I understand that, in an internal combustion engine, efficiency can often (up to a point) be improved by increasing the compression ratio, this being a major reason why diesel engines (which do not need to limit compression to avoid knock) can be more efficient than their spark-ignition counterparts.

In most engines, compression and expansion are symmetric. However, Atkinson-cycle engines allow the expansion ratio of an engine to differ from its compression ratio, typically by allowing the piston to rise substantially above BDC before the intake valve is closed and compression is allowed to begin, such that the effective displacement of the engine is reduced and the expansion ratio (which still uses the full stroke of the piston) exceeds the now-limited compression ratio.

Atkinson-cycle engines can achieve higher efficiency (lower specific fuel consumption) than Otto-cycle counterparts, usually at the cost of reduced specific output (since they use only a fraction of their displacement during compression). My question, however, is how this (low compression, high expansion) compares to the alternative - high compression and high expansion.

All else being equal, and assuming knock can be avoided in all cases, I would expect an Atkinson-cycle engine with an expansion ratio of 20 and a compression ratio of 10, and an Otto-cycle engine with a compression ratio of 20, to both exceed the efficiency of an Otto-cycle engine with a compression ratio of 10. However, how would the efficiency of the Atkinson cycle engine compare to its high-compression Otto cycle counterpart? Is it the expansion (extracting more heat from the same amount of combustion gases before what's left goes out the exhaust) that provides the efficiency improvement, or does the high compression itself also contribute (perhaps by allowing a higher peak combustion temperature)? If high compression does contribute, how does it compare to the contribution of high expansion? Does it account for half the improvement? A small fraction of it? Most of it?

TL;DR does the Atkinson cycle allow you to gain all or most of the efficiency of a higher-compression Otto-cycle engine without risking knock (at the cost of reduced power output), or does a higher compression ratio contribute efficiency of its own which is lost when increasing only expansion ratio?

2 Answers 2


Let me clear up some misconceptions it seems you might have.

... understand that, in an internal combustion engine, efficiency can often (up to a point) be improved by increasing the compression ratio ...

It is a rule of thumb, that each point of static compression ratio increases power output of a gasoline engine by ~3%, everything else being equal.

... this being a major reason why diesel engines (which do not need to limit compression to avoid knock) ...

Diesels need a higher compression ratio so that it will create enough heat in the cylinder during the compression cycle to ignite the fuel. You are saying "knock", but what you are really talking about is pre-ignition. Diesel engines don't have pre-ignition because of direct injection (at least most modern diesel engines are direct injected ... some older ones were indirect injected, but I don't believe those are sold as new anymore).

... can be more efficient than their spark-ignition counterparts.

There are two reasons besides the compression ratio as to why they are more efficient than gasoline/spark-ignition engines if you were to do a gallon per mile type of evaluation:

  1. Diesel is more energy dense than is gasoline. Gasoline has an energy density of 33,867 megajoules per meter cubed. Diesel has an energy density of 27,184 mj/m3. Therefore it takes less diesel to produce the same amount of energy as does gasoline. This is the same reason you get less mileage out of ethanol than you do gasoline.

  2. Diesel engines are more thermally efficient than are gasoline engines. Gasoline engines are about 20% efficient, while diesel engines are about 40%.

I would expect an Atkinson-cycle engine with an expansion ratio of 20 and a compression ratio of 10, and an Otto-cycle engine with a compression ratio of 20, to both exceed the efficiency of an Otto-cycle engine with a compression ratio of 10.

Something which maybe will help you with the Atkinson Cycle engine and how it runs is, quit thinking about the compression ratio being less than the expansion ratio, and think more on the line of the compression area being less than expansion area.

If you think of it this way, if you are running a 1.2L engine and only using up 1.0L of the compression area during the compression stroke, you're only burning 1.0L of engine displacement during the power stroke. With 1.0L of displacement being used, you still want the air/fuel mixture to be near stoichiometric when the air/fuel is ignited. If it isn't, you're going to be rich, which defeats the purpose in the first place. The extra combustion stroke travel (extra in relation to the effective compression stroke travel) allows for the engine to draw more power from the expanding air fuel mixture. In my example, the extra .2L of travel, allows the engine to extract more power from a given amount of air/fuel.

