Air-Fuel Ratios by Marco Alsterfalk

In this article Marco Alsterfalk of the Swedish tuning company www.MTE.se explains issues such as the fuel enrichment effect on high load operating points, definition of knock, the fundamentals of knock, what the optimum lambda is and how the knock limit and indicated mean effective pressure (imep) are affected by variations in lambda.

April 2010


I am a Volvo enthusiast, and have a sound education together with many years of experience as a professional in the field of Internal Combustion engines (IC engines), and Engine Management Systems (EMS). I hold two masters (M.Sc.) degrees in these fields - one from the Royal Institute of Technology, Stockholm, Sweden (Vehicle dynamics & Internal Combustion engines), and one from the University of Michigan, USA. (Internal Combustion engine & advanced control systems) I have worked within the field of Internal combustion engines for about 15 years and have experience from several vehicle manufacturers including Volvo, Saab Automobile, Porsche AG and Ford Motor Company, to name a few.

I want to help performance enthusiasts make sound choices of performance products. I am well versed with this field of science and, hence, can shed some light on some common, but important topics. I do believe that enthusiasts, who may not always have the same level of in-depth knowledge in this specific field of IC engines and Engine management systems, are often misled by profit searching parties who themselves may have limited knowledge in the field. This may possibly occur because the majority of enthusiasts do not have the ability to professionally judge the information given and merely take it on the assurances of the party giving the information.

In many cases, with the best intentions, enthusiasts share what they heard from someone, who in turn heard from someone, who knows a guy at "the manufacturer" etc. Information is easily distorted and misinterpreted when passed on this way. There are also inevitably those who will purport to be "the one who knows" though unfortunately in some cases they may not, and this leads to further confusion. Naturally, I do not know everything in the field of IC engines, but as they say, the more you learn the more one realizes how little one knows. I am setting out to lay the bare facts, so anything I come to contribute will be well grounded. I do own a business that develops software for the vehicle industry and specializes in performance oriented applications, and have been involved in the tuning of Volvos for about 10 years. I simply want to help raise the common knowledge among fellow enthusiasts, by helping them make sound decisions when refining their cars, and possibly be able to better judge statements made by other people. Unfortunately my time for this cause is limited, but I will try my best to clarify some of the pertinent issues.

Fuel Enrichment Effect on High Load Operating Points


The lambda for maximum power (actually imep - indicated mean effective pressure) given a fix ignition angle and fix engine speed will vary slightly from application to application but occurs in the range lambda 1 to slightly rich of 0.9 (Air Fuel Ratio - AFR 14.7 to 13.2). Normally imep peaks slightly lean of lambda 0.9. Above Lambda = 1 (AFR 14.7) imep will decay quickly as lambda increases, below 0.9 it will decay slightly as lambda decreases. To make a sound choice of which lambda to run one has to consider thermal limits of the combustion chamber- and exhaust components, as well as knock limits. If the operating point is not critical with respect to knock, or with respect to excessive thermal stress on exposed components the lambda to run is close to 0.9 as mentioned before. This is because at this lambda the maximum number of oxygen molecules will take part in combustion. Adding more fuel than this portion at the given conditions will not give more power because there are no more oxygen molecules available. Any additional fuel added will flow through the engine unburned, but will absorb heat during compression and combustion giving a cooling effect.

The Definition of Knock


Knock is defined as detonation of the fuel-air mixture and is a very rapid process (almost instantaneous - the flame front spreads at roughly 1800 m/s). During normal operation, the fuel-air mixture in a Spark Ignition (SI) IC engine burns progressively (the flame front is propagating at about 25 m/s) rather than detonates. If the fuel-air mixture detonates the dissipated heat is so intense that no material used in IC engines today can withstand it. This is the reason for knock being dangerous. Had there been materials that could withstand such heat, then a detonating engine would be the ideal engine from an efficiency point of view. But that is a completely different issue which is far too detailed to be discussed in sufficient depth at this point in time.

The Fundamentals of Knock (Detonation)


The scenario an SI IC engine goes through as it is pinging (detonating) is normally as follows: as the air-fuel mixture is ignited at the spark of the sparkplug a flame front starts to propagate through the combustion chamber like a growing ball of fire. Naturally, behind the flame front there will be burned gases and in front there will be unburned gases. As the fuel-air mixture burns heat is released. As the gas temperature increases, so will the pressure. The laws of physics dictate that the pressure spreads instantly. Hence the unburned fuel will be exposed to the same pressure as the burned, and as the pressure of the unburned gases increase so will its temperature. If the temperature becomes too high the unburned gases will self ignite and this results in combustion occurring with one instantaneous bang - this is detonation a.k.a. knock.

So whether an engine knocks or not is dependent on whether the flame front consumes the last of the unburned gases before it self ignites. If it doesn't the knock limit is exceeded.The knock sensitivity naturally will increase if there are sharp edges in the combustion chamber that becomes hotter than the average combustion chamber surface. If the knock limit of the application is reached what needs to be done is find a way to cool the unburned air-fuel mixture to give the flame front the time it needs to reach the last of the unburned gases. Examples are to add extra fuel, or add some other liquid (e.g. water, as in water injection), retard ignition to decrease the effect of the piston's upward movement on pressure and hence temperature etc. Any way to cool the unburned gases in front of the flame front will decrease knock sensitivity.

Some Facts


I would like to introduce 3 important facts at this juncture:

  • The knock limit at high load with respect to ignition advance in practice lies at an ignition angle much later (retarded) than the optimum ignition angle for the engine speed and application at hand. By optimum, I refer to the ignition angle that would produce maximum imep / torque, if knock did not exist.
  • The torque (imep) of an engine doesn't decrease much as lambda is decreased beyond 0.9 (within reason of course, say above 0.7).
  • In addition, the knock limit of an air-fuel mixture increases significantly as lambda decreases.

These three facts collectively imply that there is power to be gained by richening the mixture beyond lambda 0.9 and then utilizing part of the increased knock limit to advance spark and in this way produce more power.

What Is the Optimum Lambda?


Well, it depends on what you are optimizing for - power, durability (thermal component protection) or fuel economy or a compromise thereof. In real life this should to judged from application to application, and it also depends on which of the limits is reached first: thermal stress, knock limit, or the mechanical stress limit? Which of these bad things is the most important to avoid? For private persons increasing the performance of their cars, the most devastating thing that can happen is usually a breakdown of the engine internals because of the expense it implies. Therefore the sound decision is often "better safe than sorry", so with the knowledge above one realizes that when optimizing for power it is, in some cases, possible to make a safer and yet more powerful approach than blindly going on the said to be perfect lambda of 0.9 or 0.85 or what ever. The sound path is the one that takes into account the complete application at hand and optimizes it for its purpose.


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