| name | engine-design |
| description | Engine design — thermodynamic cycles (Otto, Diesel, Atkinson), BMEP, BSFC, volumetric efficiency, bore-stroke ratio, valve timing, combustion analysis, turbocharging, friction estimation, SAE J1349/ISO 1585. |
| metadata | {"priority":7,"promptSignals":{"phrases":["engine design","Otto cycle","Diesel cycle","BMEP","volumetric efficiency","engine combustion"],"minScore":3}} |
Engine Design — Complete Skill
Thermodynamic Cycles
Otto Cycle (Spark Ignition, Gasoline)
Thermal efficiency:
η_th = 1 - 1/r_c^(γ-1) [r_c = compression ratio; γ = ratio of specific heats = 1.35–1.40 for air-fuel]
At r_c = 10: η_th = 1 - 1/10^0.4 = 1 - 0.398 = 0.602 = 60.2% (ideal Otto; actual ~35%)
Practical limit: knock limits r_c to 10–13:1 (gasoline); higher with direct injection, octane boost
Diesel Cycle
Thermal efficiency:
η_th = 1 - (r_c^γ / r_c^γ) × (r_e^γ - 1) / (γ(r_e - 1)) [r_e = cutoff ratio = V3/V2]
Or: η_th = 1 - (1/r_c^(γ-1)) × (r_e^γ - 1) / (γ × (r_e - 1))
At r_c = 17, r_e = 2: η_th ≈ 63% ideal; actual ~45%
Diesel advantage: higher r_c (no knock limitation) → higher η_th; lean operation → no throttle losses
Atkinson / Miller Cycle
Extended expansion: late IVC (intake valve closing) → effective compression ratio < expansion ratio
→ higher thermal efficiency; less work out per cycle but better efficiency
Application: Toyota Prius hybrid; gasoline engines with variable valve timing
Key Performance Metrics
Brake Mean Effective Pressure (BMEP)
BMEP = Net work per cycle / displacement volume:
BMEP = T_brake × (2π × 2/n_cylinders) / V_d [4-stroke: divide by 2 for 2 revolutions]
= P_brake / (V_d × N × n_strokes/2) × 60 [kPa; P = power in kW; N = RPM; V_d in liters]
Typical BMEP values:
| Engine type | BMEP [kPa] |
|---|
| Naturally aspirated gasoline | 900–1200 |
| Turbocharged gasoline | 1400–2500 |
| Naturally aspirated diesel | 700–1000 |
| Turbocharged diesel | 1400–2000 |
| Racing (F1, high boost) | 3000–4000 |
Specific power (power density):
P_specific = BMEP × V_d × N / (2 × 60,000) [kW/L]
High-output: > 100 kW/L (turbocharged gasoline); diesel: 50–80 kW/L
Brake Specific Fuel Consumption (BSFC)
BSFC = fuel_mass_flow / power:
BSFC = ṁ_fuel / P_brake [g/kWh]
Typical values:
| Engine type | BSFC [g/kWh] |
|---|
| Naturally aspirated gasoline | 250–280 |
| Modern DI gasoline | 230–260 |
| Turbocharged diesel | 200–230 |
| Diesel heavy-duty (best) | 175–195 |
| Gas turbine | 300–400 |
Relation to thermal efficiency:
η_brake = 3600 / (BSFC × LHV_fuel/1000) [LHV_gasoline ≈ 43,600 kJ/kg; LHV_diesel ≈ 42,700 kJ/kg]
BSFC = 200 g/kWh diesel: η = 3600/(200×42.7/1000) = 3600/8540 = 42.2%
Volumetric Efficiency
η_v = actual air mass / ideal air mass:
η_v = ṁ_air / (ρ_ambient × V_d × N/2) [for 4-stroke; N/2 = cycles per second]
Typical: 0.80–0.90 (naturally aspirated); > 1.0 (supercharged/turbocharged)
Factors affecting η_v:
- Valve timing (cam profile; VVT improves ηv across speed range)
- Port flow coefficient (C_d of intake valve; 0.3–0.7 depending on lift)
- Charge heating (hot intake runner → density drop)
- Back-pressure (exhaust restriction)
Bore-Stroke Ratio
Square engine: bore = stroke → balanced between breathing and friction
Over-square (short stroke): bore > stroke → better valve area / displacement; lower piston speed → high revving; less friction
