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So auto-rich/auto-lean wasn't about covering altitude but simplifying the amount of fuel/air ratio adjustments for the different conditions of flight?Most aero engines have mixture adjustment to accommodate changes in mixture required due to change in altitude. The main issue is that engines require a range of ratios of mass of fuel to mass of air. Carb venturis work by feeding fuel into the air stream based on density and velocity. With changing altitude, both the mass of air and volume of air reduce however the rate of change is different between them. Thus the required mixture strength needs to change with altitude. [I'm not explaining this well, can someone jump in and help out.]
The auto-rich and auto-lean was implemented to provide a very simple method for the pilot to select an appropriate mixture for the current flight phase.
Auto-rich was for take-off, climb and combat. It provided a suitable mixture strength for high power operation and sufficient detonation margin. The downside was high fuel consumptions. Roughly best power on the figure below.