I teach the method for leaning as specified in the engine manufacturer's operator's manual which is often partially copied into the AFM / POH.
If you fly with a Lycoming then this is essential reading;
http://www.lycoming.textron.com/supp...Operations.pdf
I am in agreement with Cows getting bigger regarding
agressiveleaning on the ground. This must be agressive to prevent full power being set with a lean setting. In this regard it is a good exercise to taxi the aircraft using the mixture to adjust the RPM (fixed prop)while also maintaining a smooth operation.
Very few pilots will have ever read the Engine Operating Manual for their aircraft. This is the first big mistake.
The second one is that few if any schools ask that the aircraft is operated at a particular power setting in the cruise. They frequently ask that the aircraft is cruised at 2400 RPM (fixed pitch prop) or 23" / 2300 RPM (VP prop) and ignore the fact that the power output at those figures will vary from both day to day and from one altitude to the next.
Lycoming recomends that the engines are operated at 65% or less and give excellent instructions on how to lean for both Best Power and Best Economy. The AFM/POH will specify fuel flow for various cruise (pressure) altitudes at 65% power with either best economy or best power leaning.
Unfortunately, if you ask an instructor what RPM they are going to use to get 65% power at 3000ft QNH 993 and ISA -10 they will give you a very blank look. They simply use 2400RPM but don't know what that gives and therefore have no idea of what the fuel consumption should be.
A number of years ago a pilot flying a C172 with 3 pax got his fuel sums a little wrong and realised that he was getting somewhat low on his return leg. He therefore slowed down to what he thought was the speed for maximum range and leaned out his engine as much as he could (2000'). He made it home - just and the following day the aircraft was found to be unable to develop its normal static full power R.P.M. The licensed engineer arrived and discovered that five out of six cylinders were cracked due to being overheated. An expensive bill for the owners!
Can't comment on the Continental powered 172 - would have to look at the continental engine manual. However, if it was the bog standard Lycoming 4 cylinder version that was in use as above, Lycoming would clearly refer you to their publication above which dismisses the posibility of leaning being a cause of such damage at low power settings.
Such damage is more likely to be caused by shock cooling and was probably already there prior to the flight and the extra fuel consumption being a good possible indication.
I can tell you from experience that pilots do damage club engines by excessive leaning. They hire the aircraft at £x per hour (take-off to landing + 10 minutes) including whatever fuel they happen to burn. What they do is fly at very high power settings to reduce the flight time (on which they are billed) as much as possible and then lean the mixture to prevent the excessive fuel burn being noticed. Since most clubs don't have that accurate a fuel burn figure they get away with it. The engines don't meet their full life and the report from the overhaul shop cites over leaning and the school bans leaning. But people still do it anyway!!
Operate the engine in the cruise at 65% or less and Lean as per the engine manufacturer's instruction (best economy or best power) and you will a) have a long engine life and b) get very close to the published fuel burn figures if you keep accurate records.
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PS
Most of the "don't lean" / "leaning will damage the engine" instructions come from training organisations. They often have stories about how they had engines damaged by excessive leaning.
They seem to ignore that on a regular basis the aircraft cruises for 10 minutes after departure and sudenly the throttle is closed, the engine idles (with a few brief demands of high power) for 5 minutes then operates at max power for 5 minutes which is followed by a brief cruise and again the throttle is suddenly closed. This is repeated several times per hour and the exercise happens daily sometimes and often more than once a week. But they blame leaning for the engine not reaching it's recommended number of hours before overhaul.
Lycoming don't design an engine for training in PFL's or Stalls or EFATO and are adamant that shock cooling is to be avoided. They even specify a maximum rate of cooling. Ignoring this is what breaks engines.