About Coastdown Testing
Wednesday, August 25, 2010 at 06:40PMThe engineering department at Edison2 is pleased about the informed and civilized discussion on car efficiency that we see on our blog. A constant strand in the discussion is: where does the crossover come between rolling resistance and aero drag?
The procedure used by the automotive industry to determine resistance to motion is the coastdown. There’s an SAE standard for how to do this but, broadly, the car is either driven, pushed or pulled up to a certain speed, usually a little over 70mph, after which it is put into neutral (or released) and coasts until the speed drops below 10mph. Speed and distance during this are recorded very accurately by special purpose instrumentation. Some checks and balances are applied to make sure the results are good: it’s done multiple times in both directions on a straight road to make sure the data is consistent and to cancel out the effects of wind and gradient. Analysis of the recorded speed and distance information yields the car’s drag “fingerprint”.
Although it’s obvious that the car’s speed will decay as it coasts, this does not happen at a constant rate because of multiple different components of the total resistance to motion. The drag that causes the car to slow down fits very precisely an equation of the form
In the equation, drag is in pounds and x is speed in miles per hour. The equation’s A term is a constant value representing static drag: it takes this much to make the car move at all and this drag is always present regardless of the car’s speed. The B term changes linearly with speed and is best thought of as mechanical drag, such as bearing friction. The C term is aero drag and it varies with the square of speed.
Thousands of these tests have been carried out over the years and there is vast accumulated experience showing that a car’s total resistance to motion very closely follows the simple three term equation. In fact, this method and analysis are so well accepted that A, B and C numbers for many current cars are available on the epa.gov website.
The Very Light Car’s A, B and C numbers are 6.31, 0.1862 and 0.00433 respectively. Plotted on a graph against speed, they look like this:
Inspection shows the static drag figure dominates at low speed. Static drag is in large part due to tire deflection caused by car weight and consequently the Very Light Car does extremely well. From numbers Edison2 obtained from the EPA, the corresponding figure for a 2 wheel drive Escalade is 33.61, more than 6 times as much.
The B value, mechanical drag, is similarly low because of the very careful attention we gave the VLC’s mechanical design. The corresponding Escalade figure is 1.0442, more than 5 times as much as ours.
Aero drag (the C term) becomes important above about 40mph and above about 70 it is higher than static and rolling drag combined. That this only happens at such a high speed is testament to the extremely slippery shape devised by Barnaby Wainfan.
It’s interesting that at about 40 mph, static, mechanical and aero drag are close to equal. Even with our particularly light and efficient car, if aero drag were zero, at 40mph there would only be about a 30% reduction in power required and therefore fuel consumption. Low aero drag is important, of course, but so is mechanical efficiency. The VLC has them all.
We would like to emphasize that these numbers are not guesses, estimates, projections or simulations. They are measurements taken in accordance with a recognized SAE standard by experienced and competent people. Edison2 was told by the test facility (Chrysler Proving Grounds, Chelsea, MI) these are the best numbers they have ever seen, by far.
In these measurements are the key to getting acceptable range from an electric car. We’ll be writing more about that in a future post.
Reader Comments (60)
Greetings,
I have a question, based on my very limited and amateur experience with coastdown testing: how is rolling resistance (B) measured, and is it a separate test from the aero coastdown test? Are there 3 separate tests? I understand that the coastdown test generates data that determines the aero drag, and as I understand it, the rolling resistance has to be known in order to get the aero.
Also, since the VLC was measured in the GM wind tunnel, how did that Cd jibe with this one?
Sincerely, Neil
Thank you Edison 2 for that detailed information with real evidence and numbers. You are doing the right thing, and that kind of candor is rare and appreciated.
If I'm remembering my high-school physics correctly, terms A & B are probably proportional to vehicle weight, yes?
That would imply that adding batteries to a VLC would significantly increase power required at low speed - not just for acceleration (which is obvious enough), but to an almost equal extent for cruising (which was a lot less obvious to me at least).
Thanks for posting this info for us techies! In my prior guesstimates I had entirely forgotten the viscous (Bx) component, making my estimates inaccurate. I'm still having a little difficulty making all the numbers reconcile, however. Here are some details of my current state:
1. If I use 800 lbs weight (can you confirm weight ?) the rolling resistance coefficient becomes .0079 (about halfway between my prior estimate and JCBriggs').
2. The rolling and viscous components are equal at approx. 35MPH, with Aero passing both by about 40MPH (not 60MPH as you said).
3. The Aero force seems to have a problem in that when I use a Cd of 0.16, the frontal area needed to match the stated drag forces is 1.0 square meters, which seems much too small. I'm guessing the VLC frontal area is more like 2.0 meter^2. Can you provide us the frontal area used for the Cd calculation?
