The purpose of this experiment is to determine your vehicle's drag coefficient Cd and coefficient of rolling resistance Crr. This is done by measuring your vehicle's speed as a function of time while coasting in neutral.
Why would you want to know Cd and Crr for your vehicle? Well, suppose you're interested in modifying your vehicle for improved fuel efficiency. You might consider modifications such as air dams, wheel skirts, removing mirrors, switching to low rolling resistance tires, etc. Cd and Crr offer a quantitative method of comparing vehicle performance before and after these types of modifications to see if you made any improvement.
For other experiments you can do on your car see my website IWillTry.org.
Why would you want to know Cd and Crr for your vehicle? Well, suppose you're interested in modifying your vehicle for improved fuel efficiency. You might consider modifications such as air dams, wheel skirts, removing mirrors, switching to low rolling resistance tires, etc. Cd and Crr offer a quantitative method of comparing vehicle performance before and after these types of modifications to see if you made any improvement.
For other experiments you can do on your car see my website IWillTry.org.
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Signing UpStep 1: Equipment
You will need the following equipment:
- a vehicle (and someone with a driver's license)
- a clock or stopwatch
- a pen and paper (and someone other than the driver to record data)
- a flashlight (driving at night avoids traffic)
- a long stretch of flat road with little traffic or wind
- Excel or another spreadsheet application. I prefer OpenOffice Calc because I like to support open source software, but its Solver function does not handle non-linear systems (yet) so you'll have adjust input variables manually by an iterative process to fit your model to the data (it's not too hard).
- The spreadsheet I created to analyze the results. Download here: Drag_Coefficient.xls
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My biggest challenge is estimating the rolling resistance of my tires. I wish I had been able to do a test before making the mods, to calibrate things, because I know the "factory" Cd.
Oh, and if you take a frontal photograph with a reasonably long (telephoto) lens, with a measuring tape that is readable at the high point of the roof, you can insert it into a CAD program (I used DataCAD) and then trace the outline, for a pretty accurate frontal area. I included the side view mirrors, even though i believe these are excluded from the "factory" number. (One of my mods is to replace the mirrors with video cameras.)
Sincerely, Neil
http://www.mayfco.com/geo.htm
http://www.evconvert.com/tools/evcalc/ (This calculator is not accurate)
Wikipedia Geo Metro has dimensions
So I put the correct area in your Excel file and it gave me a Cd of .47 and Crr .010. So it seems to me like there is a mistake here. I also found a PDF that shows equations for what you are doing, maybe it will help:
http://physics.technion.ac.il/~rutman/car/Roll-down%20test.pdf
However, I believe there IS a mistake in one of the underlying assumptions: that the force of rolling resistance is constant independent of V. The rolling resistance measured in a coast down test includes a component from viscous forces (drivetrain) which vary with V. Vehicles are also designed with negative lift (so they get pressed into the road at higher speeds for improved handling) so there is also a component of force from rolling resistance that varies with V2.
The model assumes the drag force is related only to V2 and the force of rolling and drivetrain resistance is constant. The reality is that the force of rolling and drivetrain resistance is also related to V2 and V.
So a better model of the force on a moving vehicle would be:
F = iV2 + jV + k where i, j, and k are constants.
A curve based on that model will much more closely match actual coast down data. But after solving for i, j and k, there is no way to extract meaningful Cd and Crr values since they are part of a completely different model that assumes i is affected only by Cd, and j is always 0, neither of which appear to be true.
To illustrate the point, if you do a coast down test while holding your doors open (which should affect only Cd and not Crr) you'll find that the indicated Crr changes too. That is a clear indication that the model itself is lacking. For this reason I don't advise relying on Cd or Crr values calculated from coast down data. If you really want an accurate Cd value you need to eliminate rolling resistance and viscous forces from the test (think wind tunnel). But by the same token, knowing an accurate Cd value isn't particularly useful. It will allow you to calculate the force on your car in a wind tunnel but it won't allow you to accurately calculate the force on your vehicle on the road.
If you want to compare the performance of a vehicle before/after making mods, the change in coast down time itself is MUCH more meaningful than any change in Cd or Crr extracted from the coast down data.
