Questions: Otto and Diesel Cycles: Internal Combustion Engines

Question 1

A student claims: 'Diesel engines are thermodynamically superior to gasoline engines because the Diesel cycle formula always gives higher efficiency.' A second student disagrees. Who is correct, and why?

• A. The first student is correct — the Diesel cycle's constant-pressure heat addition is always more efficient than the Otto cycle's constant-volume addition
• B. The second student is correct — at the same compression ratio, the Otto cycle is more efficient; diesels win in practice because they access much higher compression ratios that gasoline engines cannot use without knock
• C. Neither student is correct — efficiency depends entirely on fuel type, not cycle type
• D. The second student is correct — the Diesel cycle is fundamentally inefficient, and any advantage over gasoline engines comes only from diesel fuel's higher energy density

Answer: (B)

At the same compression ratio r, the Otto cycle (constant-volume heat addition) is thermodynamically more efficient than the Diesel cycle (constant-pressure heat addition) — the cutoff ratio term in the Diesel efficiency formula is always greater than 1, penalizing it relative to Otto at equal r. However, gasoline engines are knock-limited to r ≈ 9–12 because the air-fuel mixture autoignites at high compression. Diesel engines compress only air, so they can safely reach r = 16–22. Since efficiency rises steeply with compression ratio, the diesel's access to higher r more than compensates for the cycle's lower efficiency at equal r. Real diesel engines outperform real gasoline engines — but for reasons of *achievable compression ratio*, not cycle formulas.

Question 2

Why can diesel engines use compression ratios of 16–22:1 while gasoline engines are limited to roughly 9–12:1?

• A. Diesel engines are built with heavier materials that can withstand higher pressures
• B. Diesel fuel has a higher energy density, so less compression is needed to ignite it
• C. Diesel engines compress only air during the compression stroke, so there is no flammable mixture present to autoignite prematurely
• D. Gasoline engines use spark plugs, which limit the compression ratio to values where plug heat doesn't pre-ignite the charge

Answer: (C)

The knock limit arises because the air-fuel mixture in a gasoline engine has an autoignition temperature. At high enough compression ratios, the mixture temperature at top dead center exceeds this threshold before the spark fires — producing knock, a damaging pressure spike. Diesel engines solve this by not introducing fuel until after compression is complete. They compress only air, which has a much higher autoignition temperature than any fuel-air mixture. When diesel fuel is injected into the hot compressed air, the controlled autoignition that occurs is the entire ignition mechanism — what is a hazard in gasoline engines is the design intent in diesel. This architectural difference unlocks the higher compression ratios responsible for diesel's efficiency advantage.

Question 3

At the same compression ratio, the Diesel cycle achieves higher thermal efficiency than the Otto cycle.

• T. True
• F. False

Answer: False

False — this is the central misconception about diesel efficiency. At equal compression ratios, the Otto cycle is more efficient because constant-volume heat addition (occurring in a fixed volume at TDC) is thermodynamically preferable to constant-pressure heat addition (occurring as the piston moves down). The Diesel efficiency formula includes a cutoff ratio term [r_c^γ − 1] / [γ(r_c − 1)] that is always greater than 1, representing a penalty compared to Otto. Diesel engines achieve higher *real-world* efficiency because they can use higher compression ratios than gasoline engines — but the thermodynamic formula comparison at equal r favors Otto.

Question 4

Diesel engines can achieve higher compression ratios than gasoline engines without knock because they compress only air (no fuel) during the compression stroke.

• T. True
• F. False

Answer: True

True. Knock in gasoline engines occurs when the compressed air-fuel mixture reaches its autoignition temperature before the spark fires, causing uncontrolled combustion. In a diesel engine, only air is present during compression — air alone has a much higher autoignition temperature than any fuel-air mixture. Diesel fuel is injected at top dead center directly into the hot, high-pressure air, and the resulting autoignition is precisely the intended mechanism (it is a compression-ignition engine). This structural difference allows diesel engines to operate at r = 16–22:1 versus r = 9–12:1 for gasoline, which is the primary reason real diesel engines achieve higher thermal efficiency despite the Diesel cycle being thermodynamically less efficient than Otto at equal r.

Question 5

Explain why diesel engines achieve higher real-world thermal efficiency than gasoline engines, despite the Diesel cycle formula predicting lower efficiency than the Otto cycle at the same compression ratio.

Model answer: The Diesel cycle formula is indeed less efficient than the Otto formula at the same compression ratio r — the constant-pressure heat addition carries an efficiency penalty compared to constant-volume. However, gasoline engines cannot use compression ratios above about 10–12:1 because the air-fuel mixture will autoignite before the spark fires (knock), causing damaging pressure spikes. Diesel engines compress only air during the compression stroke, so there is no premixture to autoignite; they safely reach r = 16–22:1. Since thermal efficiency rises steeply with r (for the Otto formula, η = 1 − 1/r^(γ−1)), the diesel's access to much higher compression ratios outweighs the efficiency penalty of constant-pressure heat addition. The diesel's real efficiency advantage is a consequence of its architecture enabling higher compression — not because the Diesel cycle formula is thermodynamically superior.

This reconciliation — 'worse formula, better real performance' — is a common source of confusion. It illustrates that ideal cycle analysis must be combined with engineering constraints to understand real performance. The efficiency ceiling imposed by knock on gasoline engines is a practical constraint that the ideal cycle comparison ignores. Modern turbocharged direct-injection gasoline engines have narrowed the gap (up to ~40–42% peak vs. ~44–48% for diesel) through improved combustion management and downsizing, but the fundamental compression ratio advantage of diesel remains.