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 Autocycle, and the compression ignition internal combustion reciprocating engine model, the diesel cycle is that of ignition type. In the Autocycle, 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 1 to 2. 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 isochordic 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 2 and 3, during which the fuel is burning. And then from 3 to 4, we expand the rest of the way, hopefully that's most of the length of the cylinder, but not always. And then from 4 to 1, we have hysochloric cooling, just like we did in the auto cycle. So from 1 to 2, we have isotropic compression. From 2 to 3, we have heat addition that's no longer isochoric. From 3 to 4, we have isotropic expansion. And from 4 to 1, we have isochoric heat rejection, just like we did in the auto cycle. So 1 to 2 is the same process. 3 to 4 is the same process. 4 to 1 is the same process, but 2 to 3 is different. And if we look at the process from 2 to 3, we can reflect on the fact that the volume is different. So it's not going to be that much. 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 temperatures, 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 isotropic compression from 1 to 2 isobaric heat addition from T to 3 isotropic expansion from 3 to 4 and isochoric heat rejection from 4 to 1. 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 1 and 2 and 3 and 4. It's not 3 to 4, it's just 1 to 2. Because 3 is not the same as 2 anymore. So this is not repeat not v4 over v3. To provide some comparison between these, we can also describe another volume proportion, and that represents v3 over v2. 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. 1. Or rather, just to the right of 1. Because if it's 1, it's actually just an auto cycle. So if it was on a line graph, it'd be like a square bracket. No. Which one is the one that is up to but not touching? One, it's that parentheses or square bracket or whatever. So lowest value is slightly more than one point, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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. You'd be getting all your power in the combustion process, not the power stroke, which is now 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 1. 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.