It may be that the viscous force proportional to V is small, but there may still be a component of the force of rolling resistance that is proportional to V2 due to negative lift at high speeds. This should result in an overestimate of Cd and an underestimate of Crr which seems to be the case (the Cd spec for this vehicle is supposed to be around 0.36)
It would be useful to compare the rolling resistance calculated to that measured by inclined plane as you suggested, or by pulling the vehicle at constant speed (a walking pace) with a spring scale on level ground.
But you can get pretty good results without matching the whole curve. Rearranging the formula for drag and rolling resistance gives
M*a = -Crr*M*g -Cd*A*0.5*rho*V2
You can look at a 1 second interval near 60 MPH and another 1 second interval near 30 MPH. Using your VSS data you can calculate "V" and "a" in each case. Everything else is known except Cd and Crr. You will have two equations (one for 60MPH and one for 30MPH) and two unknowns (Cd and Crr). Use basic algebra to solve for Cd and Crr in terms of known values.
dv/(v2 + K12) = K2dt
where K1 and K2 are constants:
K1 = sqrt(2mgCrr/(rhoACd)), and
K2 = -0.5rhoACd/m
This was integrated over v from v0 to v and over t from 0 to t. The result was:
arc tan(v/K1) = K1K2t + arc tan(v0/K1)
The assumption of values for Cd and Crr, establishes K1 and K2. Then, plotting arc tan(v/K1) versus time should produce a straight line with slope K1K2 and zero intercept arc tan(v0/K1). The least squares fit will produce estimates of slope and intercept which can be used to calculate K1 and K2. We have thus created an iterative process which should converge upon an estimate of K1 and K2. The definitions of K1 and K2 can be then used to establish the corresponding estimate of Cd and Crr. By rearranging those definitions,
Cd = -2mK2/(rhoA) , and
Crr = -K12K2/g.
I modified your Excel spreadsheet accordingly. Using your data, the process converged upon
Cd = 0.3902 and Crr = 0.01079 .
Then I used a guessing approach like yours to find the coefficients resulting in minimum error in the least squares fit. The results were:
Cd = 0.4261 and Crr = 0.01022 .
These differ slightly from your results:
Cd = 0.3697 and Crr = 0.01057 .
I don't know which is the best estimate of the coefficients. It's hard to argue with iterative convergence though. Maybe they are close enough to each other that it doesn't matter.
The modified Excel spreadsheet is available to anyone. I wrote it using manual iteration, since I don't know how to do recursive programming in the Excel language. (It's easy in other languages.) Also, I have a Word document that may make the above a little clearer. I'm a little restrained by the format capabilities here.
In any case, since posting this instructable, I've come to the realization that the assumed model, despite its wide acceptance is a poor one. See update I just added to the end of the instructable. Therefore I don't have much faith in the values generated by this spreadsheet except as extreme approximations.
Overinflating vs. safety:
The main consideration is the footprint of the tire. The footprint is the amount of rubber in contact with the asphalt. It is the flattened bottom of the tire as it sits on the asphalt.
Why is the footprint so important? When force is exerted on the pavement to change the car's motion--when you hit the brakes, for example -- the force must be transmitted through the footprint to the tires and to the mass of the car. Obviously, if the footprint is partly ice, the car will go sliding when you hit the brakes or otherwise try to accelerate (in the physics sense of "change its inertia") it.
Consider the car sitting on the pavement. Its footprint is a certain size, in square meters. Consider the car driving on the pavement at 70 km/hr. The axle is moving forward at 70 km/hr.
The bottom of the tire is rolling on the pavement. Therefore its speed relative to the pavement is zero km/hr. (If it had speed relavative to the pavement, it would be skidding and would leave black rubber on the pavement. ) The tire is spinning so very, very fast to make this speed of zero on its bottom possible. So the speed of the tires' footprints is still zero km/hr.
Hence, so long as the tire air pressure hasn't changed, and the car's weight hasn't changed, then the tires' footprints are EXACTLY the same size as
they were with the car sitting at rest.
