[serialk11r]

So the spark ignition internal combustion engine is extremely efficient at mid range rpm, full load. Good engines have peak thermal efficiency of around 40%. This seems like a low number, until you consider that your local power plant with its constant power, highly controlled operating conditions only manages 40%. However when we are at constant speed cruising, the power requirement is TINY, and most cars use only 20% of maximum torque. At these low specific output levels, two phenomena are by far the most important; friction and pumping loss.

Higher rpm means less torque is needed for the same power, so pumping loss increases. In addition, friction increases as a proportion of output with rpm, due to the fact that bearing forces are much higher when reciprocating mass is moving faster. An additional problem with choking the engine off so much is that the effective compression ratio is much lower, and if the gearing is bad enough, the piston does negative work on the bottom portion of the power stroke (although this typically doesn't happen). Also, much of the friction in an engine is not load dependent; as mentioned before, the reciprocating mass is always creating substantial friction. When you are asking less torque of the engine, friction only decreases slightly, and becomes a much larger proportion of total output. Add in the power lost to pumping air past the throttle, and you get that half the fuel you are burning is burned just to overcome these losses.

Now running at higher rpm does have one efficiency advantage: cooling losses. At lower speed, each power stroke occurs in a longer period of time, and so the amount of heat lost to the cooling system as a proportion of power is higher. At higher rpm the absolute quantity of heat lost is higher, but this indicates that the cylinder temperature is higher, which is good, because it means more heat is doing useful work rather than warming up the cooling water. This is why efficiency can drop off at low rpm, particularly on engines with poor surface area to volume ratio cylinders (aka, less displacement per cylinder). Another aspect that varies quite a bit is combustion efficiency; Higher rpm=intake air is moving faster=fuel mixes better, but direct injection basically rewrites this rule.

However, it is almost always the case that the relatively lower friction and pumping losses overcome the inefficiencies of low rpm cooling loss. Power and torque are directly related, thus rpm and torque at the same power are inversely related. Thus if you halve the gear ratio (the torque multiplication ratio between engine and wheel), you double the torque requirement. It's not hard to see that dropping rpms from say, 2500 to 2000 would increase the torque requirement by 25%. That would be, using 25% of the engine's torque rather than 20%. This might not seem like a big difference until you consider the fact that by increasing output by 25%, and decreasing rpms by 20%, the non-load dependent part of friction has been reduced by 20% in absolute terms, but because power is up 25%, friction has effectively been cut something like 40%! In addition, the work going into pumping the air through the throttle has decreased while your total work per unit air is increased, another win-win for efficiency.

Typically, around 50-60% volumetric efficiency is thermodynamically ideal in the sense that it dumps the least amount of heat out the exhaust. However because of the effects of friction and pumping loss, as well as the fact that more compression raises the thermal efficiency, a typical gasoline engine hits maximum thermal efficiency at about 75%-80% maximum torque. Now if you have an Atkinson cycle style engine, the maximum torque is limited about 75%, and maximum thermal efficiency is at 100% torque output.

Variable valve timing makes all this much more complicated, but the basic principles still stand. That is why a BMW 3.0L engine fails to get >30mpg even though it has a very fancy valvetrain that eliminates pumping loss at part load; the extra cylinders pose a large increase in friction, among other things.

As for this engine, what we see is that it has a relatively long duration cam that is optimized for high rpm power, and it has no variable lift/duration system of any kind. What this tells us is that at lower rpm, the inevitable thing that happens is that part of the charge is pushed back out the cylinder on the compression stroke! To achieve this however, the lift needs to be relatively high to not pose pumping resistance. This makes our engine in essence a direct injected Prius at low rpm, with a little more displacement and shorter gears. As I noted, the gears are pretty typical (aka, too short for fuel economy), so fuel economy won't be Prius stellar, but it will be pretty good because the car is so small and takes relatively little power to go through the air.