with standard pressure p = 2116.22 psf and standard density ρ = 0.0023769 slug/ft³ (the only number we were required to memorize in Systems Design—because density is so important to aircraft performance!).
 
The ISA model also introduces a temperature offset, ΔISA or DISA, for non-standard days. These DISA offsets are reported at airports in degrees Celsius, even in the US where absolute temperatures in aviation are typically given in English units.
 
Run through the equations and plot everything, and you get "standard day" atmospheric parameters as a function of altitude that look like:

Now that we’ve got a model of density as it changes with altitude and temperature, let’s turn to our theoretical car. Whether you drive your car in the heat of summer or cold of winter, its drag area doesn’t change (approximately; in reality, it does slightly)—and let’s assume here that you’re driving at the same constant speed in either season. In this case, aerodynamic drag force acting on your car only changes with density, to which it is simply proportional (since we’re holding all other variables constant). Thus, the percent change in drag is given by the percent change in density, or

Throw this in a program to plot it as a function of temperature, referenced to STP density as our ρ_hot, and we get the following:

This model predicts that, at sea level, drag may vary by as much as +12.5% (-15°F day) to -12.1% (+115°F day). That’s a pretty wide swing! Considering more reasonable temperature variation, your car on a 32°F day will have nearly 5% more aerodynamic drag than on a temperate 60°F day. Going the other way, on a balmy summer day at 90°F your car will have to contend with 6.6% less aerodynamic drag than on that springlike 60°F day.
 
Now, this assumes that we’re driving at sea level. But density varies with altitude as well, becoming smaller as you go up (as we saw in the plots above). Plotted at altitudes up to 5,000 ft:

You can see that as altitude increases, the trend in drag change is the same but our "standard day" temperature changes (at 5,000 ft, "standard day" temperature is about 41°F, for example). At 5,000 ft, that 90°F summer day will reduce your car’s drag 8.7% compared to standard temperature at that altitude, and at 32°F it will only increase 1.4% (and this is referenced to a smaller drag force, due to the lower density at altitude on a standard day compared to sea level).

So, the variation in aerodynamic drag due to atmospheric density can be more than 10% from cold-to-hot over a normal temperature range for much of the US, with the exact number dependent not just on your climate but also altitude. For example, if you live in Chicago (at about 600 ft elevation), your car will generate 13% more aerodynamic drag on a 20°F winter day than a 90°F summer day from the change in air density. That's pretty significant.

 
Atmospheric Wind
 
Since we’re talking about changes in your car’s drag with the weather, we can go on and discuss (some of) the effect of wind. Now, we’ll hold drag area and density constant while varying air speed due to the effect of a headwind or tailwind. Instead of a reference density, we’ll need to define a reference velocity; the chart below shows percent difference for a range of vehicle reference speeds.

Notice something important here: due to the variation of aerodynamic drag with the square of velocity, you don’t get as much benefit from a tailwind as you do a penalty from a headwind of the same magnitude. At 70 mph a 10 mph tailwind, for instance, will reduce your car’s drag by 26.5% while, in the opposite direction, a 10 mph headwind will increase it 30.6%. This might not be intuitive for a lot of people, so it’s worth pointing out.
 
Keep in mind here, too, that reference drag is different for each speed, and goes up with the square of that speed. The percent change from a given head- or tailwind might be smaller at higher vehicle speed, but reference drag at that higher speed could be significantly higher than if you choose to drive at a more moderate speed (increasing your highway speed from 70 mph to 80 mph, for example—a 14% increase in speed—increases aerodynamic drag more than 30%).
 
The Point
 
The moral of the story here is: when it comes to physics and vehicle performance, don’t argue things based on your intuition or feelings (one such exchange, which happened across one of my social media feeds this morning, prompted this post!). Reality might not behave the way you think it does.