THE DIESEL CYCLE

Ignite by compression alone — no spark. Squeeze air until it is hot enough to light the fuel, then burn it at constant pressure while the piston is already moving. You trade Otto's constant-volume flash for a higher compression ratio, and win efficiency the spark engine cannot reach.

source Diesel, Theorie und Konstruktion eines rationellen Wärmemotors — treatise 1893, running engine 1897 · AMBER (no single canonical DOI; year cited as 1897 per the working motor). Rendered, not quoted.

Blue Team · builds & defends
3
The Model

Four strokes on an ideal gas, γ = 7/5 (diatomic air):

1→2 adiabatic COMPRESSION V1→V2 r = V1/V2 2→3 heat in @ CONST P V2→V3 rc = V3/V2 3→4 adiabatic EXPANSION V3→V1 4→1 heat out @ CONST V V1

The burn (2→3) happens as the piston moves, so it does work. The closed exact law:

η = 1 − (1/r^(γ−1)) · (rc^γ − 1)/(γ(rc − 1))

Net work = the enclosed P–V area; first law dU = dQ − dW holds each stroke.

5
The Lineage

Ignite by compression — Diesel 1897. Set the cutoff ratio rc → 1 and the burn shrinks to a point at constant volume: the factor (rc^γ−1)/(γ(rc−1)) → 1 and η collapses to the-otto-cycle 1 − r^(1−γ). Both sit strictly beneath the-carnot-cycle reservoir bound.

rc=1 → Otto · rc>1 → Diesel · both < Carnot

7
The Witness live

Re-computes η(r=18, rc=2) from the honest closed form and compares it to the panel's engine every render. Green = intact; the moment window 6 drops the cutoff factor, this flips red.

witness idle
The Machine
4
Data In in ▼

Ideal air, γ=7/5, T1=300 K. You set the squeeze and the burn:

18.0 2.00
0
The Panel LIT
η Diesel
–
η Otto (same r)
–
Carnot bound
–
Burn work W(2→3)
–
8
Data Out out ▼

Proven at boot (r=18, rc=2): η Diesel ≈ 0.6316, below Otto's 0.6853 at the same r, and far below Carnot's 0.8427. The burn does W ≈ 953 R·K of work — never zero.

litbadge: pending…
Red Team · attacks & breaks
1
The Adversary WALL
"Diesel beats Otto because its formula is higher — same engine, more efficiency."

False. At the same compression ratio the cutoff factor >1 makes Diesel lower. Diesel wins in the real world only because it can run at much higher r without knock — a different operating point, not a free lunch. That advantage is AMBER: material limits, turbo, NOx, and soot cap it.
2
The Graveyard

"Constant-pressure burn does no work, like Otto's."
Wrong — 2→3 moves the piston: W = P·ΔV = R(T3−T2) ≠ 0.

"η rises without limit as rc grows."
No — larger rc raises the cutoff factor, so η falls; only higher r helps.

"A real Diesel reaches Carnot efficiency."
Never — 1 − Tc/Th is the hard ceiling; the cycle stays strictly under it.

6
The Tamper

Drop the cutoff factor — model the constant-pressure burn as if it were Otto's constant-volume flash (η = 1 − r^(1−γ)) even though rc > 1. The heat added is mis-accounted; the reduces-to-Otto-only-at-rc=1 invariant breaks. Window 7 catches it live.