 For the ideal model of the compression ignition internal combustion reciprocating engine, we are using the diesel cycle. And the primary difference between the spark ignition internal combustion reciprocating engine model, the auto cycle, and the compression ignition internal combustion reciprocating engine model, the diesel cycle, is that of ignition type. In the auto cycle, we are firing the fuel with a spark from a spark plug. In the diesel cycle, we are compressing the air to a high enough pressure that the temperature has increased enough that it's above the flashpoint of the fuel. That way we can just inject the fuel and it combusts upon contact with the air. So again, we are compressing the air until it's hot enough that the diesel auto ignites. And then because we don't want it to auto ignite arbitrarily during the compression stroke, we are injecting the fuel after the compression process. So once the piston gets to approximately top dead center, we inject the fuel and it ignites upon contact with the hot air. That means that it takes a non-zero amount of time for the fuel to burn. It takes some time for the injection process to happen, and in that time the piston has moved a bit. So in our diesel cycle analysis, we first have compression, and we are assuming that that occurs isentropically. That's from one to two. And then we have combustion, which takes some time, and the piston moves. Then in the power stroke, the piston goes the rest of the way to bottom dead center. And then just like with the auto cycle, we are closing the cycle with an isochoric cooling process. And that cooling actually represents exhausting the air, allowing it to spread into the atmosphere and cool back off and then be brought back in again. So we're closing the cycle because we are treating it with the air standard as though it's the same air the whole time. So compression, the piston moves up, compresses the air, and then we inject the fuel for a bit between two and three, during which the fuel is burning. And then from three to four, we expand the rest of the way, hopefully that's most of the length of the cylinder, but not always. And then from four to one, we have isochoric cooling, just like we did in the auto cycle. So from one to two, we have isentropic compression. From two to three, we have heat addition that's no longer isochoric. From three to four, we have isentropic expansion. And from four to one, we have isochoric heat rejection, just like we did in the auto cycle. So one to two is the same process, three to four is the same process, four to one is the same process, but two to three is different. And if we look at the process from two to three, we can reflect on the fact that the volume is different. So it's not going to be isochoric. Furthermore, as a result of the fire happening, there's going to be an increase in temperature, so we shouldn't model it as isothermal. So what should we model it as? Well, for the purposes of the idealized compression ignition internal combustion reciprocating engine, we model it as isobaric. So we say that the piston moves down, keeping approximately a constant pressure. Now, of course, in the real thing, it's not actually a constant pressure, but it's closer to being a constant pressure than it is a constant volume. And we model it that way to allow for some comparison between different operations under the same circumstances. It's close enough for our model. So the diesel cycle is isentropic compression from one to two isobaric heat addition from two to three isentropic expansion from three to four and isochoric heat rejection from four to one. The compression ratio is still a parameter that is very useful. Here, it's going to be the volume at bottom dead center divided by the volume at top dead center, which is no longer both the proportion between one and two and three and four. It's not three to four. It's just one to two. Because three is not the same as two anymore. So this is not a repeat not v four over v three. To provide some comparison between these, we can also describe another volume proportion. And that represents v three over v two. And this we call the cutoff ratio. And the cutoff ratio represents the amount of volume change, the proportion of volume change during the combustion process. It essentially means how long did the fuel take to inject a high compression ratio does not necessarily mean a high cutoff ratio. We want a very small cutoff ratio because we want the fuel to burn as early as possible, so that we can get as much power in the power stroke as we can. Now, think about this for a second. What is the lowest value the cutoff ratio could be? That's right, one, or rather, like just to the right of one, because if it's one, it's actually just an auto cycle. So it would be if it was on a line graph, it'd be like a square bracket. No, which one is the one that is like up to but not touching one? It's that parentheses or square bracket or whatever. So lowest value is slightly more than one 1.000000000000000000000000000000000000000000000000000000000000000001 let's say, what is the maximum value that the cutoff ratio could be? That's right, the compression ratio. If the combustion process expanded all the way back to where it started, which, by the way, would be like the worst diesel cycle ever because there'd be nothing left to do in the power stroke in beginning only your power in the combustion process, not the power stroke, which is not what you want. That would be the most expansion that could occur, which would be the proportion that the compression ratio was. Does that make sense? So the lower bound is one, the upper bound is R. I will also point out that both of these can be represented as specific volumes as well, because it's the same mass the whole time. And again, you want a small cutoff ratio. Smaller cutoff ratio implies better performing engine.