Leaving aside the claimed pros and cons of lean-of-peak (LOP) vs. rich-of-peak (ROP), the C172S Lycoming IO-360-L2A handbook I have says "Continuous operation at mixture settings lean of peak EGT is prohibited", and indeed I was always taught to run the engine ROP.
Obviously you should always follow the POH for your aircraft, but considering piston engines in general, why would running LOP be prohibited?
Considering piston engines in general there's a few reasons not to run "lean of peak", but the arguments I'm aware of all fall into three broad categories:
Poor Instrumentation
Most folks advocating Lean-of-Peak engine operation will also tell you that you need a good engine monitor (with Exhaust Gas Temperature (EGT) and Cylinder Head Temperature (CHT) probes for each cylinder) so you can ensure that all your cylinders are operating within safe temperature limits.
Manufacturer CHT/EGT systems are often "single-probe". On the IO-360 in your Cessna example that leaves you with a 3 cylinder blind spot in your monitoring, and the potential risk of damaging your engine based on the incomplete information you have.
Uneven mixture distribution
Some engines simply can't run lean of peak because of uneven mixture distribution: Either the engine will get rough as some cylinders "miss", or you'll have some cylinders lean of peak EGT and at a safe cylinder head temperature while others are redlining their CHT and potentially causing damage to your engine.
This sort of uneven mixture distribution happens frequently in carbureted engines, but there are many injected engines which also have poor fuel distribution & significant variation in mixture between cylinders (This is where GAMIJectors makes their money - by providing balanced injectors to even out fuel distribution).
"In Case Something Breaks"
Hypothetical scenario: you are cruising at 8000 feet, you've leaned for cruise, and your mixture control suddenly fails in such a way that your engine is stuck at the current mixture setting. All the airports within your endurance range are roughly at sea level.
An engine running lean of peak may begin to run rough as you descend for landing (the mixture becomes too lean to support combustion). An engine running rich of peak may continue to run acceptably through the descent. (The mixture may transition into "the red box zone" where operation at high power settings are dangerous, but you'll theoretically be reducing power for your descent, so the chance of doing damage to your engine isn't that high unless you have to perform a go-around or other high-power maneuver.
A prohibition on Lean-of-Peak operation in your POH is probably historically based on #1 or #2 above -- the manufacturer doesn't want to advise you to do something that might damage your engine. Running Rich-of-Peak is conservative operating guidance, where the downside is slightly increased fuel consumption and the possibility of fouling a spark plug (which is not likely at normal operating power settings) versus the downside of potential engine damage from improper Lean-of-Peak operation.
The most direct answer to your question has little to do with physics and a lot to do with a typical pilot's understanding of how a piston engine works. The manufacturers specify ROP because it's "easy." Most pilots (myself included, over the course of 2900 hrs of flying) were not exposed to the whys of proper engine operation during training. We were all taught the "LOP = burned valves" which simply isn't true. The manufacturers compensate for this lack of understanding by oversimplifying engine operation directions to keep us safe from ourselves.
Contrary to popular belief, LOP is not bad for piston engines. What is bad is mixture setting within what is commonly referred to as the "red box." Running LOP safely requires you to lean further than what most standard fuel injectors can support. Leaning with unbalanced ("standard") injectors will eventually lead to a rough running engine that would otherwise run just fine ROP. This is where Gami or Continental balanced injectors become necessary. They are precision injectors that allow you to lean far enough LOP while still delivering even amounts of fuel to each cylinder to keep the engine running smoothly (oversimplified). Google "mixture setting redbox" to get started. Note that you can be ROP and still inside the red box. ROP alone is no guarantee that you're running the engine properly.
There is a TON of research out there that will lead you to the conclusion that LOP is not bad when set properly (just as ROP is fine when set properly). In fact, in most cases the engine will run cooler and cleaner LOP than an identical engine run ROP. Mine does.
I strongly recommend that you read the following several times:
Pelican’s Perch #63: Where Should I Run My Engine? (Part 1)
Pelican’s Perch #64: Where Should I Run My Engine? (Part 2 – The Climb)
There is a third article in the series but the site won't let me post it...need more reputation!
(edit: Pelican’s Perch #65: Where Should I Run My Engine? (Part 3 – Cruise)) +
(edit: Pelican’s Perch #66: Where Should I Run My Engine? (Part 4 – Descent))
I fly my IO-520 LOP in cruise (waaaay ROP in the climb) and see about 1.5gph savings compared to my POH fuel burn. It costs three or four knots but that's a fair trade! My 1470 hour Continental clyinders hold great compression and I burn very little oil. I use an EDM700 engine monitor and Gamis. Do not be afraid of LOP, just learn how to do it correctly!
Happy flying!
Another poster already linked to 2 articles from the "Pelican's Perch" series. Although this discussion is 4 years old, I'd like to add the 3rd link that acpilot probably wanted to post:
https://www.avweb.com/features_old/pelicans-perch-18mixture-magic/ This article can be seen as a prequel to the other two, starting with the basics and later making the points for running LOP:
Money Quote:
For high power, maximum-performance operation, you should run richer mixtures and higher RPMs. For low power, maximum-efficiency operation, you should run leaner mixtures and lower RPMs.
Deakin answers OP's question implicitly in this article supposing engine manufacturers wanted to be on the safe side (emphasis by me):
It appears to me that running in accordance with the POH will provide good results in the worst possible cases, and TCM probably felt this was their best option.
This and the other two articles convinced me back in the day to fly LOP (on an IO 360 A1A, EDM 700 monitor, fuel flow meter). That gave me a smooth cruise with ~ 10% less fuel consumption.
FWIW, I read all of John Deakin's articles on AVweb and highly recommend them. They provide great insight from a aviation veteran - sometimes grudgy but mostly substantiated with sources as far back as the Wright Co.
The lyc O-320 happens to be prone to exhaust valve guide wear. Heat accelerates wear. Running LOP generally causes the exhaust valve to run hotter than running ROP and wear out much faster.
In an ROP environment, the extra fuel that is not burnt lands on many of the top end components including the exhaust valve. As it evaporates off the surface or out of the fuel/air charge, it cools the component or charge slightly (kinda like water evaporating off your skin cools it down). May not sound like much, but it makes a big difference in the rate of wear of top end components.
The EGT at 50d ROP is exactly the same EGT @ 50 dF LOP. The same temperature. It is not cooler at LOP or warmer at ROP. The CHT at EGT of 50d ROP is significantly higher than the CHT at EGT of 50 dF LOP. No LOP operation can harm the cylinder being monitored,as the ICP and the CHT is always lower at any time during LOP operations.
Running too far lean of peak is bad for the engine. That's easy to do if the mixture isn't precise enough, or if you descend and forget to adjust the mixture. If there's not much leeway in a particular engine or if the engine is susceptible to damage from running a little too far lean of peak, the manufacturer will prohibit the practice.
