# Simple question about gas mileage

fdj1986
Maybe gas mileage isn't the right term. I was always told that you got further on a tank of gas driving faster as opposed to driving slow. Now obviously there are extremes at both ends where this wouldn't hold true. But from what I have been hearing lately this is not true.

Imagine a hypothetical situation, where you are driving on a road, no stops, no intersections, no other vehicles just you driving at a constant speed. Assume that you have 10 gallons of gas. If you drive 60MPH, will you not be further away from your starting point when you run out of gas than if you were just driving 20MPH? I assume that it really depends on what gear you are in and how efficient that is. Also I would assume that there are extremes, for example traveling at 90MPH or more would be detrimental to your gas efficiency, so would 5MPH. And driving at a constant rate will increase fuel efficiency, rather than starting and stopping. I am just wondering if generally, do you go further on a tank of gas at higher speeds than at lower speeds?

I really don't know where I picked up on this. I really think this is one I heard from my grandfather at one time and it just kind of stuck with me. I would just really like to know which side is true.

Thanks

Staff Emeritus
There is probably an optimum speed, and I would guess it is probably less than 60 mph. Unfortunately it is difficult to calculate from theory, you'd have to measure it.

What we can say from theory is that your automobile engine is very inefficient at low power outputs. So at low speeds, it is the inefficiency of your engine that is the concern.

At high speeds, frictional losses become more important. Rolling forces shouldn't vary that much, but the drag force is proportional to the square of the car's velocity (and the energy lost to friction is proportional to the velocity^3).

At some intermediate point, the optimum is reached, where the engine is running with a reasonable effiiency, and the drag forces are not yet too high.

Mentor
The analysis is not so simple, but a car has an optimal speed that maximizes fuel economy. This site gives a pretty good explanation: http://auto.howstuffworks.com/question477.htm

fdj1986
Thanks!

That article really helps. It kind of proves that what I was told was right, just that my window was a little too high. I always figured the upper end of the optimum speed was somewhere around 60 or 70. But its really probably between 40 and 60. I guess I am an extremist, whenever someone would say "if you drive slower you'll get better gas mileage" and that didn't seem to make sense, but I guess I was thinking slower mean 20 to 30MPH, when really they meant somewhere in that 40 to 60 range.

Thanks again.

Mentor
A simple rule of thumb is the lowest speed a car can easily hold on to in its top gear is the most efficient speed. For some cars, that may be 35, for others, it may be 55.

Gold Member
Staff Emeritus
Gold Member
Dave,
Interesting results. If you used your onboard computer to optain you gas consumption rate, it is possible that the computer ASSUMEs a linear relationship? Thus giving you a very nice graph, but based on questionable data.

Does your car actually meter gas comsuption?

Mentor
Along the same lines, have you compared the gas consumption/fuel economy over a full tank: fill-up to fill-up?

Staff Emeritus
Gold Member
Doc Al said:
The analysis is not so simple, but a car has an optimal speed that maximizes fuel economy. This site gives a pretty good explanation: http://auto.howstuffworks.com/question477.htm
Wasn't this the basis of setting highway speed limits at 55 mph back in the 70s during the gas crisis? That was my understanding, that 55 mph was chosen as the speed limit because it was supposed to be "optimal" for fuel conservation (or at least close to optimal for most cars).

Moonbear said:
Wasn't this the basis of setting highway speed limits at 55 mph back in the 70s during the gas crisis? That was my understanding, that 55 mph was chosen as the speed limit because it was supposed to be "optimal" for fuel conservation (or at least close to optimal for most cars).

Yes, I think so. But most cars today are so different than they were back then that I doubt the optimum speed (if such an average is even useful) is still at 55.

Gold Member
Integral said:
Dave,
Interesting results. If you used your onboard computer to optain you gas consumption rate, it is possible that the computer ASSUMEs a linear relationship? Thus giving you a very nice graph, but based on questionable data.

Does your car actually meter gas comsuption?

I'm not following you.

My computer will tell me what my mileage is "at this moment". If I am doing 100kph, it will say 30.8mpg. If I slow down to 80, my mileage display will climb to 35.

If it weren't accurate data, then my DTE (distance to empty) reading would be meaningless. As it is, my DTE will change as my driving conditions change.

You might be right, I'm just not sure how to tell.

Gold Member
russ_watters said:
Along the same lines, have you compared the gas consumption/fuel economy over a full tank: fill-up to fill-up?

I know that I get about 400km out of a 50L tank. This of course, gives an average, which is not much use for figuring out the different mileages related to different speeds (since you can't drive for a whole week at one speed).

That' why I'm figuring mine is more accurate.

Reciprocal of gas mileage is gas volume per distance traveled. But gas volume represents a quantity of energy. Assuming constant efficiency, this energy can be thought of as proportional to the work put out by the vehicle's engine. As we know, work divided by distance is force. What is this force? it is the force of resistance to moving. So reciprocal of gas mileage is proportional to this force. Now we only need to know how this force changes with speed. As everyone knows, there are 3 components: constant, linear, quadratic. The first 2 are rolling resistance and the last is aerodynamic. In any case, this force increases monotonically with speed. This predicts better and better gas mileage as you drive slower and slower. This is in agreement with Dave's measurements. How slow can you go? At some point, you can no longer use top gear or else the engine's efficiency suffers. By gearing down, you increase engine speed, thus increasing the amount of losses in the engine. So there will be an optimum, but this optimum is much slower than anyone is willing to travel; probably about 30mph.

krab,
The efficiency is nowhere near a constant. If you look at p. 27 of http://me.queensu.ca/courses/MECH435/2.%20Engine%20Performance.ppt [Broken], you'll find a contour plot of specific fuel consumption versus engine speed and torque (sorry I couldn't find any links to this type of image on its own).

Fuel efficiency is
$$\frac{\rho_{f}}{F (bsfc)}$$
$$\rho_{f}$$ is the fuel density (a constant), F is the force required to keep the car at speed, and bsfc is the (brake) specific fuel consumption (mass of fuel per time per power delivered).

As you've said, F=F(v) is a monotonically increasing quadratic. But bsfc depends on both engine torque and engine speed. These can be related here to F and v by numbers which change only with the chosen gear. In a fixed gear on level ground, the bsfc can therefore be read off the graph by finding the intersections of the contour lines with an increasing polynomial. Depending on the details, this is likely to change quite drastically with speed. And that change is not monotonic.

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"Nowhere near constant" means to me factor of 2 or so. What I call efficiency is basically ratio of gas into energy (power times time) out. That can be expressed as the bsfc. I'm looking at slide 26 of the link you gave (nice presentation BTW): From 500 rpm to 6000 rpm, this varies by about 6%! In my book, that's pretty near constant.