Questions: The Diesel Cycle and Compression Ignition Engines

Question 1

A diesel engine and a gasoline engine both have a compression ratio of 16:1. Which cycle has higher theoretical thermodynamic efficiency?

• A. The Diesel cycle, because diesel fuel releases more energy per unit
• B. The Otto cycle, because constant-volume heat addition is thermodynamically superior to isobaric heat addition at the same compression ratio
• C. They are equal, because efficiency at the same compression ratio depends only on r
• D. The Diesel cycle, because higher compression always means higher efficiency

Answer: (B)

At the same compression ratio, the Otto cycle is more efficient than the Diesel cycle. The Diesel efficiency formula includes the factor (r_c^γ − 1)/(γ(r_c − 1)), which is always greater than 1 when r_c > 1, reducing efficiency below the Otto value of 1 − 1/r^(γ−1). Real diesel engines are more fuel-efficient because they operate at much higher compression ratios (14–22:1) than gasoline engines (8–12:1), not because the Diesel cycle is inherently superior at the same r.

Question 2

What happens to the Diesel cycle as the cutoff ratio r_c approaches 1?

• A. Efficiency goes to zero because no fuel is burned
• B. The cycle becomes identical to the Otto cycle
• C. Efficiency increases without bound as combustion becomes instantaneous
• D. The isobaric process becomes an isothermal process

Answer: (B)

When r_c = 1, the fuel cutoff occurs instantly at the start of injection — no volume change during combustion — and the isobaric heat addition collapses to a constant-volume process. The bracketed efficiency penalty term equals exactly 1, and the Diesel efficiency formula reduces to the Otto efficiency formula 1 − 1/r^(γ−1). The cutoff ratio is the structural parameter that distinguishes the two cycles.

Question 3

In the Diesel cycle, heat addition occurs at constant pressure rather than constant volume.

• T. True
• F. False

Answer: True

This is the defining feature of the Diesel cycle. Diesel fuel is injected gradually during part of the expansion stroke, and combustion continues as the piston moves outward. The competing effects of combustion releasing energy and volume increasing together produce roughly constant pressure during this phase. This isobaric process contrasts with the Otto cycle's isochoric (constant-volume) heat addition, where all combustion is modeled as occurring instantaneously before the piston moves.

Question 4

Diesel engines achieve better real-world fuel economy than gasoline engines because the Diesel cycle is more thermodynamically efficient than the Otto cycle at the same compression ratio.

• T. True
• F. False

Answer: False

This is the most common misconception about diesel engines. At equal compression ratios, the Diesel cycle is actually LESS efficient than the Otto cycle due to the cutoff ratio penalty. Diesel engines achieve better fuel economy because they operate at much higher compression ratios — typically 14–22:1 vs. 8–12:1 for gasoline — which is possible because diesel fuel is designed to ignite only when injected into hot compressed air, avoiding the premature knock that limits gasoline engines. The higher r more than compensates for the r_c penalty.

Question 5

Why can diesel engines run at higher compression ratios than gasoline engines, and why does this matter for fuel economy?

Model answer: Gasoline is pre-mixed with air and ignites spontaneously above a threshold compression (knock), limiting compression ratios to ~8–12:1. Diesel engines compress only air; fuel is injected after compression is complete and ignites on contact with the hot compressed air. Because there is no premixed charge to ignite prematurely, diesel engines can reach 14–22:1 compression. Since both Otto and Diesel efficiency increase with compression ratio, the much higher r available to diesel engines more than compensates for the efficiency penalty from isobaric combustion, yielding better overall fuel economy.

The key is the physical difference in combustion process: premixed-charge combustion (gasoline/Otto) is knock-limited, while compression-ignition (diesel) is not. This mechanical constraint, not fundamental thermodynamics, is what limits gasoline engines to lower compression ratios and explains why diesels are more efficient in practice despite being theoretically less efficient at the same r.