Fuel flow to power formula

The SFC (specific fuel consumption i.e. HP per fuel flow) is supposedly proportional to the square root of the CR so if you increase CR by 13.3% (7.5 to 8.5) you should expect a 6.5% improvement in SFC whereas 14.9/13.7 is 8.8%. I can’t account for the difference. But it could be the usual matter of which percentage.

Stochiometric (not stochastic) combustion occurs roughly 25F LOP but it is very close to peak EGT. I wrote some notes here.

I doubt any real engine gets 31% efficiency. If you look at performance charts like here and redraw the chart so it can be extrapolated to zero power, and look at the fuel flow there, it is obvious that the losses are pretty significant. Big slow revving engines are generally more efficient.

Low RPM means lower friction at same hp output. So more MPG.

Rightly or wrongly when I first started flying twins, in particular the Beech Baron B58, I was taught just to set everything by the fuel flow which is in the POH. Fussing with all the other things just gets complicated.

Low RPM means lower friction at same hp output. So more MPG.

Indeed, though this second-order effect is quite small – of the order of 2-3% between 2400 and 2200rpm. And you pay a price in that the operating ceiling goes down quite a bit; for example the TB20 loses a few k feet when flying at 2200rpm. So I use that at lower levels e.g. FL100, in nice wx, on long flights.

Engine management (I posted an article link above) is quite easy in reality: You set up the MP (say 23"), set some rpm at which the engine is happy (2400 for me), and lean for peak EGT or LOP (11.7 USG/hr for me, 138kt IAS). The foregoing is for low levels; a few k feet. At 8k or above, non-turbo, it is WOT (wide open throttle) but the rest stays the same. Climbs (all climbs) are best done at max rpm and some 200F ROP (I do them at 1330F EGT).

If you set peak EGT or LOP then the fuel flow takes care of itself.

@hazek

Could you please elaborate how RPM changes the “efficiency” factor number.

Aside from mixture (if ROP, fuel not burnt, efficiency drops) and the fact that your aircraft needs to fly (so you can’t always aim for the best efficiency point – nor is it desirable because you want the least fuel burn per mile and not per shaft energy), the main effects of RPM on efficiency as I understand are as follows :

• when the RPM is very low, a lot of heat is lost through cylinder walls, and there is less pushing on the piston (by the time the piston moves, the gas has cooled a little). Energy is lost via engine cooling (air or water cooling). Cooling losses can be up to 15-20% in some cases (generally lower).
• when the RPM is very high, the piston is so fast that the hot gas has more trouble keeping up with its speed and pushing. The piston recedes before the gas has a chance to push, and the piston even transfers some energy back to it by pushing really fast during exhaust. Energy is lost in the form of exhaust heat.
• when the RPM is high, as has been said you also get more fluid friction (but not more solid friction, per cycle ; solid friction like ball bearings does not depend on speed. Maybe we will one day have graphene-coated oil-less engines ^^)

Also, if you reason at a certain amount of required power (cruise power, lower than max power on takeoff), reducing RPM is the best way to increase engine load. When the RPM is high and the load is low(ish), most of the fuel goes into pushing against the engine itself (like an idling engine, burning fuel but producing no power). The engine’s power is “oversized” for what you ask. So if you lower the RPM and increase MP, you make it work more per cycle and improve efficiency. But book values have to be followed anyway in order not to over-torque the gearbox.

There are so many factors, it’s really hard to calculate exactly (and I think engine manufacturers don’t provide the curves).

Efficiency is usually a 2D description (actually 3D, for turbines we call them hill charts for that very reason). For an SI engine it will look something like this:

What it shows is that max efficiency is obtained with one rpm at one specific load (remember that power is torque*rpm). Lowering the RPM to increase the efficiency is only a good thing to do if the BEP is on the left side (and higher up) of your actual RPM in the diagram for the same power. These diagrams can be very different for different engines. A (family) car will typically have a broad range of best efficiency (could possibly also have several peaks in the diagram for all I know, due to valvetrain control, turbo control and whatnot), while an engine designed to run at high power over longer durations, like a boat or an aircraft, will have a one clearly defined point at high torque and one specific rpm.

The best efficiency engines in the world are those humongous 2 stroke diesels in super tankers. They only run at one rpm. For the same reason, turbines in airliners also have super high efficiency at one specific altitude and speed (pressure and temperature).

A Lycosaurus definitely has a sharp peak at one rpm and one load. That’s where the best efficiency is. Going outside that point will reduce efficiency. You will use more fuel for each hp produced. However, miles per gallons (MPG) is a different concept altogether. It will for an aircraft, as for a car, be a product of both the engine and the aircraft. The efficiency of an engine doesn’t really say all that much about MPG. Clearly an aircraft is most efficient where the total drag is minimum, which is at best L/D speed. If the engine also is designed so it produces the required power at that speed, the total package will be very efficient (airliner flying at 30k feet). Very high MPG. This doesn’t really work for a SEP because we want more power for take off for instance, more power to carry more load and so on, the more the better. Unless the aircraft is rather under-powered (as it could be), at best best L/D speed, the engine hardly sputters along at a point on the diagram where it doesn’t really like it all that much.

An engine will typically last longest if it can run at best BEP and with all temperatures inside the greens for as long as possible. For this reason, “best” cruise speed should be where the engine operates at BEP. This will in most cases be well above the speed for best MPG. Thus any reduction in engine power will increase MPG, no matter how it’s done, and it will decrease engine efficiency.

hazek wrote:

Would you be able to say anything towards power settings, load on the engine and danger of detonation? How does one ensure they’re outside the danger area with the settings? Is it even possible or is it as Lycoming warns that only ROP one is safe not to damage the engine.

I don’t know, but common sense say that the engine manufacturer knows more about their engines than others. Only the engine manufacturer put guaranties behind their words, everybody else can say whatever they wish without any consequence whatsoever. Besides, the auto industry must have used billions and billions of € and Yen (mostly ) to develop engines that runs on the very edge of “LOP” without detonating. It requires at least an ECU of some sort and HP direct fuel injection, it’s definitely not something a human can do reliably, and certainly not with engines that were designed 50+ years ago. On the other hand it’s probably more a definition of what “LOP” actually is. The newest Mazda engines run “LOPer than LOP”, almost like a diesel. Way beyond what a Lycoming could ever do.

Large multi engine piston aircraft from WWII and after had one person dedicated to nursing the engines. They probably were able to run them pretty efficient in cruise, probably as good as those engines would be able to by any means. Smaller fighters had none of that. They typically had just 2-3 notches on the mixture (cut off, cruise and full power or some similar). German fighters didn’t even have that, just a basic analogue computer (pretty amazing piece of technology actually, but nothing like a modern ECU). For them it was a race for max possible power, all other other optimizing was uninteresting.

What has been the driving force behind the development of Lycomings and Continentals? I don’t know, but I would bet reliability would be at the top. This means running at BEP and running ROP. Jeopardizing that reliability for a few ounces of fuel, sounds like a silly thing to do IMO, at least in a SEP and without a dedicated engineer nursing that engine.