Lambda Calculation from
Exhaust Gas Measurements
Determining how close the A/F ratio
is to the stoichiometric point using
exhaust gas analysis.
Presented to East Bay ATA, Hayward, CA
May 5, 2004
By: Robert J. Schrader President, Bridge Analyzers, Inc.
What is Lambda?
• Lambda is Oxygen Balance
Oxygen available
 (Lambda)  Combustibl
es demand for Oxygen
Lambda is the ratio of O2 available to the Combustion Process vs the
Combustibl e Demand for O2 to attain complete oxidation.
Lamdba is equal to 1.000 when O2 and Combustibl e Demand for O2
are in balance - the perfect stoichomet ric point.
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.
Combustion Efficiency (CE)
• Engine out CE for Gasoline Fuel is no
better than 95%.
• Tailpipe-out CE for CAT equipped vehicles
improves to 99.0-99.5%.
– Factor of 10 improvement
– Required for Current Emission Standards
– CAT CE is very Lambda-Dependent
Engine-Out Gas Values
16.00
15.50
15.00
% Concentration
14.50
14.00
CO2 - Ca rbon Diox ide
13.50
13.00
12.50
12.00
11.50
11.00
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
1.01
1.02
1.03
1.04
1.05
1.03
1.04
1.05
1.06
1.07
1.08
1.09
1.10
La mbda
4.00
3.50
3.00
% Concentration
2.50
2.00
CO - Ca rbon Monox ide
1.50
O2 - Ox yge n
1.00
0.50
H2 - Hydroge n
0.00
0.90
0.91
0.92
0.93
0.94
0.95
0.96
0.97
0.98
0.99
1.00
La mbda
1.01
1.02
1.06
1.07
1.08
1.09
1.10
CAT Oxidation and Reduction
Efficiency vs Lambda
100%
90%
80%
70%
Reduction Efficiency
60%
50%
Oxidation Efficiency
40%
30%
20%
10%
0%
0.950
0.960
0.970
0.980
0.990
1.000
1.010
1.020
1.030
1.040
1.050
CAT Out Gases
0.50
1000
0.45
900
0.40
800
0.35
700
0.30
600
0.25
500
CO - Carbon Monoxide
0.20
400
0.15
300
NOx - Oxides of Nitrogen
0.10
200
H2 - Hydrogen
0.05
100
0.00
0
0.950
0.960
0.970
0.980
0.990
1.000
1.010
1.020
1.030
1.040
1.050
3-Way CAT vs Lambda
• NOx Reduction Bed
– Requires Lambda to be not greater than 1.020.
• CO/HC Oxidation Bed
– Requires Lambda to be not less than 0.980.
• Modulation Depth
– Cycles Rich and Lean Between the Limits
Above.
Brettschneider Equation
- a balance equation that
calculates Lambda
Oxygen available
 (Lambda)  Combustibl
e demand for Oxygen
Lambda is calculated as the ratio of Oxygen available (as O2) to the
combustibl e demand for O2 to attain complete oxidation.
Lambda is equal to 1.000 when O2 and Combustibl e demand are in balance
- the perfect stoichomet ric point.
Calculating A/F Ratio from
Lambda
• Lambda = 1.000 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 14.71 to 1.00 for
Gasoline.
• Thus, A/F = 14.71 x Lambda
Sensitivity to Combustion
Efficiency
(Pre CAT vs Post CAT)
• Brettschneider Lambda uses all the oxygenbearing 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.
Lambda for Emissions Control
•  = 1.000 when Oxygen available and
Combustible demands are in balance.
• ECM controls =1.000 at 0.5-1.0 Cycles/Sec
using ‘lambda sensor’ input.
• 3-Way CAT operation requires   0.980 to 1.020
• Lambda can be confirmed by exhaust gas
measurement, either pre or post CAT.
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.
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.
iATN Lambda Calculator
• Created by iATN Tech Support staff, and
available to iATN members on-line at
http://members.iatn.net/tech/lambda.html
• 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.
Bridge Excel Worksheet
• Available as email attached Excel file by
contacting: support@bridgeanalyzers.com
• 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.
iPaq Palm Computer Worksheet
• Written by Miles Wada using the Brettschneider
equation - a’la Bridge.
• Available for download at:
http://www.aeswave.com/
• Operates on the iPaq using CE Excel.
• Can operate on other CE-based units.
Palm Computer Worksheet in
Excel.
• Written by Greg Meyer using the Brettschneider
equation - a’la Bridge.
• Available from Greg via email at:
gsmeyer@attbi.com
• Operates on Palm OS computers in Excel.
A/F Ratio From Lambda
A/F = 14.71 x Lambda