189 comments on Fuel Economy Factors - Part 1: The Role of Aerodynamic "Drag"
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189 comments on Fuel Economy Factors - Part 1: The Role of Aerodynamic "Drag"
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Will (and Nate),
As a one time student in Aero & Astro, I would like to point out something which might be a small problem in your presentation.
You defined the area used in the drag equation as being the frontal area of the vehicle. Then, you presented a list of Cd values for different bodies, including aircraft wings. In aircraft design, the area usually used for wings is the surface or plan area, not the frontal area. That's because the corresponding variable of interest, lift, is a function of the wing area. And, for wings, lift and drag are measured or calculated as a function of angle of attack, since the lift increases with greater angle of attack. Please check your numbers to be sure that they are indeed intended for frontal area, not plan area.
About 25 years ago, I built a high mileage project vehicle. I used a small 100cc motorcycle and added a complete fairing around it. I tested it on the freeway at a steady 55 mph and achieved 235 mpg. I also found that it was very sensitive to cross winds, as might be expected, since it was rather like a vertical wing and had a vertical tail for aerodynamic stability. It was quite thrilling to ride while being passed by a dump truck, as the "bow wave" from the boxy truck tended to push the bike around quite a bit. Others have built similar vehicles over the years and there was a contest to test the various designs under simulated road conditions on a closed track. Back in 1985, the best design achieved 470 mpg...
Also of note is the fact that the lowest drag coefficients are the result of good aerodynamics at the rear of the vehicle. That's why hatch back coups do better than the vehicles with sharp cutoff rear ends, such as one sees in vans and SUVs. There is no way which I am aware of to reduce the drag on the rear of a van or SUV, since the gentle curves which reduce drag result in long aft bodies, which won't work on these larger vehicles.
E. Swanson
You are correct, lift and drag calculations for wings are treated differently, as those two factors are closely related to efficient aircraft design. On ground vehicles, lift is not sought (indeed, is discouraged), so the overall aerodynamic drag is the key variable, and virtually all ground-based vehicles use cross sectional area in their Cd calculations (trains and other articulated vehicles use a more complex set of calculations referenced above).
In reference to your link, I've had a number of discussions with Craig Vetter, who is in the middle of another design effort to create a high-mpg motorcycle/scooter fairing.
I agree with your assessment of aerodynamics at the rear of the vehicle (see image above). Indeed, even the air traveling under the vehicle needs to be considered in the overall streamlining design effort.
Also of importance, aerodynamic stability is another area of concern, as the drag on the rear of a typical car tends to stabilize the vehicle. Man powered vehicles don't (usually) go fast enough to produce much of a problem, but cars like the VW 1 Liter might prove to be a problem if the rear were fully faired. A design which works at 55 mph might go unstable at 75 or 80, which are now common speeds on the freeway. My first design resulted in unstable oscillations at around 45 mph, which I addressed by adding a vertical stabilizer on the rear. On a motorcycle, the drag on the rider's back provides some stability, IMHO. And, as you note, cross winds can be a problem as well.
So, all you kids out there playing in the garage, don't try this at home until you have your design checked by someone who understands aerodynamics...
E. Swanson
Yet another reason that we need to reduce highway speeds.
I expect that when fuel becomes very scarce and expensive that speeds will be lowered both by statue and by drivers themselves.
Fuel has not yet been expensive enough here in the states to make it good strategy to just slow down.The fuel savings are less than the increased expenses involved in paying commercial drivers to work longer hours(or drive by the mile at lower speeds)and the need for more trucks.
A few old fogeys drive thier personal vehicles at less than the normal speed to cut thier fuel costs but not many.If gas gets to ten bucks that will change.
And if the economy keeps going down hill, truck drivers will probably be glad to drive slower in exchange for a fuel savings bonus- something not yet common but not unheard of either.The shortage of trucks will take care of itself if there's nothing much to haul.
