Just wondering. I thought about Googling it, as Page & Brin are very good buddies of mine, but I decided I’d rather spark a conversation instead.
So why DOES mileage get so much worse at higher speeds? Anyone?
Note that the power needed to push an object through a fluid increases as the cube of the velocity. A car cruising on a highway at 50 mph (80 km/h) may require only 10 horsepower (7.5 kW) to overcome air drag, but that same car at 100 mph (160 km/h) requires 80 hp (60 kW). With a doubling of speed the drag (force) quadruples per the formula. Exerting four times the force over a fixed distance produces four times as much work. At twice the speed the work (resulting in displacement over a fixed distance) is done twice as fast. Since power is the rate of doing work, four times the work done in half the time requires eight times the power.
Yes, as Zomby says, the power spent on air resistance goes up as the cube of the speed, but the miles/gallon goes up as the square (since you add miles faster). Thus the gallons per mile needed to overcome air resistance doubles between 50 mph and 71 mph.
I would suggest playing with this app in its free DOS revision to learn about vehicle physics.
There’s a feature that shows you where power goes in different vehicles at different speeds
Efficiency also varies with engine speed. I know people that claim they get better millage in fourth gear than fifth. So at some point, engine efficiency starts going down adding to the air resistance problem.
Without the Hot Air has a excellent discussion of this point.
http://www.inference.phy.cam.ac.uk/withouthotair/cA/page_254.shtml
There are some cars that actually get better mileage on the highway than in the city, but I still think the best mileage is still under 65MPH.
That is not to say you couldn’t design a car with the best mileage over 65MPH, but it would probably suck at lower speeds.
65 mph was chosen pretty arbitrarily. But two months of experimentation with my Volvo convince me that I get better mileage on the freeway than taking city streets, so long as I turn on the cruise control and set it to about 60. I drove to and from work on city streets, taking the same route each time and obeying the speed limit; then, in August, took the freeway and, as implied above, stayed at 60 as much as possible. I kept a record of my mileage and it was much better on the highway.
Peak MPG comes from a driving style that will probably get you pulled over for obstructing traffic or suspicion of DUI.
Howto:
Get on interstate
Put car in right lane
Set cruise at or about 35-45 MPH depending on your particular vehicle
Don’t actually do that.
Any time you have to stop or start, you’re wasting gas. That’s why city driving is so bad for gas mileage.
The reason I designate the 40 MPH range as ideal is that’s above where your fans and accessories are no longer using half of your power, and at the same time below the point where wind resistance becomes a serious issue.
On edit:
Also, I charted out my MPG at 55 vs 65 in one of my previous cars, using a Scangauge. 65 was between 15 and 20% less efficient than 55.
I do that, except the cruise is at about 60. Not only would the 35-45 mph get me ticketed, but it would make my commute unacceptably long.
To sum up, there are two reasons why MPG goes down at high speeds.
- Wind resistance/air drag/whatever you want to call it. Drag goes up quickly as you go faster, so MPG starts dropping dramatically at higher speeds.
- Internal combustion engines (gas, diesel) are most efficient at a certain power. Changing gears helps of course, but for most cars the engines are still losing efficiency at high speeds.
But MPG also goes down in city driving:
- Stopping wastes energy. Every time you stop, you have to accelerate back up again, and that uses gas.
- As in point 2 above, engines are not that efficient at slow speeds, either.
- Finally, there’s some overhead in running a car – the various sensors, computers, radio, etc. – which is basically constant. At slower speeds, the overhead cost per mile is higher, so efficiency per mile is lower.
For most cars, somewhere around 40 MPH is probably maximum efficiency.
I think most cars’ performance envelopes are optimized for highway speeds (55-65 MPH) and give the best mileage at that speed. The best fuel economy for a given gear is at RPMs at the point of maximum torque (IIRC). I think this generally occurs in the OD gear at around 60 MPH. I have a hard time believing that someone would get better mileage in 4th at highway speeds than OD (5th). It would be true at lower speeds but a car with an automatic transmission would be in 4th at lower speeds anyway.
For air drag alone this is true, but air drag is not the only source of drag. There is also driveline friction and rolling resistance, which increase linearly with speed. Engine internal friction goes up with speed and load, but pumping losses (due to sucking air past a mostly-closed throttle plate) decrease at higher load, so that the total energy wasted on friction+pumping remains fairly constant.
