| name | engine-breathing |
| description | Engine breathing — volumetric efficiency, valve timing, cam profiles, intake manifold tuning, variable valve timing (VVT/VVL), scavenging 2-stroke, port flow coefficients. |
| metadata | {"priority":7,"promptSignals":{"phrases":["engine breathing","volumetric efficiency","valve timing","cam profile","intake manifold tuning","variable valve timing","VVT engine"],"minScore":3}} |
Engine Breathing — Complete Skill
Volumetric Efficiency
η_v = (mass of air inducted) / (ρ_ambient × V_displacement)
Typical values:
- Naturally aspirated gasoline: η_v = 0.80–0.90
- Tuned intake (Helmholtz): η_v up to 1.05 (ram effect)
- 2-stroke crankcase scavenged: η_v = 0.50–0.70
Factors reducing η_v:
- Heat transfer to intake charge: residual gas dilution
- Valve curtain area limitation: A_curtain = π × d_v × L_v
- Flow losses (discharge coefficient C_d = 0.60–0.80 for poppet valves)
- Friction in ports and runners
Valve Geometry and Flow
Curtain area (flow area at lift L):
A_curtain = π × d_v × L [up to L ≈ d_v/4, then seat throat limits flow]
Throat area (limits at high lift):
A_seat_throat = π/4 × (d_v² - d_stem²)
Effective flow area:
A_eff = C_d × min(A_curtain, A_seat_throat)
Mean flow velocity (Mach index Z):
Z = V_p / (C_d × π/4 × d_v² / A_valve) [should be < 0.5 for good η_v]
V_p = mean piston speed = 2 × L × N / 60
Cam Profile Design
Fundamental Cam Types
Harmonic (simple sinusoidal): smooth, low jerk; limited lift
Polynomial cam (3-4-5 or 4-5-6-7): zero velocity, accel at endpoints; standard design
Spline cam: optimized for specified constraints; best for high-rpm
Kinematic Relationships (translating follower)
y(θ) = lift profile [mm vs cam angle θ]
ẏ = velocity = dy/dθ × ω
ÿ = acceleration = d²y/dθ² × ω²
Maximum acceleration limit (spring force):
F_spring > m_follower × |ÿ|_max (no valve float condition)
Contact force: F_c = k × x - m × ÿ > 0 always
Typical Valve Event (4-stroke SI engine)
| Event | Typical timing |
|---|
| Intake open (IVO) | 10–25° BTDC |
| Intake close (IVC) | 40–70° ABDC |
| Exhaust open (EVO) | 40–70° BBDC |
| Exhaust close (EVC) | 10–25° ATDC |
| Overlap | 20–50° total |
Overlap benefits: scavenging at high rpm; penalty: rough idle, high HC at low rpm
Valve Duration and Lift (typical NA gasoline)
- Intake duration: 240–280° (performance: 280–310°)
- Exhaust duration: 235–270°
- Max valve lift: 0.25 × d_valve (rule of thumb)
- Typical: intake lift = 10–14 mm for 35mm valve diameter
Helmholtz / Intake Runner Tuning
Tuning frequency of intake runner:
f_tune = V_p / (4 × L_runner) [for open-end λ/4 resonance; approximate]
Pressure wave travel:
f = c / (4L) where c = speed of sound in intake air ≈ 340 m/s
Resonance boosts charge at f_tune → optimized for target rpm N_tune:
L_tune ≈ c / (4 × f) = c × 60 / (4 × N_tune × n_cylinder_events)
Plenum (Helmholtz resonator):
f_H = (c/2π) × √(A_pipe / (L_eff × V_plenum))
Variable Valve Timing (VVT / VVL)
Phase Shifting (Cam Phasing)
Rotates intake or exhaust cam relative to crankshaft
- Range: 40–60° crank angle authority
- Actuated by oil-pressure vane-type phaser
- Benefits: optimize overlap for rpm/load; reduce pumping loss
Variable Lift (VVL)
Honda VTEC: low-rpm and high-rpm cam lobes; rocker arm locking pin
BMW Valvetronic: eccentric shaft changes follower geometry → full range 0–10mm lift
Camless (Electrohydraulic/Electromechanical)
Fully variable event; typical prototype response < 3 ms
Industry: Koenigsegg Freevalve; Lotus
Two-Stroke Scavenging
Loop scavenging (Schnürle): transfer ports direct flow up opposite side, exhaust port on same side
Uniflow: transfer at bottom, exhaust valve at top; best scavenging efficiency
Scavenging efficiency:
η_sc = (fresh charge retained) / (total cylinder charge)
Trapping efficiency:
η_tr = (fresh charge retained) / (total fresh charge delivered)
Delivery ratio:
Λ = delivered charge mass / (ρ_ambient × V_displacement)
Well-designed loop: η_sc = 0.75–0.85; η_tr = 0.65–0.80
Port Flow Testing (Steady-State Flow Bench)
Discharge coefficient C_d:
C_d = Q_actual / Q_theoretical = ṁ_actual / (A_port × √(2ρΔP))
Flow coefficient C_f:
C_f = Q_actual / (V_p × π/4 × d_bore²)
Standard test: ΔP = 25 inH₂O (6.23 kPa) across valve/port at each lift increment
Record C_d vs L/d_valve curve
Port flow number:
FN = CFM / (0.2576 × d_bore² × stroke^0.5 × lift^0.5) [Reher-Morrison form]
Exhaust System Tuning
Primary pipe diameter:
d_pipe = 1.15 × d_exhaust_port (general rule)
Primary pipe length (tuned for extraction):
L_primary = (850 / N_rpm) × [(EVO_degrees - 180)/360 + 0.5] × stroke [rough]
Collector: 3:1 or 4:1 merge; increases exhaust pulse extraction
Muffler back-pressure: target < 0.1 bar to prevent η_v loss
Output
Provide: η_v [%], mean piston speed V_p [m/s], Mach index Z, recommended valve lift [mm], cam duration [°], intake runner length L_tune [mm] for target rpm, VVT phaser authority [°CA], port C_d at max lift, overlap angle [°], and relevant diagnostic (valve float rpm limit).
