engine-breathing

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).