Something that has intrigued me is the possibility of adding some sort of airbags to existing trucks that could be inflated once up to speed out on the highway-they would have to be very tough and strongly attached and designed or customized probably for each individual truck model, but once inflated they might cut drag considerably.I have seen this idea batted around in various magagazines and on the net for a long time.
Might this be cost effective in the near future?
A little off topic but does anyone know how well current hybrids such as the Prius work in mountianous country?
Another somewhat off topic-if somebody builds one of these superstreamlined bikes and powers it with a really good three or four horsepower diesel(I'm not such such an engine exists commercially yet)it could maintain a good speed , probably thirty five or forty up a long grade with a heavy rider.
How many mpg would such a motorcycle get at a steady forty or forty five mph?
A job change a few years back took me from a bikeable job location to one that is 30 miles away in a bike-hostile 'job center' area with no reasonably safe approach for bikes. Carpooling now, whenever there are only 2 people, I drive my 2 seater Honda Insight at 55mph on a three lane 65mph toll road where people normally drive 75mph. When the oil price shock occurred last year, I started noticing people pulling up behind me in a recognition of 'hypermiling' at a more reasonable speed. I would often end up at the end of the toll road with 20 cars behind me, much like a caravan. When prices began dropping, the line grew gradually smaller; now there are rarely times when cars line up behind me.
If I stick to no more than 55mph, I can achieve mpg readings in the high 70s to mid 80s. At 65-70mph, it drops to the low 60s to high 50s.
On the topic of motorcycles with full wrap-around fairings and smaller engines, see the link E. Swanson posted above to Craig Vetter's motorcycle mileage competition in the 80s. Note the care taken with streamlining on the results achieved.
Will,
Are you getting this super mileage by driving technique only or have you made some modifications to your car? Thanks!
Driving technique alone. When I say no more than 55 mph, sometimes that means I dip down to 53-54. I don't do anything fancy, like turning the car on and off, and there is usually no one to draft behind at that speed.
Using low-rolling resistance tires also help.
John Taylor and his wife recently completed a 48-state drive averaging
67.9 miles per US gallon in a 2009 VW Jetta TDI.
http://www.nytimes.com/2009/09/13/automobiles/13MILEAGE.html?no_intersti...
Yes, my car came with low rolling resistance tires, and that will be part of the next article.
I was talking with someone in TDIClub about them, and he was telling me that the low rolling resistance tires were quite expensive. The question was whether using those tires would save enough $$ in fuel to pay for the tires or not. I think the conclusion was that it probably would, but it wasn't clear cut.
Maybe those tires have come down in price since then however..
My tires are Bridgestone Potenza RE92, which are not expensive (though that can be a relative term).
How do you like their ride?
Are there any compromises in terms of safety?
They are more than adequate in wet/dry traction; snow is not their strong point.
My take on them is it's probably not worth it to replace new tires, but the price differential if you are replacing a set anyway is minimal and will definitely pay off.
550 lbs at 30 mph on a 6% grade would eat 2.64 hp from the vertical rise. That's neglecting drag and friction.
2.64 HP is correct.
Assuming a diesel density of 0.835 kg/litre, a heating value of 42.5 MJ/kg and a 30% efficiency for a small diesel engine (normally aspirated) this means:
about 170.6 miles per US gallon (from the vertical rise only) [72.5 km/litre]
If the efficiency is 35%, then:
199 miles per US gallon [84.6 km/litre]
OLDFARMERMAC,
The Indian manufacturer BAJAJ makes a 125cc motorcycle that can attain up to
86 km on 1 litre of gasoline (202 miles per US gallon!)
The engine is a 4-stroke, 1-cylinder type with 2 spark plugs.
http://www.bdmautomotos.com/noticiasview.asp?key=22
A couple of years ago I dropped my highway speed on the commute from 80 (like everyone else) to the speed limit, 65. I noticed two things. First, was that driving was far less stressful, and second, was that my gas mileage went up by 10%.
