Capt Smithy:
By your method of leaning, will the resultant mixture be slightly ROP EGT since you enrich slightly after the rpm drop?
To get the best SFC, I would have to be slightly LOP EGT. So does that mean I don't enrich after getting the rpm drop?
Actually, what you would theoretically want to achieve is to run at exactly max EGT all the time. This gives the best SFC. However, because the induction system isn't 100% perfect, injectors aren't perfectly matched and you typically don't have the instrumentation to find out what's going on in each individual cylinder, peak EGT doesn't happen in all cylinders at the same time. You've got to err on the side of caution. That's where the 25/50 ROP rules comes from, to a large extent. Of course, this can only be done if you have an EGT gauge.
If all you have is an RPM then it's nearly impossible to lean accurately for best economy. On Robins, the advice I've seen is to lean until the engine no longer runs smoothly, then increase the mixture to restore smooth running. On Pipers, I've seen the advice to run with wide open throttle, then reduce the mixture until a certain RPM is reached (the table is on the pilots sunvisor, of all places). But as IO said, the fuel flow near the flat top of the engine performance curve means that finding the exact setting doesn't matter all that much. Heck, even running with an engine leaned for "best power" instead of full rich all day long will give you maybe a 25% fuel savings vs. 30% fuel savings when leaned for "best economy".
Also, I'd like to clarify on the terms "best economy" and "best endurance".
Best economy refers to a fuel/air mixture that gives optimal combustion. So to get best economy above 3,000 ft, we lean the mixture to slightly LOP EGT.
Best endurance on the other hand refers to the power setting that gives the lowest fuel flow (gallons/hr), thus allowing maximum time aloft.
Is my understanding correct?
The other thing you are confusing yourself with, is the difference between airspeed and power.
"Best endurance" and "Best range" all refer to a certain airspeed. In the first case, it refers to the absolute lowest drag airspeed (bottom of the power curve) and in the second case it refers to the best trade-off between total drag and speed (the tangent). The first thing you need to do for max performance is to know these speeds and fly them.
Second step is then to set and optimize the engine power to maintain this speed. That's where the terms "best economy" and "best power" come in. Best economy refers to the mixture setting that uses the least amount of fuel to deliver a certain amount of power. Best power referes to the mixture setting that allows you to get the most power out of the engine in the circumstances.
So in both the "best endurance" and "best range" scenarios you will want to set the power mixture to "best economy". In fact, you will want to fly at the "best economy" mixture settings in all flight conditions, with the exception of situations where maximum power is required or may be required shortly.
That's the theory at least. Practically speaking, there is an influence by the engine efficiency on the power curve, and IO540 mentioned that earlier. It's got to do with pumping losses, alternators producing electricity and so forth. You can think of this as the "parasite drag" of the engine. Because of this, by increasing the power output of the engine, engine efficiency increases. After all, more total energy is generated and since the "parasite drag" (pumping losses etc) stays more or less the same, more energy is converted into thrust.
Because of this, it may be more efficient to fly slightly faster than the airframes "best range" speed. Because at this slightly higher speed the engine works more efficiently. But the trouble is that you need to match the exact power/drag curve of the airframe with the exact fuel/power curve of the engine/propellor combination, then factor in the effect of the increased propellor slipstream onto the airframe and so forth. Generally the information to do this is not available and dependent on too many factors anyway (dirty airframe, avionics added etc.).
Your aircraft manufacturer has done testing on the airframe/engine combo, and the result of all this testing, plus all the theory behind it, is in the "performance" section of the POH. In there, with a bit of luck, you will find the best endurance and best range speed and tactics. In the real world, that information is the best you have. The theory behind it is nice to know but since you've got to match two compound (and generally unknown/unpublished) curves to arrive at the best range tactic for your specific circumstances, you can hardly call that a practical method to be used in the cockpit.