Power output of automobile at different engine rpm

[Steve Aplin]

I figure my 2.4 liter Volvo will burn about a liter of gasoline over an hour of idling (source: Natural Resources Canada). Since a liter of gasoline contains roughly 33.8 million joules (~9.4 kilowatt-hours) of energy, I figure that that means my car idles at a power output of around 9.4 kilowatts.

The tachometer indicates rpm of ~700 while idling.

Can I infer from that that when I'm climbing a steep hill at 100 kilometers per hour and the tach is showing rpm of around 3,500 that the engine at that moment is outputting around 47 kilowatts?

It seems logical to me to assume that if the engine speed is 5x on the hill climb then its fuel consumption is 5x that of idling, and that fuel consumption = power output.

Is this a reasonable assumption?

(I know my gasoline engine is at most 20 efficient, and I am not trying to say that moving a 3-ton vehicle at 100 kph up a steep hill requires 47 kW. I am talking only about the gross power output of the fuel.)

 

[DEvens]

Engine power is not especially linearly related to RPM.

All engines will have a range of RPM for which they are most efficient. This has to do with such things as the speed the fuel-air mixture gets into the cylinder, the time the burning fuel has to push on the piston, and the time the exhaust has to get out of the cylinder. The typical design will put this "sweet spot" in the middle of ordinary driving conditions.

Further, the engine RPM is not the only estimate of power. The engine can be exerting different forces at the same speed, depending on the load. So if you were going uphill as in your example, it may be working very hard. If you were going along on level ground with the same RPM, it would probably not be working nearly as hard.

 

[Steve Aplin]

DEvens, thanks -- I guess I'm trying to figure out only gross power output from the gasoline... sounds from your reply that there is some feedback relationship between fuel consumption and the force going into the powertrain. Going up the steep hill at 3,500 rpm, would there be more fuel consumption than down the same hill at the same rpm? Pistons are moving up and down at the same rate, but the force they are imparting to the connecting rods etc. is vastly different.

 

[russ_watters]

Engine power is not especially linearly related to RPM.

Engine power is not really related to RPM at all. An engine has a wide range of possible amounts of torque that it can generate at any particular rpm. That's why at any particular rpm you might be accelerating, decelerating or staying at the same speed.

Going up the steep hill at 3,500 rpm, would there be more fuel consumption than down the same hill at the same rpm? Pistons are moving up and down at the same rate, but the force they are imparting to the connecting rods etc. is vastly different.

Sure. You might be using 30L/hr on the way up and nothing at all on the way down, at the same RPM.

Since a liter of gasoline contains roughly 33.8 million joules (~9.4 kilowatt-hours) of energy, I figure that that means my car idles at a power output of around 9.4 kilowatts.

Since a car engine is at best 33% efficient (and probably a lot less at idle), it is probably more like 3 kW output at idle...
...of course, depending on your definition, at idle you could also say the power output is zero.