Aerodynamics: Drag
[ August 10th, 2008 ] By: Mark Ozimek Posted in » Technical Articles
Aerodynamics is quite an interesting subject, and also one of the more complex. Seeing as I’m still learning this stuff myself, this series will be an introductory lesson on aerodynamics, I’ll just cover the basic concepts that are a good framework to understanding a lot of other important things.
An important thing to keep in mind is that aerodynamics is more or less the study of how fluids move (aka: fluid mechanics), with the fluid in this case being air, and a car’s body pushing the air out of the way. As long as you think of it as air being pushed around, the rest of the concepts are pretty straight forward.
First up is drag. Drag is a force opposing motion. In the case of aerodynamic drag, it’s the force applied against the car as it moves through the air. There are a few variables that affect the aero drag. The faster you go (velocity, or V), the more drag there will be. Also, more total surface area and frontal area increases drag. The frontal area (Af) can be thought of how much area the car takes up when viewed from the front. Or if the car is moving sideways, the side area would be used, or some combination thereof. There is a coefficient of drag (referred to as Cd) that is a function of the body shape. The final important factor is fluid density. The density of air varies with altitude, temperature and humidity, as I have pointed out in the past.
There is an equation that puts all of these things together to find the aerodynamic drag that will be seen:
Drag = (Density / 2) * Cd * Af * V²
Just make sure the measurement system is the same for all and the answer will be a force. As an example, let’s look at how much drag there is on a VW Golf GTI from the late 80’s going 80mph. I have a book here, Theory of Ground Vehicles by J. Y. Wong that has a list of different cars and their Cd and Af. The GTI has a Cd of 0.35-0.36, and Af of 1.91 m². 80mph is 35.76 m/s. I’ll assume standard temperature and pressure, so the density of air is 1.292 kg/m³.
Drag = (1.292 kg/m³ / 2) * 0.35 * 1.91 m² * (35.76 m/s)² = 552.2 kg-m/s² = 552.2 Newtons
Now for some fun with math to see what this means. Let’s convert the force and speed into power.
552.2 Newtons is the same as 124.1 pounds of force. 80mph is 117.3 ft/s, multiply the two together to get 14,556.9 lb-ft/s. There are 550 lb-ft/s in a horsepower, so this hypothetical GTI needs 26.5 hp to overcome aerodynamic drag at 80 mph. If we increased the speed to 100 mph, that number changes to 51.7 hp! Note that this is power at the wheels, and is neglecting any incline, rolling resistance, drive train resistance, and so forth that increase the power requirements at the crank.
I’m going to cover lift and downforce in a later article, but while it may seem obvious, one major cause of drag is fins and spoilers that create downforce while the car is moving. The extra turbulence and changes in airflow usually turn up as an increase in the Cd. Why is this? Well, the fins are designed to push air up as their way to get downforce. When a car is going down the road pushing lots of air upwards, there will be similar amount of drag. Let’s look at F1 cars, since they make good examples. The car is basically covered in wings that make enough downforce to allow the car to drive upside down at speeds over something like 100mph. They have to make a tradeoff when setting up for every race to balance between downforce and drag, which effectively means they have to choose whether the car can corner faster, or have a higher top speed. Rally faces a similar dilemma, although in rally, there is a lot less space for wings, and there are many slow hairpin turns where wings don’t do a lot, so the emphasis on wing setup is diminished.
So hopefully now it is obvious why when driving down the highway, you hit a speed where the gas mileage suddenly drops off really fast: The power required to overcome aero drag increases with the cube of velocity! Stay tuned for the next part of aerodynamics, and feel free to suggest topics that you would like to hear from me on!