4. If the frontal area is indeed about 2.0 square meters and the Cd=0.16, then the "C" parameter would be twice = .00866 Can you please check this out...to help reconcile things? This would mean that the aerodynamic drag force is actually about twice what is shown on the chart vs. speed.
thanks!
Kevin
Static drag is definitely relative to vehicle weight. The heavier a ball is, the less distance it will roll, versus a lighter ball, with still the same volume, rolled at the same release speed, would roll farther as it relates to static drag. Mechanical drag also deals with other things, one of the most important is rolling resistance, which can be a product of weight assuming you were to use equal types of bearings, wheel and tire dimensions, etc. At least in this way you could show that the weight alone contributes heavily to rolling resistance. I hope you liked the pun. Yes, batteries and lightness are currently mutually exclusive. I hope that Edison 2 does consider designing the electric VLC, if one ever could exist anyway, with adding solar power on the top part of the body. It would at least help on the range or climate control.
It's amazing that a four seated car is getting less than 70 lbs of drag at 100 mph!
68.23 by my approximate calculation.
Edison2 appreciates the thoughtful comments we see here. Our eyes have been opened many times in the course of the Very Light Car project and we're still learning every day. We'll write a follow-up post on coastdown testing and post it here soon.
The mechanical drag, so to speak, is surprisingly high for running unloaded. All it has to do is stir up a little lubricating oil and otherwise it should be free wheeling. As Kevin noted, this is a viscous load, but I am thinking that viscous load transferred through gears gets magnified, otherwise how could it be this high? Perhaps the gearing is not so efficient as we might have thought.
Now what does this mean where there is a real load carried by the drive train? If gear friction is this much for almost no load, it must be a lot more for real loads. But that can not be measured in coast down, and only can be captured in dynamometer testing; but there it can not be separated from engine losses.
Have been waiting for the day when an automobile makes the wheel worth turning. I think it's finally arrived in the Edison2. I had driven nearly every muscle, luxury and exotic car built beginning with my 1957 Chevy (283), limited edition 1969 Road Runner (440 6-pac), and finally settling for the comfort and superb handling of a 1969 Rover-200 TC.
Although the 1985 Mercedes 300 SD (5 cylinder Diesel), gave me the best mileage for the money, I wasn't comfortable with the overall box like feel of the car. Several of the very small English cars of the 60s were great on gas but made me feel like I had no protection if even a Volkswagen rammed me.
If what I saw, (briefly), in the tubular construction of the Edison2 frame, is based on the same principals and will be incorporated in the actual car, I would like to place my order for one now. I've never lost a bet in my life and I am confident that the Edison2 is the absolute future of automobiles.
By the way...if you guys can do this with the automobile - you can do it with trucks, trains and boats.
Congratulations and best wishes all around.
Jim Bullis and Edison2:
I agree with Jim that the B parameter (viscous drag) seems way too high. Also, I can't seem to reconcile the C parameter with the stated Cd of 0.16. In fact, it's off by
I've been thinking about the A+Bx+Cx^2 model for coastdown. Although I've never done coastdown modeling myself, the physics <should be> pretty simple. Also, I've always seen coast-down data which shows parameters A & C (for rolling friction and aero drag), but B is not there.
After thinking about it for awhile - I think I can venture a guess: First (of course) the parameters are just curve-fit to the coastdown velocity vs. speed. The B parameter is for viscous friction, which will be a combination of bearing friction (with grease), transmission / differential loss (with oil), and my new thought - maybe it includes the SKIN FRICTION component of aero drag (which varies directly with velocity, not velocity squared). Normally, only the FORM drag (proportional to velocity squared) is considered and skin drag is insignificant and ignored....but maybe because the Edison2 car has such good aero design (and low weight) that the Skin Friction becomes a significant fraction of the total ?
If this guess is true...then 2 facts emerge: A) viscous bearing friction and skin friction are lumped together, and you can't really separate the two except with other tests. B) the meaning of "Cd" kind-of falls apart. Assuming the Skin Friction is the dominant factor of parameter B, the Aero drag at a given speed is the sum of Bx + Cx^2, where X is speed. To normalize back to an equivalent Cd, it would have to be stated at a specific speed, and the Cd would be reverse-calculated to give the same Form Drag at that speed. This "effective Cd" would vary with speed. Also, of course, the frontal area needs to be known...which I'm thinking should be between 1.6 and 1.9 square meters.
To add to my confusion - I checked out the EPA database, and found some of the data for various cars. Some of the models actually have NEGATIVE numbers for parameter B. This seems physically impossible, so....I guess there must be something fundamental I'm missing, or possibly the EPA's methods aren't very accurate ?
Edison2 - can you help explain ? How was the Cd of 0.16 calculated, and what is the frontal area ? (and does the frontal area include the rear wheel pods too, or not ?). Sorry for all the questions - but I thought I was doing so well in understanding everything, and now...not so much !
