This is one of two notes to summarize what I learned from the voluminous data already presented in this thread. This note addresses US aircraft built around the P&W R2800 engine. The second note deals with what we have learned about the La-7, built around the Ash-82FN engine.
Thanks to charts contained in the posts by F4UDOA, it does not take much work to nail down the fuel economy of two versions of the R2800. I’ll focus on just the R2800-8, the workhorse of the F4u-1. I’ll pretend this is also the engine used in the F6f, when in fact that plane used an engine that was a little less powerful. F4UDOA also gave us numbers for the –21 model (used on the P57) which are only a little different, primarily because of the turbo supercharger installed.
I have generated a table and two charts of the resulting data (see below). The table tells it all, but the charts may be easier to follow. The first point to start with is Specific Fuel Consumption (SFC), which is really what the argument about endurance is all about.
The first chart plots SFC in US gallons/horsepower/hour. Note there are really two lines to consider which are driven by the choice of fuel mixture – auto lean or auto rich. SFC at minimum fuel consumption or maximum cruise are very similar and do not very much with altitude. That’s why it pays to fly higher at a modest manifold pressure. On auto rich settings (other than WEP), SFC is about 80 percent higher and it is somewhat more sensitive to altitude. The difference between normal and military power is not very great. SFC for WEP is higher, for the reasons described in our thread – you are substituting water for fuel and adding more air, so you are leaning out the fuel mixture.
How does this translate into endurance (hours in the air)? That is illustrated in the second chart. I have to caution that these numbers are somewhat over estimated because they may assume you are get to the specified altitudes without burning any fuel (below I present an alternative calculation where this is not an issue and I can show nearly the same results). Also I’m am using the wrong engine model for the F6f, but that too does not matter much.
The result is that all settings that use a rich fuel mixture, internal fuel gets you about an hour’s flight time in the F6f and slightly less in the F4u-1. The military setting is a little worse, giving you only about 50 minutes of time. The max cruise setting gives you 3 hours of flying time at virtually any altitude and would be what most of us should expect if we are serious about missions like CAP or long haul escorts. The minimum fuel economy would get you an obscene 4-6 hours of flying time on internal fuel. But we should remember that it may not include the climb and it is much more sensitive to altitude.
From the table we see that fuel consumption varies by nearly 7 times from the most economical to the most rapacious settings. The worst performance on auto lean is more than twice as good as the best setting on auto rich. Maximum cruise is attained using half the engine's rated horsepower and only 30 percent of the fuel consumed at the rated horsepower.
Should we believe the fuel economy numbers?
I would say yes because we can observe nearly the same data from two economists who carefully studied how radial engine performance affected costs in civil aviation before and after the war (Miller and Sawyers, Technical Development of Modern Aviation). Here are their numbers for engines of the same era:
Wright Cyclone (R 1820) 87 octane 0.57
Wright Cyclone (R 2600) 100 octane 0.47
P&W Double Wasp (R 2800) 100/130 octane 0.42
The Cyclone was known for its fuel efficiency in its day. Note the primary gain in specific fuel consumption across these engines is due to the substitution of fuel with more energy. Note also these numbers almost certainly assume a lean fuel mixture, as the authors’ focus almost exclusively on civil aviation where fuel economy is important.
Another implication is that one should not believe a SFC below 0.40 for a 1940s high output radial engine. It’s possible that the really good water cooled engines did better, because their lower cylinder head temperatures allowed them to run on a leaner fuel mixture. Heron's history of aviation fuels (1949) suggests the best SFC obtained from a high output engine was 0.37 on 115 PN avgas on a postwar US engine (the Wright Turbo-Compound Cyclone R3350).
I point this out because some calculations in this thread based on data for the Ash-82FN imply a SFC of 0.30 or lower, which is simply incredible.
A better calculation of endurance for the F6f
Now I turn to the data contained in the Standard Aircraft Characteristics chart (dated 1949) from Hal Andrews, "F6F Hellcat," Naval Aviation News Sept-Oct 1988. A copy can be downloaded from
http://www.history.navy.mil/branches/hist-ac/fighter.htm.I work right off the chart to minimize the chances of introducing an error. That means I will use the standard fighter load out with full fuel and a drop tank, and assuming a climb to 15,000 feet.
There is separate estimate of range in which the drop tank is dropped prior to combat, but this introduces a lot of uncertainty into the calculations so I ignore it.
Based on the chart, the F6f-5 with a full load of fuel (internal and external), has a “combat range” of 950 nautical miles at an average speed of 178 knots an hour. 950 knots/178 knots/hr = 5.3 hours of flying time
We can also work out the best fuel consumption using the SAC. Assuming the tanks are empty at landing (there should at least be 20 gallons in the reserve), we have 400 gallons/5.3 hrs = 75 gallons/hr, a number in between the estimates for minimum fuel consumption and maximum cruise in F4UFOA’s charts. Note that on internal fuel only (250 gallons), we are getting an estimate of endurance of 3 hours and 20 minutes, just a little better than what is shown in the previous chart.
One other thing to note from this source - In the description of the Fighter combat Radius formula, we see the climb-out calls for 60 percent normal sea-level power. The chart is good enough to tell us that at 6,200 ft, normal power is 1,710 HP. Given the plane is at low blower there is practically no drop-off in performance of the R2800 at such a low altitude so we can assume this as a good approximation of normal sea-level power. Sixty percent of this amount is 1026 HP, just about half the maximum output of this engine. That is pretty much what we observe for economical cruise settings in F4UDOA’s charts.
I mention this because it is a plausible way to approximate horsepower at a cruise setting when you don’t have the information and you’d like to estimate specific fuel consumption. For example, with the La-7, we have numbers on the engine’s rated and emergency horsepower but not at a cruising power setting. That’s one reason why the thread took so long to converge.
-Blogs
p.s. I don't seem to know how to post more than one attachment at a time so I'll drop them in a sequence of posts