I think you can see that the larger the tires' footprints are:
(1) the easier it is to accelerate the car (e.g. braking to a stop) without something breaking
(2) the greater the car's coefficient of rolling resistance
(3) the less shear force each square cm of tire will have to bear when subjecting your car to a given acceleration (again, in the physics sense of changing your car's velocity)
The larger the area in contact with the pavement, the safer the car will be, at the expense of fuel efficiency.
Now the relevant question is, as you change the air pressure in the tires, does the tire's footprint change significantly, or does it remain about the same?
I don't know the answer. I think it would probably depend on the particular tire. However, using the principle I stated above, it would be EASY to test
whether or not the tire footprint changes with tire air pressure.
First equalize the air pressure in all four tires and measure it with a tire pressure gauge. Record the air pressure.
Get a big piece of cardboard, like a cardboard box from a refrigerator, and a can of spray paint and a Sharpie marker. (You can get cardboard for free from any retail distributor or from neighbors.) Park the car so its tires rest on the cardboard. Lie down on the cardboard with your spray paint. Spray the cardboard completely around each tire. Then move the car forward and trace the outline with your Sharpie. Mark the four outlines with #1 to signify your first air-pressure test.
When the paint dries, you're ready for your second test. Change the air pressure in your tires--either inflate it to higher pressure or let some air out. Record the air pressure. Then flip the cardboard over and repeat the test.
You can check as many different pressures as you want to see if the tire footprint changes size with air pressure--until one of your tires bursts, hahaha!
A simple proof: Suppose the coefficient of friction is 0.8 (typical of rubber on concrete). Let's compare a 1x1 inch square of rubber with 100 lb of weight evenly distributed on it to a 10x10 inch square of rubber with 100 lb of weight evenly distributed on it. In the first case, each square inch of rubber supports 100lb so each square inch can tolerate a shear force of 0.8*100=80lb before slipping. Multiplying this by the number of square inches (1) gives a maximum total shear force of 80lb. In the second case each square inch only supports 1lb, so each square inch can tolerate a shear force of 0.8*1=0.8lb before slipping. Multiplying this by the number of square inches (100) gives a maximum total shear force of 80lb. I say again... the size of the footprint makes no difference to the force that can be transmitted without slipping.
This assumes a constant coefficient of friction. However, surface conditions aren't always constant and there can be localized areas (ex patches of ice) where the coefficient of friction is lower. What matters is the average coefficient of friction over the entire footrpint. I agree a larger footprint is safer for inconsistent surface conditions. Clearly a 1x1" block of rubber will have more trouble dealing with a 2x2" patch of ice than will a 10x10" block of rubber assuming they are supporting the same load.
But under non-freezing conditions on asphalt roads the surface is relatively consistent and the size of your tire's footprint will have little effect on your stopping or accelerating ability. Here's a better test: Inflate your tires to maximum pressure, go to an empty parking lot and measure the distance it takes you to stop with wheels locked up. Deflate your tires to half the maximum pressure and repeat, noting whether your stopping distance changes.
kPa - PSI Converter
It may seem that it makes a difference and it does, but it can actually reduce traction since not all of the tire is meeting the road equally. What you are experiencing is a greater feel of when the tire is about to break traction, and the sidewall twisting between the tread and rim more. Your tire size has a lot to do with it.
It is better to learn how to brake properly (you'd be surprised that almost all drivers on the road don't know how to), than to try altering tire pressures to modify that. Resisting the impulse to slam on the pedal goes a long way to shortening stopping distance, as well as knowing when to let off.
I've measured coast down time's for my car ('92 Geo Metro) with windows open vs windows closed and at 32 PSI vs 45 PSI tire pressure and found there was hardly any difference with windows open vs closed, but there was a noticeable increase in coast down time at 42 PSI vs 32 PSI. This is for coast down from 70 km/h to 20km/h. At higher speeds I could imagine the windows having a more significant effect since drag force is proportional to velocity squared, while force due to rolling resistance is relatively constant, independent of speed. At city speeds, though, increasing tire pressure has a greater effect (at least for my car).
In any case, it doesn't matter much to me which has more effect. They both have an effect so I do both.