Cars do tend to get better fuel economy at 50 than at 71, but they don’t get double the fuel economy. My car can get about 30 MPG at 70; cruising steadily at 50 (in sixth gear), I might see 40-45 mpg.
This is why the reaction to the oil crisis in the 70’s was a national 55mph limit. (remember that?) It was supposed to save a huge amount of oil.
Hybrids like the Prius make their mark by recapturing the braking energy with a generator, and using it to assist in acceleration; so stop and go traffic is almost as efficient as highway driving, and the engine runs usually at a pretty constant speed feeding the batteries as well as a CVT, instead of revving up and down with accelerator pedal. Plus when the electric motor assists acceleration, you don’t need as big a gas engine as most cars to get decent acceleration - just a bit more than enough to maintain cruising speed.
20 years ago or so, I drove a Ford Festiva (not Fiesta, Festiva). Please don’t laugh.
On highway trips, if I nailed the needle to 55 and didn’t go over, the silly thing got 50-52 mpg on the whole tank – even though part of the tankful was used for city driving. So it might have gotten even higher mileage just strictly on the highway part.
It was a fuel-efficient car, but I’m sure self control with my speed was a big part of scoring that mileage.
Nowadays I see car advertisements touting their 35 mpg cars as fuel-efficient high technology and I wonder what happened. If I could get 50 mpg 20 years ago I ought to be able to do better now.
I hesitate to post this, as I don’t deal well with hoots of derisive laughter. But I’ve noticed that my Prius gets about the same mileage at 50 or 65mph, with or without the AC on, averaging about 53mpg. I’m assuming this is because of the info in your post.
I want to make sure I get this right:
The effect of air drag on fuel consumption goes up at the square of the speed for a given distance?
As in, not taking into account engine efficiency: If you want to travel 10 miles at 50mph and it takes you 1 gallon, travelling 10 miles at 100mph will take you 2 gallons? Or is it 4?
Or, to put it another way:
If I want to shoot a bullet at 1000 fps and this requires 5 grains of powder, shooting it at 2000 fps will require 10 grains of powder or 20?
First of all, the US government changed the fuel economy test back in 2007, to one that has higher speeds, harder acceleration, and actually turns on the AC for part of the test. Checking FuelEconomy.gov, the estimated MPG under the new test for a 1990 Ford Festiva would be 30 city / 37 highway in the manual version, and 27 city / 30 highway for the automatic.
A modern Ford Fiesta is rated at 29/38 for the automatic, and 28/37 for the manual (yes, the auto is better than the stick). The modern Fiesta also has adds about a thousand pounds worth of crumple zones and other safety equipment on it.
aerodynamic drag force (and therefore energy requirement per unit distance) is proportional to the square of speed.
If aerodynamic drag were the only energy sink involved, yes, traveling a given distance at twice the speed will consume four times as much energy. Note that because you are traveling that given distance in half the time, that additionally doubles the power requirement from the engine: to travel at twice the speed requires 8 times as much power from the engine. This is why you can cruise at 60 MPH with about 16 horsepower (yes, your engine really is loafing at cruise), but the Bugatti Veyron requires an incredible 1000+ horsepower to achieve 250 MPH.
Assuming no difference in the efficiency with which the powder’s energy is imparted to the bullet, the answer is 20. The reality is that with the same length of barrel, more powder means a greater percentage is wasted as muzzle blast - so you’ll need a lot more powder.
The energy per unit time goes as cube of speed. So your gas consumption rate goes from 5 gallons per hour to 40 gallons per hour. But your travel times goes down, so the miles per gallon only goes up as square of speed (i.e. 1 mpg to 4 mpg).
20, but not for the same reason. Here you’re talking about accelerating a bullet to a given initial speed. When we’re talking about the fuel efficiency of a car, we’re talking about the energy needed to sustain a given speed. That is, a speed at which the engine power output is equal to air resistance.
It might have made a significant difference, if everybody did all their driving on the highway. But if your city MPG is 10, and your highway MPG jumps from 20 to 25, but you do 2/3 of your driving in the city, then your net MPG only goes from 13.3 to 15. Woot.