1. Lambda Calculation from Exhaust Gas Measurements
Determining how close the A/F ratio is to the stoichometric point using exhaust gas analysis.
Presented to East Bay ATA, Hayward, CA
May 5, 2004
By: Robert J. Schrader President, Bridge Analyzers, Inc.

2. What is Lambda?
Lambda is Oxygen Balance

3. Why is Lambda Important?
Lambda control is necessary for peak combustion efficiency in the Engine.
Lambda control is necessary for peak CAT efficiency.
Lambda Control Improves Reliability, Fuel Economy and Lowers Emissions.

4. Combustion Efficiency (CE)
Engine out CE for Gasoline Fuel is no better than 95%.
Tailpipe-out CE for CAT equipped vehicles improves to %.
Factor of 10 improvement
Required for Current Emission Standards
CAT CE is very Lambda-Dependent

5. Engine-Out Gas Values

6. CAT Oxidation and Reduction Efficiency vs Lambda

7. CAT Out Gases

8. 3-Way CAT vs Lambda NOx Reduction Bed CO/HC Oxidation Bed
Requires Lambda to be not greater than
CO/HC Oxidation Bed
Requires Lambda to be not less than
Modulation Depth
Cycles Rich and Lean Between the Limits Above.

9. Brettschneider Equation a balance equation that calculates Lambda

10. Calculating A/F Ratio from Lambda
Lambda = when the Oxygen available and Combustible Oxygen demands are in balance.
This is the point of perfect stoichometric balance.
At this point the A/F ratio is to 1.00 for Gasoline.
Thus, A/F = x Lambda

11. Sensitivity to Combustion Efficiency (Pre CAT vs Post CAT)
Brettschneider Lambda uses all the oxygen-bearing and combustible-bearing gases.
Balance Equation - Calculation not affected by the degree of oxidation.
Method is insensitive to combustion efficiency.
Either Pre-CAT or Post-CAT gases may be used.

12. Lambda for Emissions Control
 = when Oxygen available and Combustible demands are in balance.
ECM controls =1.000 at Cycles/Sec using ‘lambda sensor’ input.
3-Way CAT operation requires   to 1.020
Lambda can be confirmed by exhaust gas measurement, either pre or post CAT.

13. Lambda for Fuel Control Diagnostics
 calculated from exhaust gas indicates air-fuel mixture independent of the engine controls.
 calculated from exhaust gas indicates air-fuel mixture independent of combustion efficiency.
Cold (Open Loop) vs Hot (Closed Loop) vs CAT light-off operation can be evaluated.
 can be used to tune systems which do not have closed-loop control.

14. Qualifying EGA gas tightness prior to Lambda Calculation
High Combustion Efficiency: Measure O2 post CAT - every 5% air leak adds 1.0% O2 to gases.
Low Combustion Efficiency: Add CO and CO2 - should equal 15% for Gasoline.
Compare both Methods. If O2 indicates air dilution - then confirm this with low CO and CO2 sum. They should agree.

15. iATN Lambda Calculator
Created by iATN Tech Support staff, and available to iATN members on-line at
Plug and Play either 4 or 5 gas values.
Can select either US or European gasoline constants.
Operates in Java - can be saved and run off-line by any Java-equipped net browser.

16. Bridge Excel Worksheet
Available as attached Excel file by contacting:
Plug and Play either 4 or 5 gas values.
Can select either US or European gasoline constants.
Operates on any PC with Excel - can be saved and run off-line using Microsoft Excel.

17. iPaq Palm Computer Worksheet
Written by Miles Wada using the Brettschneider equation - a’la Bridge.
Available for download at:

18. Palm Computer Worksheet in Excel.
Written by Greg Meyer using the Brettschneider equation - a’la Bridge.
Available from Greg via at:
Operates on Microsoft PC in Excel.

19. A/F Ratio From Lambda
A/F = x Lambda

20. Case Study September 1993 Mazda Protege 1.8L, Manual Trans, No EGR
Failed Smog Check for Timing (FA99), GP HC & NOx
This case scenario illustrates the effectiveness of the lambda calculator especially for NOx diagnostics
September, this 1993 Mazda Protege failed its Smog Check inspection for the following:
High hydrocarbons (HC)
NOx levels in excess of Gross Polluter levels
Ignition timing un-checkable

21. Initial Failing Inspection (GP)
ASM 5015
Result HC CO
CO2 NO O2
RPM GP
247
0.49
13.8
2000
1.2
1624
Standards
Fail 92
0.55
716
281
2.05
1,961
AVG 21
0.06
150

22. NOx Case Scenario Lambda Calculator
Running the 5-gas readings through the Lambda calculator reflects a reading of This reading exceeds the maximum desirable lean reading of meaning the vehicle’s air/fuel ratio is too lean.

23. Case Study November 1993 Mazda Protege 1.8L, Manual Trans, No EGR
Failed its Pre-repair Baseline Inspection at a CAP station for for Timing (FB48), HC & NOx
Same car, approximately 1 ½ months later.
It’s not known what, if any repairs or adjustments were made to the vehicle
The vehicle is now failing Smog Check for high HC & NOx and ignition 45° btdc

24. Pre-repair Baseline (GS)
ASM 5015
Result HC CO
CO2 NO O2
RPM
Fail
186
0.43 16
1095 1
1683
Standards 92
0.55
716 GP
281
2.05
1,961
AVG 21
0.06
150

25. NOx Case Scenario Lambda Calculator
Running the most current 5-gas readings through the lambda calculator shows an improvement from 1.036, but the final readings are still higher than the desirable maximum lean reading of
NOTE: 16% CO2 suggests a new catalyst. Most catalyst equipped vehicles produce 14.5 – 15.5% CO2. New catalyst often put out higher amounts due the lack of any contaminants. Contaminants can shield the catalyst materials from the exhaust reducing the converter’s efficiency.

26. Case Study December 1993 Mazda Protege 1.8L, Manual Trans, No EGR
Passed & Certified
A few days later a Gold Shield station found the intake manifold was leaking air by using a smoke machine. The vacuum leak was repaired and the ignition timing returned to manufacturer’s specifications

27. Post Repair Certification
ASM 5015
Result HC CO
CO2 NO O2
RPM
Pass 74
0.21
15.5
308
0.08
1590
Standards
Fail 92
0.55
716 GP
281
2.05
1,961
AVG 21
0.06
150

28. NOx Case Scenario Lambda Calculator
Final lambda readings are well within desirable ranges. After repair lambda readings along with a passing Smog Check suggest effective NOx diagnostics and repairs.