Correct me if I'm wrong, but doesn't accelerating an object at 5mph per second for 10 seconds take the same amount of energy as accelerating it at 10mph per second for 5 seconds? Either way the object would be going 50mph. So why does the latter get worse gas mileage in a car?

russ_watters
Mentor
Welcome to PF!

Energy (work) is force times distance. Clearly, twice the acceleration requires twice the force -- so how much more or less distance is covered?

Correct me if I'm wrong, but doesn't accelerating an object at 5mph per second for 10 seconds take the same amount of energy as accelerating it at 10mph per second for 5 seconds? Either way the object would be going 50mph. So why does the latter get worse gas mileage in a car?
Yes you're right, in principle the same quantity of work is required to give the same kinetic energy; any practical difference should be explained based on efficiency (expressed in "work", in the second case you apply twice the force over half the distance). I thus suppose that common cars are more efficient in slow acceleration than in fast acceleration.

To really understand the answer you might Google "specific fuel consumption." Every engine has a set of curves showing how much fuel an engine will burn under a certain load and at a certain rpm. So they are 3 dimensional curves, which an engineer will study in great detail before making an engine selection for a particular application. Typical units would be pounds of fuel per HP per hour, or the metric equivalent grams per kw per hr. SFC varies a great deal from one load and rpm to another.

Gas use is more closely proportional to engine RPMs, not wheel RPMs. When you mash the gas pedal the RPMs go much higher. When you are going slower in a lower gear you are could be using more gas than when you are going faster in a higher gear. This is one reason we use more gas in the city. Every stop sign you start from (if you mash the gas) could result in 6000 RPMs for a period of time. On the open road you are probably hovering around 2500.

In the end, yes, you are performing the same amount of work, but the connection between the gas-burning cylinder and the road is not linear.

russ_watters
Mentor
[it was early when I gave my first response...[
Pkruse has some of it. You're also staying in lower gears longer. Lower gears have the internal components of the drivetrain moving faster and wasting more energy in friction.

There is another issue: getting to higher speed faster means traveling faster on average over the same distance, which means more wind resistance.

CWatters
Homework Helper
Gold Member
If you accelerate faster you get to your max speed sooner (in a shorter distance) so for a particular trip you spend more time at max speed.

This can be a really good question to gain a little insight to how car's engine 'uses' power, and the relationship that has with fuel consumption.
The answer to your question is that the slower you accelerate a car upto a given speed, the less fuel it will use (to a point). As suggested above, the higher the engine is reved the more power is required just for the engine to spin at those revs, plus the additional friction from the input shaft in the gearbox at those elevated revs. Friction in an engine (and the power needed to keep it spinning at those revs) increases at a proportional rate to the additional revs, so an engine spinning at 6000rpm will potentially use 4 times as much fuel as the same engine turning at 1500rpm.
An economical way to accelerate that same car to 50mph, would be to use the highest possible gear as early as possible to keep the revs down and from wasting any power to just turn the engine.
The most economical way to accelerate the car gets a little more complicated than that though, as you would want to match the amount of power used to accelerate the car with the total amount power being used to turn the engine, + maintain the instantaneous velocity due to other friction, + the amount of power to overcome the cars wind resistance at a certain speed, + the gradient of the slope the vehicle is on +/-. Then also consider the BSFC for that particular engine and try to have the engine work where it is most efficient. But you also have to keep in mind that fueling below 1500rpm, and over 85%VE elsewhere, on cars 10yo+ will not be in closed loop fueling control and will use more fuel than the BSFC suggests.

Dano