I expected my tires to wear more in the center but it simply hasn't happened. On further research, other hypermilers have reported similar experiences. See http://www.gassavers.org/showthread.php?t=6833. There is a photo on that page showing tire wear at 45 PSI after 2000km on brand new tires. The "molding bumps" show even wear.
1) To protect the rim from the road
2) To handle the immense weight on them with the durability to go long distances in less-than-ideal conditions.
Passenger car tires are built far differently...for one they are not regroovable and generally not designed to be re-capped. They are also not overbuilt for durability like commercial tires are. That durability includes overpressure, overweight, rough roads, and heavy side loads. Consumer-level car tires have to be built in a purpose-built lightweight design, and still offer some shock-absorption. If a consumer-grade tire blows-out, the vehicle still retains a great deal of controllability. If a long-hauler pulling doubles blows a front tire, the disaster makes news and nearly a day's worth of traffic hardships.
The sidewalls and treadwalls are not just thicker, but proportionally tougher for commercial vehicles because weight is less important than sheer armor to a plethora of potential abuse the tire may suffer. The rubber compound for commercial tires is much harder and has a higher threadcount for the structural ply, and because of this, they can handle more abuse.
You can take your chances by grossly over inflating your tires based on a trucker's trick, but this does not apply to passenger cars. There are far better ways to improve fuel efficiency, such as a K&M filter, increased exhaust flow with an oversize catylitic converter and a high-flow muffler, proper tuning and maintenance, buying a *quality* motor oil like Castrol, instead of the convenience-store brand, as well as intelligently matching OEM specs for oil viscosity with the actual wear on your engine.
First, I drove a 1981 Datsun 510 with a history of oil leakage. after solving the oil leak, I automatically regraded to 40W oil, contrary to the OEM spec of 30W, and gas mileage improved over 12% when used as a newspaper delivery vehicle on a fixed route (which made quantifying actual gas mileage rather easy), and a 7-10hp increase.
Then I drove a 1991 Nissan Sentra 2.0L SR20DE with the 4-spd gearbox. Base HP was 133bHp off the factory floor, with an estimated 28mpg by the EPA IIRC. After the catalytic converter suffered temperature shock from a "freeway lake", I simply patched it with a form that allowed moderate bypass, only when the muffler was being obstructive. With barely any tuning at all, it became a 155bHp 40MPG monster, and torque came out of it that would dust a V8 Cadillac STS 10 years and over 200,000 miles it's junior.
I might add that I would haul over 700lbs of newspapers (+250 GAVWR) and a gas-mileage loss was barely mentionable. Of course, I inflated the rear tires to maximum inflation to handle the load, but that had little to do with gas mileage. Properly tuning the engine, and letting it breathe properly, made more difference than any tire-inflation method could hold a candle to.
Finally, I used quality sport-grade tires. Try this with some cheap-o tires and you could find yourself in a world of hurt. I have raced enough cars for long enough to know what tire pressure means. Higher pressures can reduce your overall traction, besides putting you at risk for a blowout. There are far better ways to improve gas mileage and/or reduce drag than to risk a tire blowout. Try an airdam on the front and a corrective-spoiler on the rear of hatchbacks. Better still, buy a fastback or a sedan. Don't buy some american-made oil-burner like a Suburban and then complain about gas mileage, buy into efficient design and using your brain before you purchase a vehicle to see if it is really what you need.
Larger vehicles are not safer by any means, because the best way to keep from getting hurt in an accident is to avoid a collision in the first place. It starts with a lighter vehicle with better control, and continues with not talking on the cell-phone while you drive...some call it "paying attention and being responsible", and ends with getting a basic education into reality and realizing that automobiles are not magic, but actual machines, and Jesus is never your co-pilot with the way that you drive. Appreciate the machine more and you learn how to operate it better. This is why it is so much safer to fly than to drive....That, and it requires a proven IQ to get a pilot's license.
You go ahead and inflate your tires to dangerous levels that ompromise your actual control over the vehicle for the sake of a 0.1MPG increase, which will certainly be offset by the cost of replacing tires and possibly repair-work for accident damage. I'd rather inflate tires properly and look at the biggest loss of efficiency, the internal-combustion engine itself. I gained 12MPG simultaneously with an increase of 12 bHp with a simple exhaust-system mod. Perhaps tires aren't the best place to start to increase efficiency...
