The Relationship Between Drag and Fuel Economy

Lined up and ready to head out on track at the 2022 Green Grand Prix, an annual fuel economy competition held the Friday of opening weekend at Watkins Glen International.

We all know that reducing drag can improve fuel economy. It’s intuitive but can be proven mathematically: when your car has less force acting against it, it takes less fuel (gas, diesel, or electric) to move. But what is the exact relationship between aero drag and economy? Can we measure it? Or predict it? Figuring this out can help us plan modifications to our cars with the aim of improving economy, as well as tell us if fuel economy is an accurate measure of changes in drag.
 
Rules of Thumb
 
You’ll see rules of thumb tossed about online which relate drag and fuel mileage. A common one says, “For every 10% reduction in aerodynamic drag, fuel economy will improve 5%.”
 
Is that accurate? Well, in a word: no, as we’ll see in just a minute. And its origins are murky. Some people attribute it to GM aerodynamicist Gino Sovran, but I have never been able to find the source of this claim. As far as I know, this is one of those “rules” that sprang up online and took on a life of its own, shared so frequently that it becomes “fact.” (If you have a documented source, please send me a message—I would love to know where this actually originated and its context!).
 
Quantifying the Relationship
 
Fortunately, the subject of fuel economy as it relates to aerodynamics is one that is very important to the car industry, so it is covered in just about every textbook on aerodynamics out there.
 
AJ Scibor-Rylski wrote about it in his Road Vehicle Aerodynamics (1975). Some of his assumptions are unrealistic when we try to apply his examples to modern cars.

How unrealistic? This unrealistic. There hasn’t been a car this light on the American market in decades.

He suggests that if “average aerodynamic drag coefficient could be reduced by 2% say, the engine power requirement would be reduced by about 0.5%,” and writes that engine power is “directly proportional” to fuel consumption. In reality this isn’t quite true, as power per fuel consumption can vary quite widely between engines and between operating conditions of the same engine. You can see at what load and RPM a gas engine is most efficient by looking at its brake-specific fuel consumption, or BSFC, map.

BSFC maps for the 2nd (left) and 3rd (right) generation Toyota Prius engines (image credit: Ramli, W.R.B.W. et al, "Organic Rankine Cycle Waste Heat Recovery for Passenger Hybrid Electric Vehicles," in Energies 13(17): 4532).

More recently, RH Barnard wrote about the relationship between aerodynamic drag and fuel consumption in Road Vehicle Aerodynamic Design (2009). Using the example of a mid-size European sedan with a 1.5L engine and C_D = 0.35, he points out that any reduction in fuel consumption will be proportional to the change in total drag force at a steady speed, not the change in aero drag coefficient. (This is an important distinction, as many online commenters try to use the 10%:5% rule with C_D rather than F_D). Reduce the car’s drag coefficient to 0.25, a 28% reduction, and you change the total drag force—which includes aerodynamic and mechanical drag, remember—by only 22% at 75 mph, which decreases fuel consumption by the same percentage. Also keep in mind that fuel consumption is not measured in MPG but its inverse, volume per distance (usually L/100km, as most of the world outside the USA uses).
 
Barnard goes on to point out that any “assumption of unaltered engine efficiency is not usually valid” and must be taken into account; lower drag could keep the engine in a more- or less-efficient part of its BSFC map. Further, the car’s drag coefficient at 0° yaw is not its real-world coefficient, so to calculate a change in efficiency we need its wind-averaged drag in the conditions it actually sees. And finally, no one drives a car solely at a steady speed; even on a long highway trip it must be accelerated and decelerated numerous times.
 
There’s another factor that both authors leave out: as drag coefficient is decreased, aerodynamic drag becomes a smaller and smaller proportion of the total force acting against the car and thus the same percentage change in aero drag will have less of an effect. In other words, reducing C_D = 0.50 by 20% to 0.40 will have more effect on the overall drag force than reducing C_D = 0.25 by the same percentage to 0.20. So it matters how low-drag your car is to begin with.
 
Energy
 
In physics and engineering, problems that are difficult to solve by analyzing forces or momentum or motion can often be figured out—sometimes quite simply—by looking at the change in energy. In the case of an automobile, there are three energies associated with its movement. First, there’s the energy it takes to accelerate the car of mass m to speed v—its kinetic energy, K = ½ mv². Second, there is the energy expended to overcome the resistance of mechanical drag (or rolling resistance)—this form of energy is called work, and it’s proportional to the resistive force and the distance traveled, W_R = F_Rd. Finally, there is the energy required to overcome aerodynamic drag, which is the same work as before but this time proportional to the aerodynamic drag force, W_A = F_Ad. K and W_A are both proportional to the speed of the car squared, while W_R changes linearly with speed.
 
Looking at energy can clarify the difficulty in trying to nail down a formula for relating aero drag changes to fuel economy improvements. Any change in aero drag and its effect on fuel economy will be overly sensitive to what speed you’re considering because of the squared term. Since the overall contribution of aerodynamic drag to the total energy requirement changes with the square of speed, where aero drag can be the dominant energy expenditure at high speeds, it will have more of an effect on fuel consumption at those high speeds and less effect at lower speeds e.g. a 5% improvement at 80 mph which turns into 3% at 60 mph might drop to 1% at 50 mph. Because of this, it is impossible to issue a blanket rule such as “10% reduction in aero drag = 5% improvement in fuel economy” without specifying the car’s drag area, its mass, its coefficient of rolling resistance, its BSFC and gearing, and its exact speed.
 
What Now?
 
So it seems the only confident statement we can make regarding a broadly quantifiable relationship between aerodynamic drag and fuel consumption as measured on the road is this: Reducing drag should reduce consumption somewhere between the same percentage change and zero.
 
That’s not very helpful. But even if we can’t easily quantify a relationship between changes in fuel economy and changes in aerodynamic drag, I think it is still a useful measure. If repeated testing at high speeds and over long distances shows a reduction in fuel consumed, that’s a pretty good indication that whatever change you’ve made to your car has reduced its drag. Just don’t bother trying to use the percentage change in consumption to figure out a percentage change in drag or to predict the percentage change in fuel economy based on the change in drag; there’s too much going on that you can’t account for on the road to make either of those anywhere close to accurate. Try one of these methods to measure changes in drag directly instead, especially if your goal is to optimize aerodynamic modifications.

69.0 mpg at the 2022 Green Grand Prix, up from 59.2 mpg in 2019. That suggests that the (measured) changes I made to this car in between are working, but it’s not possible to say just how much (and how much was weather, wind, and my driving).