One last thought is that the viscous drag (parameter B) really CAN'T be all bearing+gear loss. At high speed (80-100MPH) this would represent a staggering amount of heat that would fry the components that were generating this drag. That's what led me to think that the Skin friction must be the main component of this, and being aero drag - doesn't heat up the car (just the environment).
Anyone else know about this stuff, or have different thoughts ?
cheers,
Kevin
Sorry - small typo. for my last message, I meant to say of the calculated Cd that I can't get it to reconcile, and it seems off by nearly 2X.
Kevin,
I agree that this is all quite unclear.
I think your explanation of the curve fitting is valid. I was under the impression that drive trains would be disconnected for the coast down testing, but that seems not to have been the case. But how do you suppose they handled the electric drive cars? It seems like the coast down should have been done with the drive trains disconnected if they wanted to know the aero drag. The drive train effects will be measured at the dyno test stage, I think, quite well. The validity of Xprize judging continues to be a big question. (And they got $12 million to educate kids about car efficiency?)
On the skin friction issue, I think this is handled by the Reynolds number, and that the Cd is not a constant as we tend to oversimplify it. I am away from home so can not review, but my old book by Rouse and Howe, 1960 or so, shows graphically how the Cd varies with Reynolds number which is a function of velocity and length of the body forms that they display there.
Even when I took Fluids under Prof Howe long ago, I found the transition from physics to this world of fluids to be not at all 'seamless'. After much discussion, Prof. Howe always concluded that accuracy of analysis was poor and that the only real way to know the answer was to do a measurement.
To see real data you might like to get your teeth into the reports at the NASA reports server, and speifically look at the 1934 paper by Freeman, on measurements of the USS Akron, ZRS-4. I think I show that on my web site (miastrada.com). Note that they formulate drag coefficient on a volume basis in that paper.
I look forward to the more detailed explanation by edison2 on this.
OK...after work today I had some "spreadsheet fun". I modified the spreadsheet which originated with John C Briggs (and I had previously modified to attempt to reconcile the Aptera data) - and I changed the drag data to match the coastdown data. I believe that my "theory" about the viscous parameter B being mainly aero skin friction is correct, and also my theory about the "equivalent" Cd being reverse-calculated from the SUM of the viscous aero skin drag plus the aero form drag at a given speed seems to be correct.
Here are the results...which I'd love Edison2 to validate: At 60-65 MPH, the "effective" reverse-calculated Cd is 0.16, using a frontal area of 1.70 square meters (Edison2 - can you confirm ?). The calculated Cd, however, changes with speed - by 30 MPH the Cd has risen to 0.23. If I try to calculate Cd using ONLY parameter C (speed squared component = form drag), the Cd number would be 0.09, which is clearly unrealistically low.
At 65MPH, the MPG pencils-out to approx. 133 MPG if the mechanical efficiency is 95% and the engine's overall thermal efficiency is 30%. This figure of 30% is only a guess (a BSFC of approx. 0.45 lb/hp-hr), but is probably pretty close. It is notable that this is "good", but not exceptional. Modern turbodiesels from VW and Audi reportedly have up-to 40% thermal efficiency (BSFC=0.34 lb/hp-hr, which could create ~30% higher MPG if there were such an engine in the size needed for the XPrize competition, which there apparently was not). Therefore, my interest in a turbo-diesel Edison2 car remains high - it could get ~170 MPG on the highway !
I also calculated drag forces and made graphs of a number of car models from the EPA database, for comparison. I picked the Lotus Elise, Ford Focus, Corvette and Mazda RX-8. While parameter A was really good (better than any other), and B was good (but others matched or even beat it) - it is of course parameter C (the aero form drag) that blows everyone away and is most important at speeds over 40 MPH. The net result is exceptional, of course, with a total drag figure of less than 40% of these other models (which are pretty good). I was surprised at how good the Ford Focus fared...at highway speeds it had equal or better drag than these other cars.
Lastly, while none of these cars had "negative parameter B's", a number of cars did: the Chrysler Crossfire and Pontiac Solstice, BMW Z4 and Ferrari F141 and Porsche Turbo. My best theory of how parameter B can be negative is that at higher speeds, the flow transitions to more turbulent - creating less viscous (laminar) flow over the body. Seems reasonable in hindsight - but strange !
Anyway - I'd love Edison2 / Barnaby to confirm that my thinking and calculations are correct. Truly a great accomplishment.
Kevin
Kevin,
The number I have from Oliver is 1.7082 square meters.
Neil
Oh, and the Cd measured by the "old" method is 0.145, and measured by the new SAE method is 0.161.
Neil
Neil,
Thanks! These numbers confirm that my calculations see to be right on the money.