Using the assumption that drag is the square of speed (I thought it was the cube) you cut drag by 33% but only improved mileage by 10%. Apparently factors other than drag have a greater effect on mileage. Some have claimed that mileage actually gets worse at speeds below 45 mph due to these other factors. Since the average vehicle speed is less than 40 mph perhaps too much emphasis is put on aerodynamics.
Drag is the square of speed.
POWER is the cube of speed.
Going at 65 means about 34% less drag (from air) FORCE than going at 80 MPH.
And, going at 65 means 46% less POWER (from air drag) than going at 80 MPH.
Power = Force X Speed
Gasoline engines operate with higher efficiencies at moderate RPM's and significant LOAD.
Below 45 MPH, very little power is needed to maintain speed, therefore
the LOAD on the engine is very low, and the gasoline engine operates with poor efficiency.
"if somebody builds one of these superstreamlined bikes and powers it with a really good three or four horsepower diesel(I'm not such such an engine exists commercially yet)it could maintain a good speed , probably thirty five or forty up a long grade with a heavy rider."
OLDFARMERMAC,
The original VW 1-litre prototype is powered by a 8.5 HP naturally aspirated diesel engine.
It could attain 264 miles per US gallon (0.89 litre per 100km)
The weight of that vehicle is just 290 kg (639 lbs)
http://www.seriouswheels.com/cars/top-vw-1-liter-car.htm
I don't know about diesel engines, but good low horsepower gasoline engines do not exist commercially. My school's supermilage racer gets 700 mpg (basically a recumbent trike in a fairing), but the winner of the last Shell EcoMarathon (Americas) got 2400 mpg with essentially the same design, but with a better engine. Both engines were running on normal gasoline.
Assuming 200 kg mass, a CdA of .15 and a speed of 45 mph, and a grade of around 15 degrees to the horizontal, I got 2 kw as the required amount of power. If you assume 2.5 kW once rolling resistance and transmission losses are factored in, I estimate 170 mpg under those conditions. That's with 25% thermal efficiency in the engine, I have no idea if that is possible with a small diesel or not.
I just zipped over the "hill" to San Francisco from Reno and back in my 2005 Prius.
(Hymotion pack thought it needed replacement, no more 75-99+ mpg on local drives and its switch LED was blinking at me).
While the engine strains going up out of Truckee to the pass, I can keep up with pretty much anyone who's not speeding too much.
Mileage drops of course, on the serious uphills at 65 going on 70 (by accident of course;-), I only get 15-20 mpg.
The nice part is once over the summit, it's 55+ mpg total from Reno to Sacramento (even with a dead Hymotion pack - which would have been used up halfway to Truckee anyway.)
Coming back uphill is only 45 or 50 mpg (Sacratomato elev. 25 feet, Donner Summit Eastbound 7227', Reno 4500 or so.)
Trips to Incline or Virginia City (winding roads) are speed limited by the curves, not the grades.
Not as peppy as the old Saab turbo to accelerate while at speed, but not an embarrassment.
Nice to have the engine brake at times, often going down from Donner Pass into Truckee with traffic I'll want to keep the speed down and the stock battery gets fully recharged fast, then I'd have to rely on the brakes really touching, so just shift into "B".
The Prius has been to Colorado (Vail) twice, once via (soon to be)Glacier(-less) National Park, several times to Oregon (Bend/Mt. Bachelor, then on to Portland), Flagstaff, San Diego via Palm Springs, etc. Jevons Paradox I guess, 71K miles on a 4 year old car, with a work commute of 7 miles one-way.
Only issue is in snow - clearance is very low, so I wouldn't try un-plowed snow deeper than about 5-6 inches. For this, I have a diesel Ford F-350 4WD, with about 2000 miles in 2 years, that has never been farther than the local ski areas or Lovelock, NV (90 miles East of Reno).
If you don't mind using control surfaces, you can add a yaw damper for stability. There are ways to use air-driven gyroscopes to provide the yaw-rate indication. It may also be reasonable to have feedback from the steering angle to help fight gusts.
