Cruise load - best lambda in aim of efficiency

I have been trying to figure out the best lambda in aim to minimize cruise load fuel consumption. Several research papers indicate a 1.12 as the optimum, while many repeat/reference the Lambda of 1.05

Have you done a test on dyno in order to determine the best lambda / ignition timing in aim of best economy ? like graphing lambda as X axis and Torque*Lambda (or Torque/Fuel_flow) as Y ? the bigger the value in Y the more efficient the engine is. (less fuel per Nm produced)

I'm asking as beyond lambda 1.0 assuming complete combustion, the engine power is governed by the fuel injected and not by the available air. The less fuel there is the less energy / torque we will get. Also lean mixtures burn slower so more advance might be needed.

yes we would need more air for same torque, but if that torques is produced by this increased energy it should still be lower consumption.

I know fuel consumption is not primary focus on any High performance boosted etc engine but on a street ("daily") car with ever increasing fuel prices.....

I think you've got the gist of it.

An IC engine doesn't run on the fuel, as such, but on the expansion of the gases in the cylinder - the fuel heats the ~81% of the unused air and the combustion by products, CO2 and H2O, which apply the force to the piston.

As you clearly understand, you are balancing the fuel burned for heating against the torque/power for each unit of fuel used.

However, every engine is going to be different. There are several factors, such as combustion characteristics, fuel mixing/percentage at the spark plug, camshaft(s) timing, heat rejection from the gas into the cylinder walls, head and piston.

Some things, like the heat rejection, you can help by running the engine at higher coolant temperatures - you may have noticed more modern engines will have thermostats 20C, or more, higher than those used on older engines, for economy. This is also part of the reason for pre-heating the intake air at light throttle, along with better atomisation of the fuel.

The best thing is to test on a braked rolling road or hub dyno, but if your vehicle has a fuel consumption readout you could try road tuning with different lambda's/AFR's and timing to see what gives the lowest cruise consumption - if the vehicle has a cruise control, it's even easier.

Sometimes this is referred to by terms like "Mean Best Power", "Mean Best Torque", "Mean Best Cruise", etc.