Under-square (long stroke): stroke > bore → higher BMEP (longer moment arm); better low-speed torque; limited by piston speed
Mean piston speed:
v_p_mean = 2 × stroke × N / 60 [m/s; N in RPM]
Limit: v_p ≤ 12–15 m/s (production); 25 m/s (racing)
Bore-stroke ratio (B/S):
Production gasoline: B/S = 1.0–1.2 (slightly over-square)
Racing: B/S = 1.3–1.5 (over-square; high rev limit)
Diesel: B/S = 0.9–1.1 (near-square or slightly under-square)
Valve Timing
4-stroke timing events:
IVO = intake valve open; IVC = intake valve close; EVO = exhaust valve open; EVC = exhaust valve close
Valve overlap: IVO-EVC region; enhances scavenging at high RPM; increases HC at idle
Optimal IVC for maximum power:
IVC_optimal = ABDC 50–80° (after BDC): Intake charge inertia continues after BDC → ramscharging
VVT (Variable Valve Timing): advance/retard cam → optimize IVC for each RPM → wider power band
Valve lift and flow:
C_d = flow coefficient (bench-tested); A_throat = π/4 × D_v² × sin(30°) × L_v / D_v (curtain area approximation)
Mass flow: ṁ = C_d × A × (ΔP_throat) × √(2ρ/ΔP) [limited by choked flow at high lift]
Combustion Analysis
Indicated mean effective pressure (IMEP):
IMEP = ∫ P dV / V_d [kPa; from measured P-V diagram]
FMEP = friction mean effective pressure ≈ IMEP - BMEP
PMEP = pumping mean effective pressure ≈ -∫P dV (exhaust-intake)
Friction estimation:
FMEP ≈ a + b × v_p + c × BMEP [empirical Heywood correlation; a, b, c from data]
FMEP_motored ≈ 60 + 0.6 × v_p + 0.005 × BMEP [kPa; rough estimate]
Combustion phasing:
CA50 (crank angle of 50% heat release): optimal for η at CA50 = 5–10° ATDC
MBT (minimum spark advance for best torque): determined by CA50 target
Knock: auto-ignition of end gas before flame arrival; detected by vibration sensor; retard timing to prevent
Turbocharging
Pressure ratio:
PR = P_boost / P_ambient [gauge boost pressure [kPa] + 101.3 / 101.3]
E.g., 1 bar boost → PR = 2.0
Compressor map:
Corrected flow: Q_corr = Q_actual × √(T_in/T_ref) × (P_ref/P_in)
Corrected speed: N_corr = N_actual / √(T_in/T_ref)
Operating point must be within compressor map; left of surge line; below choke line
Turbine matching:
Turbine inlet T estimation: T_turbine_in = T_exhaust_manifold ≈ T_EGT = f(AFR, load, timing)
Expansion ratio across turbine: determined by exhaust back-pressure and PR_comp (waste-gated for control)
Boost response (turbo lag):
Lag ≈ rotor inertia / turbine power → reduce inertia (variable turbine geometry, twin-scroll) → faster spool
Standards
| Standard | Scope |
|---|
| SAE J1349 | Engine power test code (gasoline, diesel) |
| ISO 1585 | Road vehicles — engine test codes |
| SAE J1826 | Turbocharger nomenclature |
| DIN 70020 | Engine power measurement (German) |
| ISO 3046 | Reciprocating internal combustion engines |
Output
Provide: engine type (SI/CI), cycle (Otto/Diesel/Atkinson), bore × stroke [mm], displacement V_d [L], compression ratio r_c, ideal η_th [%] and actual brake η [%], BMEP [kPa] at rated power, rated power and torque [kW, N·m at RPM], BSFC at best point [g/kWh], volumetric efficiency η_v [%], mean piston speed [m/s] vs. limit, CA50 phasing [°ATDC], FMEP [kPa] at rated speed, turbocharged (PR, boost [kPa], T_compressor_out [°C]), emission system requirements, and applicable standard (SAE J1349, ISO 3046).