The other thing which gives the Atkinson cycle improved fuel economy is because there are less pumping losses during the compression cycle. An internal combustion engine, after all, is only a super heated air pump. If you can find some efficiencies somewhere, you are going to be able to produce power at a lower cost.

You are partially right in your assumptions, though. The increase of compression ratio gives the Otto Cycle engine more power output (as stated, 3%/point of compression) as compared to the Atkinson.

The real thing to remember is, the Atkinson Cycle is being used today for two reasons.

  1. It provides better fuel economy.
  2. It can reduce NOx emissions (the stuff which makes acid rain) by up to 40%.

Most auto manufacturers using the Atkinson Cycle engine today do so in a hybrid setup, so the hybrid engine can provide the extra torque when the vehicle needs it as well as the regenerative braking refilling some of the batteries, recycling what would otherwise be lost.

As a side note, if you haven't watched it, the YouTube channel Engineering Explained has a good video on how an Atkinson Cycle engine works in comparison to the Otto. It's very informative.

  • Understood, and yes I have seen that video. Your point about extracting more power from a given amount of mixture by expanding it over extra volume is a good way to explain it. However, I'm still wondering whether it is this additional expansion (extracting more heat energy from the same mass of combusting mixture) that improves efficiency (fuel economy) in higher-compression Otto-cycle engines, or whether higher compression in and of itself also helps efficiency in their case. Sep 27, 2022 at 23:07
  • Higher compression helps with power, but remember, the Atkinson Cycle is more efficient, just less powerful (given all things are the same between the two engines except for the CR). Higher compression helps with power, not with efficiency. If it weren't so, there wouldn't be an Atkinson Cycle engine we see in many Hybrids today. Sep 28, 2022 at 0:39

The efficiency of an Atkinson cycle engine comes from expansion ratio.

An Atkinson cycle engine is often said to have a very high compression ratio. Actually this is the expansion ratio. Atkinson engines close the intake valve long after the piston has been moving towards the top dead center, meaning the true compression ratio differs from the indicated "compression ratio" that is actually the expansion ratio or geometrical compression ratio.

Usually all gasoline engines have about the same compression ratio. Not much variation there. This is mainly fixed by the quality of gasoline used. Countries with high per-liter fuel taxes make using high quality gasoline appealing to avoid those high taxes (by using less gasoline), so in these countries gasoline has somewhat higher octane than in countries like US with practically no fuel taxes. So an engine intended for US could have bit lower compression ratio than engine intended for Europe. But still they are pretty close.

The Atkinson cycle gets its efficiency from expansion ratio, since compression ratio is fixed by the type of gasoline used. The drawback is that Atkinson cycle creates less power given a specific displacement, but benefit is the higher energy efficiency.

What Paulster2 also highlighted is the lower pumping losses. Yes, a 2.5 liter Atkinson cycle engine has lower pumping losses than 2.5 liter Otto cycle engine. That's not a fair comparison though. A fair comparison would be whether 100 kW Atkinson cycle engine has lower pumping losses than 100 kW Otto cycle engine. In that case, the Otto cycle engine would have smaller displacement, and about the same pumping losses.

Also with variable valve timing, it's possible to simulate Atkinson cycle and many engines do this already. However, if an engine is designed to run as Otto cycle, the geometrical compression ratio has to be typical for Otto cycle engines, so when switching to Atkinson cycle, you lose compression ratio while maintaining expansion ratio (geometrical compression ratio), so there are two opposing forces at play: lower compression ratio reduces energy efficiency, Atkinson cycle operation (and also pumping loss reduction) increases energy efficiency. To get the most out of Atkinson cycle, an engine should be designed to run only in Atkinson cycle mode -- or alternatively have a variable compression ratio that can be adjusted on the fly when switching cycles (not common). Also if you can adjust valve timing but not duration during which valves are open, the Atkinson cycle simulation isn't perfect.

A dedicated Atkinson cycle engine would be very lazy except in a hybrid. I suppose most of the benefit of changing valve timing to cause an engine to be sort of Atkinson cycle engine, could be actually not mainly true Atkinson cycle operation but rather reduced pumping losses (in this case, the pumping loss reduction per power output is real since the engine max power isn't diminished by fixing to Atkinson cycle only). Also, such an engine can during high power periods switch back to true Otto cycle, to have lots of power which Atkinson cycle engines can only have from a hybrid battery pack.

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