Just my thoughts on an observed science through my previous career. My previous experience and observational science should carry some validity, just as well as I respect your own. Finally, keep in mind that automatic transmissions suffer more "neutral" drag than a "stickshift" does, due to reliance on hydraulic resistance instead of mechanical opposition.
I'm not suggesting that exceeding recommended tire pressure is the only way to increase mileage, but it's certainly one of the easiest ways which does make it a good starting point for anyone willing to accept the risk (whatever they believe it may be). My experience is that the gains are much more than the 0.1 MPG you suggest and I question whether it compromises control or causes premature tire wear. The main compromise I've experienced is comfort.
In this article which I posted in another comment, Sergent Dave Storton, Director of the San Jose Police Academy, claims (among other things):
- Tires do not balloon at higher pressures. They keep their shape and wear evenly.
- Responsiveness improves at higher pressures.
- Risk of hydroplaning decreases at higher pressures.
- Significant cost savings result at higher pressures.
For these reasons in 1999 the San Jose Police Dept inflated all tires on their training fleet to 50 PSI (recommended maximum was 44). There is an image in that article of a stunt vehicle riding on two wheels with those same tires inflated to 100 PSI.I can see that you have a lot of experience, and I respect that. I simply don't agree with your conclusions. Nor do I expect you to agree with mine. So let's disagree and leave it at that.
Regards.
1) If tires do not change shape at higher pressures, then how would hydroplaning resistance be changed by above-normal inflation pressures? Those two facts simply contradict one another. Tires do "balloon" slightly even if the effect is not immediately apparent by visual inspection. Few police officers have any background in racing, where one of the first things a pit-crew needs to understand is the exact effects of a tire-pressure difference of as little as 0.5PSI.
2) By "responsiveness", it is referring to cornering response and the "quickness" of the tire with lateral loads. Most drivers do not put their tires under such duress where this is helpful. Higher pressures inherently make the lateral stiffness of any given tire increase. This is part of the reason why it is easier to slide a car on underinflated tires. Inflation pressures are one of many ways stunt-drivers in cinema gain a desired performance from a particular vehicle, such as an over-steering Camaro as opposed to it's normal understeering handling characteristic.
3) Police vehicles often use special safety-rims specifically designed for their purpose. You cannot buy these rims with your stock Crown-Vic. They also use "sport-grade" tires meant to handle speeds in excess of 150MPH, and they are expected to perform reliably to a Crown-Vic's top speed of 135MPH.
4) "Bicycling" a car requires specific tires and rims, and suspension reinforcement, just ask any vehicle-stunt coordinator. Inflation at 100 PSI is simply a farce, as even with racing tires, this would cause an immediate blowout, potentially killing the person inflating the tire to this pressure. Typical sidewall-ply construction has two plies of polyester, even on sport tires, which will shear at that pressure. It is more the fact that the sidewall plies will shear from the bead itself, rather than the sidewall bursting.
5) The site you mentioned (that I have read through) is not officially endorsed by law-enforcement or the DOT. It is more a fan-site if anything. It also mentions that they do not exceed the maximum inflation pressure for anything other than training vehicles (which are operated under closely-controlled conditions on a closed "skid-pad" course). As it clearly states, 44 PSI is the maximum inflation pressure of the tire and not exceeded by anything other than training vehicles. The "Interceptor" version of a Crown-Vic gains over 400 lbs with the engine/transmission package, rollbar, communications, and body reinforcement, necessitating pressures above stock factory standard. Training vehicles are intended to have expendable parts such as tires, and the lack of traction from such overinflated tires helps to get the feel of an apparent loss-of-control. This is why I endorse ice-rinks as a driving test so that people can really understand how a car reacts with severely limited traction. This ingrains the motions with the practice and makes a better driver overall. I agree with that as I had the rear tires of my front-wheel-drive delivery vehicle inflated to maximum to handle the 600-800lb load I was placing on the rear axle daily, and only because I was meeting the maximum load of the tires. If it were simply my personal car alone, standard pressure would suffice based on the typical load the tires would withstand, even if I had a little illegal fun now and then when noone was looking (a 4-wheel drift around an onramp hairpin is pretty impressive-looking, especially with a '91 Sentra). I can take anyone to school when I perform a drift spanning 1/4 mile on a straight street of icy roads, and demonstrate how I can drive without chains in icy conditions insurmountable by an AWD vehicle with a typical driver. It's not the vehicle, but the driver, and in the United States of American Emirates, driving skill is not endorsed or even recognised. This is why I got ticketed for defensive driving, which was later thrown out in court, despite how this is encouraged by the local PD's PR department.
