Origin of the MP/RPM square rule

[Windrusher]

Is there a reasonable rationale behind the 'square rule', that the correct combination of manifold pressure and rpm for variable-speed props is that their ratio, in (inches-of-mercury x minutes per rev) is ~1/100 ? Let me pre-empt helpful comments that it ain't necessarily exactly 1/100 - it's bound to be aircraft specific and a happy accident of how the units are defined. But there seems to be much less variation than there usually is in rules of thumb, which often suggests a simple truth behind it all.
I'm also curious because, for the geared-down Rotax 912 at least, it seems to be prop rpm that fit the rule, rather than engine rpm.
Apologies for raising a rather esoteric question on a normally very down-to-earth forum, and for being an ignorant newcomer to variable-speed props.
Windrusher

[Capt Claret]

I don't know the answer but my bet goes on the "it's easy to remember" square.

[ahramin]

It's easy to remember is actually quite close. Easy not to screw up is even better.

Basically if your MP is never more than 1/100th of your prop RPM you have a very good chance of not having any detonation on any but the most worn out of engines.

The rule of thumb comes from the fact that with a variable pitch propeller it is possible to load up the engine to the point where detonation becomes likely. The square rule of thumb was designed to prevent this. However it is not necessary to follow this rule of thumb in order to be safe. Have you ever put your gas pedal in your car to the floor at a lower RPM? I do not think any of us let the RPMs on our car engines come up before we start feeding in the throttle, yet it is not often one hears pinging from a car engine and they are not designed to take the abuse that an aviation engine will (i am not referring to Rotax here).

Number one rule is to of course always stay within the limitations section of the aircraft manual. Number two rule is to follow the suggested power and prop settings from the aircraft manual. Do this and there is no need to worry about the MP/RPM square rule of thumb.

And yes, prop RPM would fit the rule better than engine RPM, but remember this is just an easy rule of thumb which was intended for regular aviation engines.

[an3_bolt]

There are some fantastic articles in the Lycoming Flyer reprints that are available for sale or to view on the web at the Lycoming site.

They do have a short article that might be of interest for your queries, regardless of engine types:

An Explanation Of Power Setting
A letter received here at the factory asked a question we have heard quite often:
"Is it a fact, or is it fiction, that engines with constant speed props should not use power settings where inches of mercury exceed RPM in hundreds? I am referring of course to non-turbocharged engines in general ."
The answer to this question is easily found in cruise power charts of the airframe Pilot's Operating Handbook. Whatever the combinations of RPM and MP listed in the charts_they have been flight tested and approved by the airframe and powerplant engineers. Therefore, if there are power settings such as 2100 RPM and 24" MP in the power chart, they are approved for use.
The confusion over so-called "squared" power settings(i. e. 2400 x 24" MP), appears to have been a carry-over from some models of the old radial engines which were vulnerable to excessive bearing wear where a MP higher than "squared" was used. More pressure on the bearings with the higher than "squared" MP was the cause of their problem. However, changes in design, metals, and lubricants permit changes in operation in the more modern flat opposed powerplants.
Let's look at the power charts in a couple of the Pilot's Operating Handbooks of two different aircraft manufacturers, but where both are using the four cylinder 200 HP Lycoming engine.
Cessna's Model 177 RAG, using the Lycoming IO-360A1B6D, in the cruise range at 6,000 feet, lists a cruise power setting range at that altitude of anywhere from 2100 RPM to 2500 RPM with variations all the way from 18" MP to 24"MP. They list a recommended power setting for 66% power at 2100 RPM at 24" MP.
The Piper Arrow, powered by the Lycoming IO-360 series engine, lists the following cruise power settings at 6,000 feet in their chart at 65% power at full throttle (about 23" MP) x 2100 RPM.
Altitude 2100 RPM 2400 RPM
SL 25.9 MP 22.9 MP
1,000 25.6 MP 22.7 MP
2,000 25.4 MP 22.5 MP
3,000 25.1 MP 22.2 MP
4,000 24.8 MP 22.0 MP
5,000 F.T. MP 21.7 MP
6,000 F.T. MP 21.5 MP
After studying the power chart, the pilot would undoubtedly then ask what combination of RPM and MP would be best to use at cruise. We recommend the pilot try the various combinations offered by the power chart over afire-minute period when flying in smooth air, and use the listed RPM and MP combination which gave the least vibration and the lowest noise level.
In addition to the quieter and smoother consideration, lower RPM means lower friction hp. This reduced loss of horsepower due to friction also translates to slightly improved fuel economy.
The Pilot's Operating Handbook is the basic reference for the pilot as this subject illustrates.

Another great reference for everything Lycoming and Continental is the Skyranch engineering manual.

With regards to the Rotax 912 engine, I have a fair bit of experience operating the fixed pitch version. Great engine and pretty much bulletproof. However I have not viewed the performance charts recently for the MP and RPM, and I am unaware of approved propeller and engine cominations. You may need to consult the engine performance charts for approved power settings and approved propeller cominations, in case of any restricted propeller RPM ranges due to harmonics. If it is used in a certified aircraft, these figures should already be readily accessible in the POH, and the operating restrictions if any, will be defined.

From my experiences and others, my only "advice" is to ensure that the engine has been properly warmed prior to application of full power. I have witnessed several "choke" at critical moments during the takeoff roll when application of full power was made prior to the engine properly brought to operating temperatures. I guess you could call it "proper airmanship".

Cheers