### 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.

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!).

Fortunately, the subject of fuel economy as it relates to
aerodynamics is one that is

AJ Scibor-Rylski wrote about it in his

**Rules of Thumb**

**Quantifying the Relationship**

*very*important to the car industry, so it is covered in just about every textbook on aerodynamics out there.*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. |

More recently, RH Barnard wrote
about the relationship between aerodynamic drag and fuel consumption in

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

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

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.

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

*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)._{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**

*m*to speed*v*—its*kinetic*energy, K = ½ mv^{2}. 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_{R}d. 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_{A}d. K and W_{A}are both proportional to the speed of the car squared, while W_{R}changes linearly with 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.**

*optimize*aerodynamic modifications.
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