That drag stabilizing effect is important. I experienced it in a place you might not expect. Back in the late 80s early 90s carbide saw tips became cheap and everyone got in the game with new designs. One outfit made great efforts to reduce the drag the tailing part of the circular saw blade had as it reentered the cut. It was noticebly easier to push that blade through material but there was problem. It was almost impossible to make a straight cut with it. A certain level of blade drag ended up being necessary, or at least way to expensive to design a way around. With our current sprawl, the range of speeds vehicles will have to operate in for some time to come will probably necessitate more drag being left in the designs than many would like.
I've met Jim Corning at a local alternative vehicle expo. He's working on a fully faired motorcycle too.
http://prometheussolar.com/Motorcycle.aspx
Mr. Corning does a good job of laying out how simple (and economical) it is to replace gasoline as a transportation fuel. This is why predictions of $500 oil and other various doomer scenarios are so absurd.
RE; Rear Drag..
I've been toying with the possibility of getting myself a Small Pickup Truck to convert to Electric as my local working and errand vehicle, and wondered if I would get an advantage out of making a Bed-cover that sloped in a positive curve down from the Cab roof and then Duck-tailed out beyond the tailgate, removing those two flat turbulence areas.
It would be able to lift up to become a level roof when the load demanded it, but for many trips, could very probably remain down and tight. (and if fortune was smiling on me, this roof would also be laced with PV panels, for a little steady income, tho' I know this wouldn't amount to more than nickels in the truck's power demands)
Yeah, I thought of something like that too when I bought my PU 11 years ago. I never got around to it, especially as my most often use fo the truck was for hauling lumber or sheet rock to build my house. One can easily cut the drag quite a bit by simply leaving the tail gate down...
In another job situation, I worked on the aerodynamics of rail cars, specifically the open hopper cars often used to haul coal. With those, the end bulkhead in each car is a drag generator when running empty. Put a top on the cars and the drag is cut considerably. Going on 18 years later, the RR's still don't do that. Now, think of how much diesel fuel has been wasted since on all the unit trains with 100 cars that returned to the mines empty. Gotta love economics...
E. Swanson
I've decided to use a trailer in those situations where I need extra carrying capacity. I've also planned out a purchase of a bike trailer for those loads which could be moved by bike.
One of our city councilors rides around town with a trailer like that one, little sparkles of hope out there.
'A dozen or so points of light'...
.. and I just voted for him again, having also seen him on the street as I walked my daughter to school earlier. Boy, it's nice being on foot.. I had two or three small exchanges with neighbors in our 3 block trek.
Craig Kelley! I voted for him too--largely on the basis of his and his wife's cool bike trailers and extenders and so on.
Good to know that there are TWO such councilors... but
Nope, this is Dave Marshall, Portland Maine.
____
BTW, I'm running in and out of the yard today, taking loads of CompostMulch and Bricks to/from the Community garden, a block away, hauling everything on the Halloween Bike/Wheelbarrow float that I assembled last weekend. Hard working wheels!
Essentially, it's that 'Ox Cart', I guess. So my costume is now an 'OX'. Lorelei will be pleased.
Don't want to sound too silly, and I don't know if Mythbusters is a valid data source here :p, but wasn't there this Mythbusters episode where they tested when a truck drove more fuel efficient: tailgate down or up?
Their result was that the tailgate up was more fuel efficient and they explained it because the tailgate would cause a 'horizontal vortex' in the loading area that directed most of the air coming over the roof to the rear of the vehicle smoothly. And in a followup episode they found out that a mesh covering the loading area was the most efficient over tailgate up/down, hardcover or mesh.
Mythbusters also tried the golfball dimples idea on what looked like a Ford Taurus and improved mileage by 11%.
Time to get out the hammer and a blunt nail.
Of all the experiments I don't want to envision explaining to my wife..
a good hailstorm would do the trick. :-)
Dimples work by creating turbulence which adds energy to the boundary layer and helps it stay attached to the surface. Vortex generators are used to do the same thing. There are ways to make vortex generators which could be attached with magnets or something like spirit gum. You might try it.
