Intro to Otto vs Prius Atkinson Thermodynamics

I'm sorry, I should have been more specific about the effect of compression ratio on engine efficiency. So let's start with this URL:

They don't really discuss compression ratio but this is the take away:

". . . The thermodynamic limits assume that the engine is operating in ideal conditions: a frictionless world, ideal gases, perfect insulators, and operation at infinite time. The real world is substantially more complex and all the complexities reduce the efficiency. In addition, real engines run best at specific loads and rates as described by their power band. For example, a car cruising on a highway is usually operating significantly below its ideal load, because the engine is designed for the higher loads desired for rapid acceleration. The applications of engines are used as contributed drag on the total system reducing overall efficiency, such as wind resistance designs for vehicles. These and many other losses result in an engine's real- world fuel economy that is usually measured in the units of miles per gallon (or fuel consumption in liters per 100 kilometers) for automobiles. The miles in miles per gallon represents a meaningful amount of work and the volume of hydrocarbon implies a standard energy content.

Most steel engines have a thermodynamic limit of 37%. Even when aided with turbochargers and stock efficiency aids, most engines retain an average efficiency of about 18%-20% . . . ."

Practical, commonly sold engines have abysmal thermal dynamic efficiencies. To be perfectly blunt, they are rubbish compared to what they could (and should) achieve such as with the Prius Atkinson cyycle. So lets look at two university web pages that go into details addressing the effect of compression ratio:

Both papers show the math to derive the same efficiency formula for a 'perfect' Otto cycle engine:

efficiency = 1 - ( 1 / (r ** (k-1) ) )

r - compression ratio k - specific heat ratio, a measure of energy in the fuel

For simplicity, here is the MIT chart:

Here is the Northwestern chart: they have have different scales with the MIT showing the fullrange and the Northwestern a more practical range we find today. Now everything in these classical, Otto cycle lessons derives from the P-v diagram: The top curve coming from point 3 towards point 4 is the power stroke curve and the longer it is, the more energy extracted. The x-axis is the "v" expansion ratio. A greater compression ratio, the longer the expansion stroke and more energy extracted. But higher compression can lead to detonation and hammer the engine to pieces. The key to efficiency is the longest possible expansion ratio to extract mechanical energy.

The Prius Atkinson cycle changes the compression stroke so the fuel- air charge is not compressed to ignition. Itt takes the line from 1 to

2 and breaks it into two sections:

1 to 1.5 - this is a flat line as the intake valve is kept open and part of fuel-air mix goes back into the intake manifold to be sucked in the next cylinder.

1.5 to 2 - this is the shortened compression stroke which being smaller, also means less compression losses as well as avoiding detonation or knock.

Qs - the energy added is less because there is less fuel-air to burn

Qout - is the same

4 - is moved to the right about 50% further (aka., 13 to 1 expansion versus 9 to 1 typical compression ratio.) So the Prius has a much longer power stroke to extract more energy.

I do not like this P-v chart but it is 'close enough:'

do not like it because the segment 3-4 implies a substantialincrease in volume without work being done and that doesn't happen. Ifyou stretch 4 over to combine it with 3, you'll have an accurate,Atkinson cycle P-v diagram. Bob Wilson