Cruising speed?

The B-17 vs XB-38 is a perfect example of the confusion in cruising speeds that Just Schmidt was wondering about.

Instead of comparing the performance of two individual aircraft operating under like conditions the XB-38 (operating as single aircraft under manufactures test conditions/not fully armed) is compared to B-17s fully equipped for combat and operating in large formations under combat/operational conditions.

It is very hard to draw any valid conclusion from such a comparison.

External tanks can easily increase airframe drag by 50%; external carriage of the bombs current in WW2 could easily double an aircraft's zero-lift drag. Increasing zero-lift drag reduces the optimal cruising speed.

An aircraft's optimal cruising speed occurs at the condition for maximum lift:drag ratio. Non-dimensionalizing here, CD​ = CD at Cl=0​​ + ((CL​)2​)/(pi * E * AR) where AR is aspect ratio (span squared divided by wing area), E is the wing's efficiency, typically 0.75 to 0.8, with lower aspect ratios (like on fighters) tending to have lower efficiency, CL​ is lift coefficient, and CD at Cl=0​​ is the aircraft's drag coefficient at the zero-lift condition. For fighters, this is typically between about 0.022 and 0.025, with a few outliers: the Bf109 is about 0.029 (some marks are a trifle better) and the P-51 is about 0.018; just about all monoplane fighters with retractable gear are between 0.022 and 0.025, with radial and V-12 aircraft pretty thoroughly intermixed. I've not seen data for multi-engined aircraft; I suspect that the Mosquito and P-38 are both between 0.020 to 0.022.

Best lift/drag ratio occurs when drag due to lift -- the CL​2​ term -- is equal to zero-lift drag. This is the point for best aerodynamic efficiency.

A couple of points here: one is that zero-lift drag for radial and V-12 engined aircraft do not differ much (see S Miley's work for some quantification of that), and plotting the two vs power results in curves which show quite a bit of scatter and overlap. The second is that pilot in fighter aircraft are not able to adjust their engines as well as the flight engineers will be able to in transports or bombers: fighter aircraft will tend to run their engines richer than the best efficiency conditions because they don't have the instrumentation or time to make the adjustments to keep them at their best efficiency settings.

So,
1) Most efficient cruise speed depends on weight. With a heavily-loaded aircraft, the best cruise speed increases, because at a given altitude, a heavier aircraft will need to fly faster to keep the same lift coefficient
2) Most efficient cruise speed tends to be significantly lower than the cruise speed that's normally selected. One reason is that at the best L/D speed, slowing down puts the aircraft on the back side of the power curve, and that's an uncomfortable place to be.
3) Because fighters tend to have lower aspect ratios than bombers or transports, their best cruising speeds tend to be at lower lift coefficients, but because they tend to have lower wing loading, their cruising speeds may be lower.
4) Human factors will tend to limit time aloft more for fighters than for transports or bombers (at least bombers with copilots).

Not really anything to do with the original question but you may find this interesting...

When Charles Lindberg was (unofficially) undertaking combat missions with the 457th FG in New Guinea, the Group's Crew Chief noticed that Lindbergh's P-38 always returned from the mission with more fuel remaining than any other aircraft. The Group's CO, Charles MacDonald, asked Lindbergh to explain this anomaly to the other pilots of the Group. Lindbergh passed on his experience in long range flying, explaining that by raising manifold pressure, lowering engine revolutions, and adjusting propeller pitch, the P-38 would use much less fuel, thus allowing a great combat radius for the same fuel load. As a result, the squadrons of the 475th FG were able to extend their mission duration to 10 hours (normally 6 to 8 hours), allowing them to strike deeper into Japanese territory.

Not trying to take anything away from Lindbergh but he was just telling them the same things that Allison and Lockheed had been telling the army. The army just thought they knew better than Allison and Lockheed.
Tony Lavier was also telling the Army units in Europe the same thing,

Lindbergh may have gone a bit further in his settings or leaned out the engine a bit more but the lower the RPM and increase the boost method of cruising was being taught to RAF pilots in 1942 using single stage engines.

A lot of fighter planes (let alone bombers) could take over two minutes to got from a slow or low medium cruise to full speed. And some pilots (and instructors) thought by keeping the RPM high, boost low and prop pitch fine they could get to full throttle (rpm) quicker and accelerate faster. For P-38s this was especially wrong as a high rpm but low boost the turbo was idling (or near) and it took a while for the turbo to pick up speed. At a higher boost cruise the turbo was spinning thousands of rpm faster and the turbo could reach full boost that much quicker.

swampyankee said:

For fighters, this is typically between about 0.022 and 0.025, with a few outliers: the Bf109 is about 0.029 (some marks are a trifle better) and the P-51 is about 0.018; just about all monoplane fighters with retractable gear are between 0.022 and 0.025, with radial and V-12 aircraft pretty thoroughly intermixed. I've not seen data for multi-engined aircraft; I suspect that the Mosquito and P-38 are both between 0.020 to 0.022.