Too bad they used two trucks side by side one with tailgate up and the other down. They never bothered to switch modes or drivers making the results very suspect.
I've heard that claim about the MythBusters test before. I haven't seen the episode (not having a TV hooked up), but I suspect that the test involved a large PU with an engine sized for hauling lots of mass. In that situation, the engine probably is producing rather little power, thus is running at a low efficiency. In that situation, increasing the drag will also increase the efficiency, which might offset the benefit of any reduction in aerodynamic drag. If the test had been run with a smaller truck using a straight shift transmission, the results of the drag reduction might have been more apparent. Or, if the MythBuster crew had used diesel trucks, the effects of load change would have been reduced, which might have produced different results.
It's clear to me that there is less drag with the tail gate in the down position. An easy way to prove that is to do a test coasting down a long hill on a freeway, such as one might find in the mountains. By putting the transmission in neutral or holding the clutch in, the vehicle speed will reach terminal velocity, which is a function of overall drag. If the slope of the hill is just right, that might be just below the speed limit. Perform the test both with the tailgate up and with it down.
For my older, smaller Mazda/Ford Ranger with the 7 foot bed, running with the tail gate down results in a faster terminal velocity. I've also noticed that when driving up such a long grade, I can stay in high gear longer with the tail gate down than with it up, which also indicates less drag. Do your own test...
E. Swanson
A couple decades ago I built a wooden tool box for a 1988 full size bed regular cab Chevy pickup. The design was accidental, in as much as materials at hand and tools needing shelter were the most important factors. That year GM put the shelf support in the bed so the tool box was elevated. I tilted its lid forward for drainage away from its rear facing tailgate styled door. The 4 foot front to back and just under 5 and half foot wide box roof tilted about 1 1/2 inches forward from bed level, extended forward to about an inch from the cab rear window the high rear edge of it was about the height of the center of the same window. I drove that truck for 188,000 miles and ran the same trips repeatedly both with the box on and off, depending on what load would have to be hauled one way or the other. For years I kept an accurate mileage log. It ended up that on the same 200 plus mile trip I consistently got 21 to 22 mpg with the box on and never exceeded 20 mpg without the box in either tailgate on or off configurations (though the latter was rare--I had a truck because I hauled stuff and the tailgate up or down generally facilitated that quite a bit). This was highway speed mileage and 68-72 mph with the box was often the best. I always thought it would be interesting to see just what location of a plane like my box roof would give the best performance at given speeds. That old chev was 4.3 litre vortec V6 with a 5 speed w/OD standard transmission and relatively mild standard 1/2 ton pickup rear end (the automatic trany rear end was steeper).
REAR-MOUNTED AERODYNAMIC STRUCTURE FOR TRUCK CARGO BODIES
http://www.wipo.int/pctdb/en/wo.jsp?WO=2008144025
http://www.faqs.org/patents/app/20080309122
Here's another link to a tractor trailer truck drag reduction project:
http://people.clarkson.edu/~visser/research/drag/truck/index.html
This device is a set of rigid vertical panels and flexible top and bottom panels. The vertical panels were hinged so that they could fold flat against the open doors during loading and unloading.
Prof. Visser and his students (undergraduate and a few graduate students) have found that it's relatively easy to knock 10% of the drag with a simple aft body extension that fits within the legal length restrictions for such devices. Filling the gap between the cab and trailer is another way to pick up a quick 5 to 10% drag reduction.
That goes back to NASA work in the 70's; I wrote a piece on it a few years ago, which I was unable to get published.
One of the more interesting issues is that decreasing the aerodynamic drag at the front of the vehicle increases the losses due to base drag at the tail (not just relatively but absolutely), so the fairing of the rear of the vehicle becomes even more important. I suspect that active surfaces (blown with air or engine exhaust) could not only reduce drag further, they could be used to stabilize the vehicle against gusts and sway.