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My driver's education teacher back in high school said 55 MPH is optimal for gas mileage of a passenger car. Just last week, I read an article in a magazine saying 60 MPH is optimal. These numbers are pretty close, so there's some validity in the statement. What's the physics explanation for this 55-60 MPH sweet spot?

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Lets say there is a speed at which the airdrag starts to increase much faster due to turbulence and other non-linear airflow effects, but this potential sweet spot might be masked by a high minimal consumption of the engine at that certain RPM, so in some cars your "sweet spot" will be a "sweet almost flat line". Just an observation, not an answer :) – BjornW Jul 28 '11 at 8:26
    
""but this potential sweet spot might be masked by a high minimal consumption of the engine at that certain RPM"" Right, but having this minimum consumption at that rpm which corresponds to that 55 mph in a certain gear, is not by chance. The primary thing is the air drag laws, I suppose. At least for USA, where those 55 mph are the cruising speed on highways, and this in turn rules the selection of gear ratios and torque curves. – Georg Jul 28 '11 at 10:47
    
I've had cars that had sweet-spots (by which I mean local maxima in fuel efficiency) at 57, 64, 72, 83, and (if my spousal unit is to be believed about the Grand Marque) 93 MPH. All judged in a very rough way by noting (1) places the cruise control "likes" and (2) computing gas millage over ~200 mile stretches on overland drives. – dmckee Jul 28 '11 at 12:42
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"These numbers are pretty close, so there's some validity in the statement." - Nothing about two sources making a similar claim without evidence lends any credibility to that claim. – Wayne Burkett Jul 28 '11 at 17:31
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Then I should rephrase the question into why those two sources chose those particular numbers and why they are so close together. – JoJo Jul 28 '11 at 23:29
up vote 10 down vote accepted

Although this is an engineering question it's one that I've had great interest in the specific values myself. Wikipedia does an alright job with the question.

ORNL fuel economy

Looking a little bit deeper into it, this seems to be ripped from some Oak Ridge National Lab report, which as been taken down, but is still on the wayback machine. In fact, a lot of the Wikipedia article looks like a copy of this.

Funny, the report references a website that sounds like it has all the credibility in the world, fueleconomy.gov. They give the following image:

fueleconomy.gov

There are a couple of things to conclude with here. I am much more tempted to believe the first graph here. The reason is because cars have gears, because of that fact, I expect jumps in the fuel economy as a function of speed. In fact, a faithful technical report should really give different curves for each gear IMO. The second graph is probably smoothing things out from a larger collection of data to make it seem easy for the rest of us.

Either way, the claim that everyone driving 55 would be better for the environment seems to have technical merit behind it, even though we don't like the fact. One of the comments says they found sweet spots at a number of different speeds, going up to 90 something, this is almost certainly wrong. There may be hope for newer cars than what is represented here, however, and in particular some new designs with streamlined shapes may one day justify driving 80 mph to save gas. We can dream.

Electric cars - better data

I was at a loss to explain very well where the efficiency losses at low speed comes from in an internal combustion engine (ICE), so I thought that an informative comparison would be to look at electric cars. It so happens that Tesla Motors made a post about their cars that would be HUGE utility to a physics class. Fuel use rate for an ICE must involve measurements of tiny flow or average data over a long trip, but electric cars have very accessible direct measurements of current available. Firstly, let's look at the energy per mile used - the analog to gas mileage.

Wh/mile for Tesla Roadster

The most efficient speed for electric cars is closer to 15-20 mph versus 55 mph for ordinary cars. This is because the losses at low speeds for ordinary cars has to do with the construction and inefficiency of the gas ICE.

Directly to the question at hand - they also give the sources of losses over the range of speeds. This graph directly answers the question better than anything else I have seen. Of course, only for electric cars.

losses

  • aerodynamic losses increase with increasing speed to possibly 3rd power, see other answers
  • tire losses are from rolling drag, tire air pressure has a lot to do with this
  • drivetrain include motor and gearbox type stuff
  • ancillary losses include electrical loads like the AC and radio, if they are constant power demands, then the power per mile demanded will decrease inversely with speed
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""One of the comments says they found sweet spots at a number of different speeds, going up to 90 something, this is almost certainly wrong."" Before You make such wrong statements, learn about the difference between local and absolut extrema! – Georg Jul 29 '11 at 14:44
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@Georg But the actual form of the function is harry anyway! Any claim that someone was rigorous enough to correctly identify a local local extrema through records during a trip is bull. The ORNL data itself doesn't have enough detail to correctly list those, in addition to the fact that beyond 60 almost all cars monotonically decrease in gas mileage. – Alan Rominger Jul 29 '11 at 14:56
    
Similar: usna.edu/Users/physics/schneide/Buick.htm – Alan Rominger Jun 7 '12 at 21:29

It's really an engineering question. Cars are designed for efficiency nowadays; especially in Europe the taxes are directly related to the MPG ratings on standardized test cycles. But even in the US, there are standard test cycles for fuel effiency. Those test cycles typically have large segments driven at ~55 mph.

