===== Lambda (λ) =====

**Lambda (λ)** represents the //air-fuel ratio// in combustion engines relative to the stoichiometric ideal. Calculated as \( \lambda = \frac{\text{Actual Air-Fuel Ratio}}{\text{Stoichiometric Ratio}} \), this dimensionless value is critical for engine management and emissions control.

=== Stoichiometric Principle ===  
The optimal λ value is **1.0** (14.7:1 air-fuel mass ratio for gasoline), where all fuel completely burns with available oxygen. This balance maximizes catalytic converter ([[CAT]]) efficiency while minimizing emissions.

=== Petrol vs. Diesel Optimization ===  
Fundamental differences in combustion create distinct lambda requirements:

| Engine Type | Optimal λ       | Operating Principle                | Key Constraints                 |
|-------------|-----------------|-----------------------------------|---------------------------------|
| **Petrol**  | 1.0 (precisely) | Stoichiometric combustion         | Three-way catalyst efficiency   |
| **Diesel**  | 1.4 - 4.0       | Always lean (excess air)          | Soot formation limits           |

**Petrol Engines**:  
  * Require precise λ=1.0 for three-way catalysts to simultaneously reduce NOx, CO, and HC  
  * Temporary rich operation (λ≈0.8-0.9) only during high load for knock protection  
  * Lean operation (λ>1) limited to specific low-load conditions  

**Diesel Engines**:  
  * Minimum λ≈1.4 at full load (prevents visible smoke)  
  * Idle λ≈4.0 (maximizes air for complete combustion)  
  * Require complex aftertreatment (DPF+SCR) due to oxygen-rich exhaust  

=== Measurement & Control ===  
Modern engines use **wideband oxygen sensors** for real-time λ monitoring. The engine [[control-unit]] adjust fuel delivery up to 100 times/second to maintain target lambda based on:
  * Engine temperature
  * Load demands
  * Emissions requirements
  * Aftertreatment status

=== Application Examples ===  
* **Petrol cold start**: λ≈0.9 (rich for catalyst heating)  
* **Diesel regeneration**: λ<1.5 temporarily (raises exhaust temperature)  
* **Hybrid engines**: λ>1.0 during electric-assist phases  

''Lambda management remains critical for meeting Euro 7/[[ULEV]] standards, with petrol-diesel differences driving distinct emission control strategies.''