Thoughts on Convoying Fuel Efficiencies

The Maxi Taxi concept describes the advantages of convoying in saving fuel during highway travel. Cars that closely follow each other can achieve impressive reductions in total air drag. Air drag is the leading overall drag component at higher speeds and therefore represents the lion’s share of a car’s fuel consumption at speed.

Air drag is a complex subject, and the original maxi taxi concept aimed to reduce overall air drag by fitting a number of cars as close together as possible and thereby to create a drag profile that is similar to a railroad train, which is basically a flexible tube that is being dragged through the air. We can achieve a similar effect with car convoys and the cars do not have to be the same, but equal width would be real a benefit.

Such a design basically has three drag (friction) components: Mechanical friction, skin friction and form friction. A railroad train has very low mechanical friction since it rolls on steel wheels on steel tracks, which results in much lower rolling friction than a car which rolls on rubber wheels on relatively rough roads. Over the last decades rolling friction has been significantly reduced, but we are starting to hit the limits on further improvements for non-autonomous cars (we can still do better if we are willing to reduce traction issues and make roads smoother, which may be achievable with autonomous driving). True skin friction (the friction of air rubbing against the car) in cars is a small component (with boats and with airplanes it is frustratingly large) and therefore form drag is where it pays to look for additional gains.

Form drag can be thought of as the effort that is required to punch a hole into the air to pass the car through. If we drive slow the effort is low and if we drive fast the effort is high. This increase in effort is not linear. If we drive twice as fast, the form drag will be four times as high.

Therefore, the form drag of a car driving at 80 is not 4 times as high as the same car driving at 20, but rather 16 times as high. However, that is still only part of the picture. The form drag of the car is also related to its cross sectional area (the size of the hole it has to punch into the air) and its drag coefficient (its slipperiness). The drag coefficient is the number that car manufacturers like to brag about.

Strangely, we have known for decades what the minimum drag coefficient for a car can be. That car design was described in Hoerner in 1965 with a coefficient of drag of 0.12. However, the problem is that the shape for the minimum drag coefficient does not make a practical car shape, since it needs to be so much snakier than is practical for road cars.

The Maxi Taxi concept (with a 5 foot width restriction) will, by itself, have 5/6 the drag of a 6 foot wide car. However, the shape of the Maxi Taxi with its blunt front end does not exactly make it a low drag coefficient car. But if we make a lot of Maxi Taxis follow each other closely, we achieve the type of shape that has to punch only one hole into the air for a large number of Maxi Taxis and then the form drag can be divided among the Maxi Taxis in the convoy. As such, one Maxi Taxi may have a drag coefficient of .5, but two Maxi Taxis following each other very closely will each have a drag coefficient of .25. Unfortunately that does not mean that in real life two Maxi Taxis following each other closely will each double their fuel efficiency, but the effect is real and shows up all the time.

I will provide two interesting examples:

The first example occurs in NASCAR racing. On super speedways, to gain maximum speed, it is necessary for at least two, and preferably more, racecars to very closely follow each other. This results in a strange tactical negotiation game that is described in this paper.

The second example is related to slip streaming behind trucks. If you have a fuel economy gauge in your car, and if you are willing to break the law, you can find a reasonably open road and wait for a fast moving truck to pass you. If you then follow that truck closely you will see that your fuel economy will go up quite a bit even though you are traveling faster.

It takes a little work to find the sweet spot which may not be hard up against the bumper of the truck, but rather can be about 10 to 15 feet back depending on the speed of the truck and the shape of your car.

In 2005, I ran a rather lengthy experiment on this approach when I had to attend to some shipping issues in Mobile and New Orleans right after Hurricane Katrina. To do that I had loaded up the family Chrysler minivan with food, water, and camping gear, and headed south to Mobile first, where I would do the first job and then drive on to New Orleans where I would do the second job and then drive on to Baton Rouge where I would meet up with other M&O staff. When I stopped in Birmingham I was told that there would be no fuel going south and that the first fuel I would find would be in Baton Rouge. I calculated the distance between those points and realized that I would never be able to make that distance on one tank of gas. Still I had to get to Mobile and decided to fill the tank to the max, leave early to take advantage of coolers temps (that will also very marginally help reduce fuel consumption)  and to drive south to Mobile first and worry about gas later.

I did decide to drive very calmly and smoothly and searched for a good compromise speed where I would drive highway speeds without hitting speeds that really started to reduce the fuel economy. I found that driving about 55 mph gave me about 26 mpg. Driving towards the Katrina devastation was a strange experience since cars were going north, but I was going south and the highway was pretty much empty. However there was one notable exception, I was being passed at much greater speeds by quite a number of Walmart trucks. Walmart had done a great job in using its sophisticated supply logistics system in being the first to send needed supplies south and their trucks were really putting on the hustle. So I slipped behind one doing about 70 mph and started to slipstream behind him. There was little traffic and plenty time and soon I was getting about 32 mpg at much higher speeds and discovered that the sweet spot was not right on the bumper (which was too dangerous anyway) but about 10 to 15 feet back from the bumper (which was still dangerous, but a manageable risk on these road conditions with my desire to really concentrate, and still less risky than the 12 inches that NACAR drivers like). I was going faster and burning less fuel and effectively driving in the sweet spot of the truck turbulence.

With autonomous driving, a similar system can be developed. As a matter of fact, with autonomous driving, one could hook up the fuel economy gauge to the autonomous driving system and follow any truck on the highway and achieve nice fuel savings while finding the sweet spot. Since an autonomous car can react much faster than a human, there is little risk in doing that.

But that is not the most interesting approach. If all cars are five feet wide, the convoy will only punch a narrow hole in the air and if the cars are autonomously aligned to make a nice aerodynamic shape, there should be very substantial fuel saving. To figure out the best alignment of different five foot wide cars would be a very complex PhD type analysis. Weirdly, in real life such an analysis would not be necessary. A rather straight forward optimization routine with feedback from each convoy member’s fuel economy combined with a neural network, in a few days, will figure out how different five foot wide cars should be sequenced to get optimal fuel economy.

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