"At some point, there might be nothing left to do except to roll up your sleeves, brew some coffee, and tell your graduate student to read the paper and report back to you." - Scott Aaronson on what to do if his filter for crackpot math papers fails to return a definitive answer.

Friday, June 29, 2007

The practicalities of drafting

As I've mentioned previously I do some drafting of trucks to increase my gas mileage. I did some estimations and calculations, described in that post, that indicate that, done with extreme caution, it could be safe and that it should be effective. But how practical is it? It's turned out that I'm only able to find a truck to draft between 10% and 15% of the time I'm at freeway speed. Trucks are frequently going too fast for my fuel saving regime, thus leading to the question of what the break even point would be for the fuel used in speeding up to draft a fast-moving truck versus maintaining a leisurely 55 m.p.h. with no truck in front of me. More on this later.



But the fact is, there is rarely a suitable truck around when I need one. I look for trucks with the following characteristics, just based on intuition: low trailer; as square a back as possible (preferably not a milk or cement tanker); not hauling rock, dirt, etc. (no dump trucks); maintains a reasonably steady speed; doesn't do a lot of lane switching, I guess that pretty much covers the candidates. But at 55 m.p.h. I'm not doing much passing of them, so I have to wait for a truck that has the listed attributes to pass me. It is rarer than I would have guessed, though if I see a likely prospect in the rear view mirror, I can slow down to let him catch me.



So when does it pay to speed up to draft? There are two aspects to this - the fuel used in accelerating to a new speed, and the balance between the reduction in drag from being behind the truck (this would be in the density term in the drag equation) and the increase in the speed. Additionally, road loads would increase by a small amount, but I assume this to be linear, and thus the increase in road load force is compensated by the increase in distance covered.



There will be a number at which my fuel savings from reduced density (the low pressure zone behind the truck) will be overcome by the increase from the speed term, since it's squared in the drag equation. For the purposes of this post, I'll ignore the fuel used to get up to a higher speed - this fuel is used to increase the kinetic energy of the vehicle, I'll assume I can recapture this energy (though of course I can't, at least not with 100% efficiency).



I have to use the figures in my previous post on drafting to calculate the reduction in drag to attribute to the truck's wake, and calculate from there. Using my best estimate of the increase in gas mileage while drafting, from 21.5 m.p.g. to about 25 m.p.g., I can calculate that air density is decreased by about 14.0% (from about 1.16 kg/m^3 to about 0.998 kg/m^3). Again, unless I receive a huge outcry demanding the details of the mathematics involved, I'll only outline the process and give the results.



Plugging these density results into the drag equation and realizing that I want to minimize fuel/distance (gallons per mile) = energy/distance = work/distance = force * distance/distance = force, I merely need to determine when drag using the decreased density behind the truck but an increased speed exceeds drag at normal density and 55 m.p.h. As it turns out, that speed is a little over 59 m.p.h. So if I have to go faster than 59 m.p.h. to draft a truck, I will lose fuel efficiency compared to driving 55 m.p.h. in the clear.



Thus, the battle becomes one of finding a truck with all the characteristics listed above AND that is not going faster than 59 m.p.h. This has turned out to be extremely difficult. As I refine my data, I'll revisit these figures.

5 comments:

maastrichtian said...

Full disclosure: I found your blog while (exhaustively - it took quite a while to come across this hidden gem) researching a used LR3 SE V8, which I subsequently bought. When I read this post, I didn't think much of it, because as you accurately state most of trucks (particularly true here in Texas) drive 70+ mph, and I tend to frump along in the right hand lane at around 55-60 mph, eyes glued to the mpg readout. My first few tanks were in the 14-16 mpg range. After thinking about it a while I came to a realization: there aren't any trucks on my commute (happens to be a toll road). On a couple of unplanned trips home during lunch I took a shorter route (via Interstate Highways) that is more congested during rush hour and discovered an endless array of trucks from which to choose for drafting experimentation. However, I did have to accelerate to 70 mph on average. *Assuming* the mpg gauge is accurate (it seems to be consistenly one mpg too high), I got about 21 mpg over some 50 miles (a few days' data).

Bouyed by this discovery, I have since started taking the more congested route, and even with bumper to bumper traffic, the occasional sprints behind a semi (even at 70 mph) have me averaging 19.3 mpg, a massive improvement. Drafting at 70, my LR3 reads 19-23 mpg (varies with hilliness).
So my point is: your calculations are interesting but do you have the empirical data for drafting at 70 mph to show that 55 mph in isolation is more efficient? My (very preliminary, qualitative and statistically insignificant) experience suggests that drag is the single greatest influence on fuel efficiency (at least at speeds greater than 45 mph, in our particular cars), completely dwarfing all other factors. An ancillary observation is that in order to maximize fuel economy, I should optimize the "truckiness" of a given route, with average traffic velocity (too slow or too fast) as a relatively meaningless (with some limits, of course) quantity. One final question: Is drafting behind, say a Prius, a good idea? Seems like any reduction in drag is a good idea. I've gotten similar results with minivans, pickups, and I *think* pretty much any car. I would expect decreased drafting effectiveness with decreasing cross-sectional area for a given model (but non-zero). You may have addressed this already...

King of the Road said...

Hi,

No, I haven't measured the fuel economy drafting and not drafting at various speeds. I had the information on the portion of my resistance attributable to aerodynamic drag from previous calculations and measurements. Since the mileage at 55 m.p.h. was a function of drag and the various rolling resistances, and rolling resistance wouldn't change (at least not significantly) from drafting, I focused on drag.

Since the frontal area, Cd, and v were the same, the only thing changing would be p, density (should be "rho" but I don't have Greek characters). That enabled me to calculate the reduction in air density drafting at that distance. I then used the equation and the various known values to determine what speed at the reduced pressure would give the same drag as 55 m.p.h. at normal pressure.

I will concede that it's not a well-designed experiment and is subject to many sources of error, some of them major. But it's the best I could do. It's very difficult (as mentioned in the post) to find a truck fitting my drafting criteria. Based on your information, I may have to do some more thorough experimentation with tighter controls.

King of the Road said...

To continue, I agree with your intuition that drafting behind any vehicle is helpful. I am sure the bigger the cross sectional area and the closer you can draft, the better will be your result. And I suspect the effect diminishes more quickly with increasing drafting distance for smaller vehicles.

I wish I had a wind tunnel. The Wright brothers built a small one (and the Mythbusters used a small one), perhaps I can do the same.

Anonymous said...

I would like to know your qualafications or even background and more about the methods to your experiments. I am a retired engineer that worked almost forty years in the bowels of General Motors-advanced vehicle development and have to say some of your findings are quit different than the data we have discovered-not to,in any way say negative comments or rude muses, but I would be interested -thank you-Michael

King of the Road said...

Hi Michael,

For qualifications - not much. I possess a B.S. in mathematics; where I graduated, the "S" in place of an "A" basically means taking six quarters of physics in lieu of three (I think). My profession is in the materials testing and inspection segment of the construction industry.

The data in this post came only from reading streaming data on miles per gallon on a Scan Gauge 2 with multiple runs over the same stretch of freeway in "drafting" and "not drafting" conditions. As I mentioned, the sources of error are manifest and the controls not so tight. Maastrichtian, in the comments, indicates that the numbers may be wrong, but they are reasonably close to those developed by the Mythbusters in their "Big Rig Myths" episode.

I'd be extremely interested in any information you might have on the data you and your fellow engineers at GM discovered.

Thanks for reading and commenting!