Now an engineer that's optimizing for fuel efficiency has to make tradeoffs. Adding more gear ratios can improve engine efficiency, but increases costs. His marketing department really doesn't ask for efficiency at 75 mph; that buys them nothing. So there's generally little commercial need for a 6th gear to optimize fuel efficiency at those speeds (You do see 6th gears more commonly on German cars - no speed limit there)

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""Cars are designed for efficiency nowadays; especially in Europe the taxes are directly related to the MPG ratings on standardized test cycles."" In which European countries is this done? – Georg Jul 29 '11 at 14:35
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The engineering trade offs is, in a sense, the real answer. Aerodynamics explains why a maximum efficiency exists, but the design and engineering are what put it at 55mph, as opposed to 45mph or 65mph. – Jay Kominek Jul 29 '11 at 17:58
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@Georg - That must be the CO2 tax that if the car emits less than 120g/km it is a "green car", and I guess that those cars must drive a specified speed when they measure. – Johan Jul 29 '11 at 18:58
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@Johan: The EU has it's own test cycle; it's not based on a single speed. In theory, that avoids gaming the system. In practice, the standard cEU ycle features very low accelerations, and modern ECU's can be tuned specifically for this. – MSalters Aug 1 '11 at 8:02

There are two things to consider.

  1. The amount of energy required to maintain constant speed. This starts at a low value and increases. Energy rate can be measured in Watts (power) and it is proportional to $v^3$. $$ P = F_{drag}\,v $$

  2. The amount of fuel supply needed to make the above energy rate. This is called the break specific fuel consumption (BSFC) and it varies widely with the % throttle applied and the engine rpm (and thus gear). An engine is typically at it's best efficiency near full thottle at mid low rpms (like 80% thottle with 4500 rpm). Incidentally, peak torque rpm usually corresponds the best BSFC area. With low throttle the air intake is restricted and you have pumping losses (it takes more energy to suck the air into the pistons). Engine friction increases with speed and combustion efficiency varies with flame temperarure and volumetric efficiency. Also at low speeds the combustion suffers and thus you cannot maintain low speeds at high gears. Remember though that the lower speeds increase travel time and there is limit on the minimum fuel per hour used, as travel times increase so is the total fuel used for a trip.

Obviously engineers target their designs to perform well during the EPA mandated duty cycles. To get the best miles per gallon you need a car with a small engine (low friction) that can operate near full throttle at low rpms, with very high gearing. On the other hand if you have a Corvette what you want to do accelerate full throttle to like 120mph and then coast down (no throttle) to 30 mph and then repeat the cycle.

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I like what you wrote in general, but it has to be said that drag isn't the only force. That fact that it scales roughly with $v^3$ is a very meaningful observation. – Alan Rominger Jul 29 '11 at 17:04
    
@Zass.. Yes, the drag term does only include the aerodynamic drag, but also the rolling resistance, driveline friction and other terms. Maybe I should re-name it to resistance force. – ja72 Jul 29 '11 at 19:40

Above the optimal speed, fuel consumption increases because air drag increases very quickly, so it takes more energy to "carve out" a tunnel through the air.

Below the optimal speed, the consumption increases because a car engine will burn fuel even when idle - there's some fuel spent just to keep the engine turning, and when you go slowly, this effect starts to become important.

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I have a Zuma 125 4 stroke gas motor scooter, and performed a lot of fuel efficiency tests during the last month. It had 8.98 hp @ 7500 rpms, and uses a CVT automatic transmission. I tested it on a backroad, with many different speeds and conditions.
I drove 28.3 miles per test, starting with a full tank, and then measured how much fuel was used after the 28.3 mile trip. I have photos of the odometer and fuel use readings. In my tests, I rode 20 mph, 30 mph, 40 mph and 50 mph. I also did a 45 mph test (sorry, I know I should have tested it at 40 or 50 mph) while tucked down to reduce aerodynamic drag. I also added some homemade fairing aerodynamic work, and tested the mpg difference.

Results: Without aerodynamic mods: 75 mpg @ 45 mph.

With aerodynamic mods: 216 mpg @ 20 mph. 135 mpg @ 30 mph. 106 mpg @ 40 mph. 85 mpg @ 50 mph.

Aerodynamic mods and tucked down: 110 mpg @ 45 mph.

I have the atmospheric conditions recorded for every test if anyone is interested. I was riding on a hilly and curvy road. No brakes were used during any of the tests, because no brakes were necessary. I minimized acceleration to be as gentle as possible, and there were no stops during any of the tests.

After analyzing the results, I realized that the mpg was declining linearly in relation to speed... And the gallons used per mile were increasing linearly proportional to the speed. If you are interested, please check the numbers... I was very interested and excited to see that the fuel consumption rate (gals/hr) was almost exactly proportional to speed squared, at any speed between 20 and 50 mph. I promise these tests were performed with pure scientific dedication, and are conclusive. No dumb errors were made :) . So as far as 4 stroke gasoline motor scooters with CVT transmissions go, I think the evidence is clear that the optimum speed is considerably less than 55 mph... The results show mpg consistently improving with reduced speed, even as low as 20 mph. But most interestingly, the mpg goes down linearly with speeds between 20 and 50 mph!

I understand the aerodynamics and rolling resistance very well, and have a general understanding of the mechanical systems... but I don't know why the mpg was inversely proportional to speed with a linear relationship. If anyone else has any idea why, please tell me. I know the aerodynamic drag increases with speed^2, and rolling resistance doesn't increase with speed at all... Why would mpg decrease linearly?

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