Everything is now making sense to me. The only result that is a bit surprising / disappointing is that the engine efficiency is a bit lower than what I would have guessed (but still is good). I guess this fact further clarifies the point that the amazing results of Edison2 come mainly from the low drag, and low weight - and there is still room for improvement with a more efficient engine.
By the way - my BSFC numbers are not for E85 fuel....they are for gasoline "equivalent".
cheers,
Kevin
An electric motor is a *lot* more efficient! ;-) And yes, the batteries weigh more -- but the electric cars at the X-Prize *on average* beat the ICE powered cars 134MPGe to 83MPGe; despite the weight of the batteries.
Sorry -- that is off topic (on this thread anyway).
Sincerely, Neil
I am currently campaigning against the Pickens plan to convert 18 wheelers to natural gas as a fuel instead of diesel. Though this is a political issue as well as an energy issue, I think the people here will understand that I think natural gas should be reserved for better uses.
Running 18 wheelers on natural gas might not be such a good idea. It certainly should be cheaper at today's prices, and even a fair amount of infrastructure cost could be absorbed in the difference between the cost of natural gas and diesel fuel per BTU. And it might help some with CO2. However, this would be a significant added use of natural gas which would drive the price of that fossil fuel up. That would drive up the price point at which reserves are calculated, and more natural gas would be developed. So far so good.
But now we should think about how a higher price of natural gas would impact electrical power generation. This would likely make the shift from coal a lot more difficult. Perhaps Pickens is content to keep coal as the backbone of US electrical power generation.
And the numbers do not work out well for the economy if we try to shift to natural gas, even as prices stand now.
One clear fact is that use of natural gas to run trucks or to run electrical power plants is a low grade use of this most desirable of our fuels. We would accomplish more if we simply converted clothes dryers, ovens, and even refrigerators and air conditioners to direct use of natural gas to make the heat that would run these appliances. This would eliminate the heat engine in the process, and thus stop the massive energy throw away that happens in all known heat engines.
A more complex way to get full benefit from natural gas would be in co-generation systems, where waste heat was used for some real purpose. This can not happen with trucks and neither can it happen with large central power plants that are mindlessly located far from places where the heat can be used. And by the way, these mindless arrangements are perpetuated by the enhanced power transmission infrastructure that we are so proud of building.
Neil
The only reason the electric cars beat the ICE cars is that the electric cars are given a factor of three cheat factor because the MPGe definition as used by Xprize officials does not include the heat engine that is required to produce the electricity.
Neil,
You really need to read through prior statements by me, Jim and others in earlier Edison2 BLOG entries to understand the issues around the distorted way the XPrize folks set the rules. The kindest way I can say it is that MPGe (for electrics) and MPG (for fuel burning cars) are apples and oranges. The XPrize folks biased their methods giving BEV's a 1.7X to 2.4X energy advantage, depending on exactly how you handle the comparison (not quite the 3X that Jim mentions...but he is basically correct). So...if we use a 2X average distortion (primarily because power plants are about 50% thermally efficient), then the adjusted comparison you mention would be 134/2=67MPGe vs. 83MPG. The electrics actually used more energy and produced more CO2 - in short, they actually LOST. This is why the XPrize rules allow BEV's to have CO2 emissions (at the power plant) of 200 grams/mile, while fuel burning cars have a limit if 116. I'm not anti BEV's, but I am against people who use distortions to promote their hidden agendas. Telling the truth is ALWAYS the best practice, in my opinion.
We should embrace electric cars for the reasons that are valid (there are quite a few), but saving energy and producing less CO2 are not among them (until the power grid gets off of fossil fuels). This is why I fear that while EV's are overall a good thing, they distract our attention, dollars, and resources away from more pressing energy needs - of which the top 2 should be: A) Get powerplants off of fossil fuels (happening, but not fast enough) and B) Reduce / eliminate CO2 emissions before we further destabilize the world's climate. Lastly, as I keep saying - there are other, more practical ways of acheiving these goals without a wholesale changeover to electric cars.
Kevin
Hi Jim,
If you include full source-to-wheels for ALL the energy type, then the electricity still has the big advantage. The X-Prize did the right thing. Gasoline doesn't just materialize out of thin air, and electricity has to be generated somewhere. They measured what was in the control of the car designer, and that was the correct thing to measure.
The fact that electricity *can* come from many different sources is it greatest strength. Just imagine: if you get your electricity from a renewable source, then you can waste it if you want to.
Lets face it: electric drivetrains are 70-90% efficient, and ICE drive trains are 10-38% efficient -- at peak. Factor in the difficultly of keeping an ICE at peak efficiency (i.e. using a transmission) vs the virtually flat efficiency of an electric motor, and the answer is obvious.
Sincerely, Neil