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I've had a discussion with my father today, about the fuel usage of a vehicle at the same rpm, but a different gear.

He claims that the following situations have the same fuel usage:

Gear: 2
rpm: 2000
fuel usage: 5.1l/100km

Gear: 5
rpm: 2000
fuel usage: 5.1l/100km

I say it should be something along the lines of:

Gear: 2
rpm: 2000
fuel usage: 4.1l/100km

Gear: 5
rpm: 2000
fuel usage: 5.4l/100km

Who is right and why? He is also claims that the force to maintain the speed will be the same across different gears with the same rpm.

By the way, I'm not sure if it should be on physics, but it fitted best here.

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I'm very likely wrong, but doesn't the fuel consumption depend on the RPM and the load on the engine? Is there an implicit assumption on the engine load based on the gear setting? – Willie Wong Jul 10 '11 at 15:10
Because a higher gear means the gear is bigger, thus you can have the same rpm. I'm also talking about the rpm displayed on your dashboard. @ Willie, I'm talking about rpm and fuel only in my first question, not the actual force needed for a certain speed or rpm. – Simon Verbeke Jul 10 '11 at 15:18
up vote 5 down vote accepted

I've had a discussion with my father today, about the fuel usage of a vehicle at the same rpm, but a different gear.

The fuel injector system does not always inject a constant amount of fuel into the engine.

If you are driving down a hill and remove your foot from the gas pedal (a little) the engine will stay the same rpm but with less fuel passing thou the system.

And if you are driving up a hill you need to press down the gas pedal to maintain the same rpm and speed, more or less you need to push more fuel into the engine.

This is why you will not have a constant fuel consumption at a given rpm.

Then when you remove some load, let's say you are on the top of the hill, you will have a small surplus of "energy released" inside the engine that will push the rpm higher until you remove your foot from the gas pedal and reducing the amount of fuel sent into the engine.

He is also claims that the force to maintain the speed will be the same across different gears with the same rpm.

The faster you travel the more wind resistance you will have, therefore you need more power to overcome this resistance. And to get more power out from a engine you need to send in more fuel (or use the amount have in there in a more efficient way).

But why do we need to switch gears up and down then, why can't we just inject more fuel into the engine?

This is where we go into chemistry since you can only make gas burn within a specified rate between fuel and air, and the volume inside the engine has a fix size and therefore has a maximum volume of gas that you can burn per rotation. Send in more fuel than this and the engine will drop in efficiency.

And when you then switch down a gear you will increase the rpm at this speed and that way increase the amount of fuel you can burn in the engine within this timeframe and you will in most of the cases more power out from the engine.

But at the end of the day there is a lot of other constraints in a combustion engine that will limit how it works beside this simplified version I just describe here.

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But with higher gear you travel longer distance per revolution. So it's mandatory to discuss this effect according to load. – Crowley Jul 11 '11 at 21:37

What anyone failed to acknowledge is that to spin the engine faster requires more work, so you would end up using way more fuel in 2nd gear than 5th. We upshift to save fuel at lower RPM, and the engines would explode if you had them spinning too fast. Engines also have accessories, such as water pumps, compressors, alternators attached to the crankshaft, and to spin them faster is more work.

While you might be able to come up with a physics formula to say how much energy it takes to move so much weight so far, that does not account for the engines losses that is performing the work.

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Maybe I'm misreading, but it certainly looks like the other answer addresses the issue of differing gears rotating faster. – Kyle Kanos Feb 22 '15 at 18:50

2000 rpm on the engine in 2nd transfers to a slower rpm in the wheels but with more torque hence more load on the engine and more fuel required.

2000 rpm on the engine in 5th gear transfers to a higher rpm (than in 2nd gear) on the wheels with less torque hence less load on the wheels.

This is because we only have to overcome friction when in the cruising gears therefore need less torque on the wheels and can use a more efficient gearing ratio.

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