Cut-off ratio is the ratio of cylinder volume at the end of heat addition to the volume at the start of heat addition in a thermodynamic cycle. In Thermodynamics II, it is used to describe how combustion timing affects engine work and efficiency, especially in cycle analysis.
Cut-off ratio is the volume ratio that describes how long heat is added during the constant-pressure part of an engine cycle, most often in the Diesel cycle. It is usually written as rho, and it equals the cylinder volume after combustion starts divided by the cylinder volume when combustion begins.
In plain terms, it tells you how far the piston has moved while fuel is still being burned. If the volume changes a lot during heat addition, the cut-off ratio is larger. If combustion ends quickly, the ratio stays closer to 1.
This term matters in Thermodynamics II because many engine-cycle problems are not just asking whether fuel is added, but how the timing of that heat addition changes the cycle shape. The cut-off ratio changes the amount of expansion that happens while energy is still being supplied, which changes the work output and thermal efficiency.
A bigger cut-off ratio usually means more heat is added over a longer portion of the stroke. That can raise the work produced per cycle, but it also tends to lower thermal efficiency because more of the heat is added after the pressure peak has started to spread out. In other words, the cycle gets more power-friendly and less efficiency-friendly.
This is one of the places where Thermodynamics II feels different from the intro course. You are no longer just naming processes like compression or expansion. You are comparing how process details, such as when combustion ends, change the area enclosed by the cycle on a P-v diagram and change the final efficiency formula.
Do not mix up cut-off ratio with compression ratio. Compression ratio looks at the volume change before combustion starts, while cut-off ratio looks at the volume change during heat addition. They describe different parts of the cycle, and they affect the cycle in different ways.
Cut-off ratio shows up whenever you analyze how an internal combustion engine converts chemical energy into useful work. In a Thermodynamics II engine-cycle problem, it helps connect the combustion process to the final efficiency, pressure rise, and work output of the cycle.
This concept is especially useful because real engine behavior is not just about squeezing the gas harder. The timing and duration of heat addition matter too. A short heat-addition period gives a different cycle shape than a longer one, even if the compression ratio stays the same.
Cut-off ratio also gives you a clean way to compare cycle performance. If two engines have the same compression ratio but different cut-off ratios, the one with the smaller cut-off ratio will usually run more efficiently in the idealized analysis. The larger cut-off ratio often indicates more sustained fuel burn during expansion, which can increase power delivery but reduce efficiency.
That tradeoff is a common theme in the course. You are often balancing output, efficiency, and how close an ideal model is to a real engine. Cut-off ratio is one of the variables that makes that tradeoff visible in the equations instead of hiding it inside the combustion process.
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Visual cheatsheet
view gallerycompression ratio
Compression ratio and cut-off ratio describe two different parts of the cycle. Compression ratio measures how much the cylinder volume shrinks before heat addition starts, while cut-off ratio measures how much the volume grows during heat addition. In problem sets, you usually need both to compute cycle efficiency, especially when comparing ideal Diesel-cycle behavior.
thermal efficiency
Cut-off ratio feeds directly into thermal efficiency calculations for ideal engine cycles. As the cut-off ratio increases, more heat is added over a longer expansion period, and the efficiency usually drops. That relationship is why many textbook problems ask you to see how changing rho shifts the overall cycle performance.
isentropic process
The steps before and after heat addition are often modeled as isentropic compression and expansion. Cut-off ratio sits between those isentropic legs and changes how much expansion happens before the heat input ends. If you know where the cut-off point is, you can track which part of the cycle is still being heated and which part is just expanding.
Power Output
A larger cut-off ratio can increase the amount of work produced during the expansion stroke, which is one reason it is connected to power output. But that does not automatically mean better efficiency. In cycle analysis, you often look at the tradeoff between producing more work per cycle and wasting more energy as heat.
A quiz problem or homework set will usually give you the cut-off ratio, or ask you to find it from volumes on a P-v diagram, then use it in an Otto or Diesel cycle calculation. You may need to plug it into the thermal efficiency formula, compare two cycles, or explain what happens when the ratio gets larger. If the question gives volume at the start and end of heat addition, your first job is to identify those two states correctly.
A common mistake is using the compression ratio instead, especially when the diagram has several labeled states. Another one is treating cut-off ratio like a temperature ratio. Here, it is a geometric ratio of volumes, so the state labels matter. On a written problem, you should be ready to show which process is constant pressure, where heat addition ends, and how that changes the cycle result.
Compression ratio and cut-off ratio both use volume ratios, but they describe different stages of the cycle. Compression ratio compares the volume before compression to the volume after compression, while cut-off ratio compares the volume at the start and end of heat addition. If you swap them, your efficiency calculation usually comes out wrong.
Cut-off ratio is the volume ratio that measures how long heat addition continues during the combustion part of an engine cycle.
In Thermodynamics II, it is used most often in Diesel-cycle analysis, where heat is added at roughly constant pressure.
A larger cut-off ratio usually lowers thermal efficiency because more heat is added later in the expansion stroke.
Do not confuse cut-off ratio with compression ratio, which describes the volume change before combustion starts.
When you see this term in a problem, look for the start and end of heat addition on the cycle diagram before doing any formula work.
Cut-off ratio is the ratio of cylinder volume at the end of heat addition to the volume at the start of heat addition. It describes how much the piston moves while fuel is still being burned in the ideal cycle model. In engine-cycle problems, it usually shows up in Diesel-cycle analysis.
No. Compression ratio measures the change in volume during compression, before heat is added. Cut-off ratio measures the change in volume during heat addition itself. They affect different parts of the cycle, so using the wrong one changes the final efficiency result.
A larger cut-off ratio usually lowers thermal efficiency in the ideal Diesel-cycle model. That happens because heat is added over a longer part of the expansion stroke, which tends to spread out the pressure rise and reduce the cycle's efficiency. Smaller cut-off ratios usually give higher efficiency.
You use it when a problem gives the volumes at the start and end of heat addition, or when a P-v diagram marks the combustion interval. It often appears in efficiency calculations or comparisons between two engine cycles. The main skill is identifying the correct states before you calculate.