# fuel efficiency and speed

My new (used) car has a fuel efficiency gauge. It’s very interesting to watch. Clearly, the slower my engine revs, the better my efficiency. It makes sense that slower my engine turns, the less fuel enters into the cylinders. But, as I reach highway speed and set my cruise, my efficiency is still very good. My car is going much faster and therefore requires velocity^2 energy and yet that same rpm can power the car. What am I missing?

Gears.

Generally, the lowest constant speed in your highest gear will give you the best fuel efficiency, I think.

How much gas you’re giving it in a given speed/acceleration/RPM situation, I think…

(Just to expand on the above, note that in certain situations you might be at wide open throttle with lots of gas entering the cylinders at relatively low RPM, while in others you might be crusing at higher RPM while barely pressing on the gas pedal.)

There are a few reasons why fuel efficiency may not be immediately intuitive.

The wind resistance of a car (essentially, the force of the air pushing you backward) increases with the speed cubed. This means the force your motor must exert on the road increases exponentially with the speed of your car, just to keep you at a constant speed. This would make it seem like a lower speed would always be a lot more efficient.

However! Any internal combustion engine must maintain a minimum speed or it will stall. (Which you probably knew.) A consequence of this is the fact that your engine has an ideal operation speed, a function of its design, at which it operates at its maximum efficiency. (It also has an RPM where it achieves maximum torque and maximum HP, and they’re probably not at all close to each other.)

Car manufacturers control these variables carefully because, in combination with the gear ratios in your transmission, they can tune your car so it’s most efficient at a particular speed (typically in the 65 mph range). This means that, in spite of that rapidly scaling force backwards, and though your fuel consumption per second is always increasing with speed, obviously so is your speed, so the fuel consumption per mile decreases.

Finally, to accelerate your car, you need to impart force to not just counteract wind resistance (and friction) but to actually have enough left over to increase your speed at a reasonable clip. This extra force is surprisingly large (in the 2 kilopound-force range for 0 to 60 in 10 seconds) and creating this extra force burns so much more fuel than just maintaining a constant speed, so you are more efficient with respect to distance travelled when you’re driving at highway speed than anything else.

Fuel efficiency is just not how much fuel goes into the engine, but how much it moves you. Higher speeds means you move more for the amount of fuel, as opposed to standing still and still using that much fuel.

I’m not saying that going faster ever increases efficiency, but it does at the lower end of the speed range before air resistance starts to really detract from it.

No, drag force increases with the square of speed. Since power is drag force times speed, this means that power scales with the cube of speed.

Since drag scales with the square of speed, the per-mile drag energy requirement also scales with the square of speed. So why isn’t fuel economy proportional to the inverse-square of speed? In other words, if you get 30 MPG at 40 MPH, why doesn’t your fuel economy drop to 7.5 MPG at 80 MPH?

The answer is that an internal combustion engine’s overall efficiency varies dramatically as a function of its speed and load. They tend to deliver best efficiency at high load (torque) and low/middling RPM, which is why cars with automatic transmissions tend to select a very high gear once you start cruising at a steady speed. For most cars, the best fuel economy seems to happen somewhere between 40-60 MPH, but it doesn’t drop a whole lot at higher speeds; if you’re getting 37 MPG at 50 MPH, you’ll probably still see ~30 MPG at 80 MPH.

the big light-load detractors for engine efficiency are mechanical friction and throttling losses. Friction doesn’t drop as much as you’d hope when you ease off of the accelerator, so when you’re only sending a little bit of work out via the crankshaft, the friction accounts for a larger percentage of fuel energy. In addition, light load means the throttle plate is mostly closed, so the engine is doing a lot of mechanical work trying to suck air past that restriction: your pistons are producing torque on the power stroke (and consuming fuel to do so), but then using up a lot of it to inhale during the intake stroke. Diesel engines do away with the throttle plate altogether, which is one reason why they deliver better light-load fuel efficiency than gasoline spark-ignited engines.