6) If there was no effect of wear on overinflated tires, then where does this apparent myth (supplied with actual pictures) come from that overinflated tires wear down the middle? I suppose that the wear line found in any basic instruction of examining tire wear is based on a manufactured picture of the effects of overinflation? I gauge you smarter than that, I just think you might have read too much into the wrong information.
If you question tire-wear diagnosis, I invite you to view illustrations accepted by the entire industry as it relates to tires. If tires do not ballon at higher pressures, then this tire diagnosis is completely incorrect along with my actual experience and research done by the industry since day one.
I might also add that since the quoted tests were done with high-grade tires, inflating your $20 tires to 50PSI is only asking for trouble. If you don't know what an "A-car" is, or in cop-speak "a 4", you may soon find out. Maximum rated pressure is not simply a limit of manufacturer liability, it is often best heeded because that limit of liability has a good reason behind it.
Now, if we're talking about tires for motorcycles, mopeds, or even bicycles, where the tires are specifically designed to "balloon", then yes, maximum inflation pressure is usually my standard, as the last thing you want on a two-wheeler is sidewall flex. But radial tires meant for 4-wheel operation run on a completely different set of rules and operating conditions, being required to retain their shape without the benefit of loading based on centrifugal correction of the vehicle, or also the lack of a substantial lateral load (as with "balloon tires" on two-wheelers). Radial tires are expected to handle lateral loads by resisting "bead-roll", or the tire deflecting laterally under a lateral load. This can be clearly observed by taking a generic american car and forcing hard cornering on generic passenger tires. The astute observer will clearly see the tires attempting to roll of the rim on the front (with your typical american car), and the outside circle of the tire riding on the sidewall because the treadwall has failed to retain it's place.
Typical tires come with 3 steel belts....one on the centerline and one for each side of the tire. Depending on actual scale of the tire, some come with as many as 7 steel belts, which is why changing a rear tire for a Ferrari F-50 can cost upwards of $900, due to it's low-profile and relatively high pressure, but replacing a cop tire costs as little as $180.
If you don't believe that radials can change shape, observe a top-fuel drag race. Those tires are steel-belted, but go from 20" wide and 5" high to 8" wide and 10" high during a burnout. Steel belts are made to have stretch in any tire, to retain durability. In fact, steel belts in tires have inspired the construction of CVT belts in automotive CVT's due to the harsh conditions they must survive.
I will concede that I mixed up "hypermiler" with "high-miler" though. But I will end this by saying, that in my many years and over 3 million miles of driving experience, and enough racing-training and upbringing to know the effect of any tuning anywhere on a car, that ignoring maximum inflation pressure of a tire is inviting fate to hand you a Darwin award. It's fine if you decide to inflate to a tires maximum inflation, this is not unsafe....but exceeding that is risking the merciless hand of fate. Various tires have their various rating for one reason or another, and I strongly suggest that under no circumstances that anyone attempt to inflate their tires to beyond the nameplate limits. To do so is juggling fate with contempt, and highly ill-advised, as the odds always favor "the house"...and fate owns "the house" in life. Not odds you want to play with, as those who win the Darwin award often don't live to brag about it, as if anyone should be proud of getting it anyway.
I say that this project is subject to your own discretion, and performed at your own risk, holding noone accountable but yourself if anything goes wrong. As a professional, I'd advise against taking this verbatim, but it is your own risk you take in your hands. While well-founded, I dispute the safety of some of the suggested steps based on my experience. Exceeding the safe limits prescribed falls only on you, and at your own risk.