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You have to be rather careful when comparing the drag coefficient as it is just one part of the drag.

A couple of points here: one is that zero-lift drag for radial and V-12 engined aircraft do not differ much (see S Miley's work for some quantification of that), and plotting the two vs power results in curves which show quite a bit of scatter and overlap.

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they can actually vary quite a bit, problem is that the cowl technology changed very rapidly so comparing a 1943-44 radial engine fighter to a 1938 radial engine fighter can show large differences. And since the flat plate area is the wing area times the drag coefficient using different size airplanes can really screw up the results. Let alone problems with individual aircraft and drag from other sources.

For instance the early P-40 had 22% less drag than a P-36 but were the same aircraft from the firewall back. Drag of a Macchi 200 or Fiat 50 are pretty high and both are rather small aircraft.
The Brewster F2A-3 had a drag coefficient of .030 (worst) and had the smallest wing of 11 wartime US fighters. the combination put it in 5th place right ahead of the P-47B in flat plate area. 6.27 vs 6.39 sq ft.
And the Drag coefficients for the F4U-D, P-38J, and F6F-3 are given as .0267, .0270 and .0272.
If you can have two V-12 engines and fuselage boom/pod for the same drag (under 2%) as as a single radial then I would say the advantage still lays with V-12

Yes the FW 190, Bearcat, Sea Fury and some Japanese fighters did much better but then they were later in timing.

I think the objections to Lindbergs ideas were understandable. Why change what you know works for something that may blow the engine. Once Lindberg proved himself that the modifications were not dangerous they were accepted.

pbehn said:

Why change what you know works for something that may blow the engine

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But the manufacturer, Allison, was already saying that the AAC was doing it wrong and saying the same as Lindberg before he did. Lockheed was saying the same as Allison. Using military intelligence (gut feelings) the army thought they knew better than Allison and Lockheed (who used research).

Allison was certainly not going to recommend the army used something that would reduce engine reliability because that would mean the engines did not meet contractual reliability guarantees.

Mitasol, I wasn't advancing a logical argument just saying what a normal human reaction is. Having been given one set of technical instructions from superiors that works it needs some good explanation to change it.

Actually in Europe the Army method was helping blow the engines.
There were about 6 or 7 different factors in what was know as the the "Allison time bomb" problem.

A number of the problems were not related but a few were, and one of them was cruising at high rpm and low boost. It lead to low intake temperatures and puddling of raw fuel in the intake manifolds. At the low boost pressures the Turbo was near idle and not heating the intake charge very much after which the inter-cooler cooled below a desirable temperature before it hit the carb and engine supercharger.
Not as big a problem in the Pacific or the Med.

None of factors had anything to do with the basic design or build quality of the engine.

The British had even made up posters with sayings like " Drop the revs and boost the boost and you will have enough fuel to get home to roost" well before the P-38 saw wide spread service.

The high rpm low boost theory has a certain amount of logic to it as far as fast response if jumped by enemy fighters. It is actually false logic once everything that goes into engine response and more importantly aircraft response is explained.

pbehn said:

Mitasol, I wasn't advancing a logical argument just saying what a normal human reaction is. Having been given one set of technical instructions from superiors that works it needs some good explanation to change it.

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While this is true to a certain extent there is a belief in the military that they know everything about everything and that the designer and manufacturer of any product knows didley squat. The fact that the manufacturer was saying you are doing it wrong for our product should be listened to and acted on. The old "we are the experts and we have always done it this way" in the senior ranks has caused far too many disasters in all military forces over the years.

A classic example in Australia not that many years ago.

The RAAF were operating ex Qantas 707's as transports and decided that they needed a training scenario with both engines on one wing failing and a simultaneous rudder boost failure.

They asked Boeing to write the procedure.
Boeing said that not one of the 2,500 odd 707/C135/c137 etc series aircraft had suffered such a failure and that training for such a failure was far too dangerous and very strongly advised against trying it.

The RAAF decided that Boeing were incompetent and designed their own training procedure which they carried out once AT LOW ALTITUDE. Needless to say the aircraft rolled on it's back and almost went vertical. There were no survivors.

Refusing to admit that the designers of a product know anything about the product and its capabilities is often SOP in the military. Most do not get a Royal Commission or other similar civil investigation necessary to bring the truth to the public's knowledge.

Another classic - In Queensland they elected a military man as Premier (Governor). He decided that the ideal person to head up his new police task force was another military man. No civil police experience or knowledge, no civil law training or qualifications, etc etc. Fortunately he only lasted one term and his party went from having 90% of the seats in parliament to 45% in that one term.

Shortround6 said:

You have to be rather careful when comparing the drag coefficient as it is just one part of the drag.

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The zero-lift drag coefficient collects all the aerodynamic drag except that due to lift and compressibility, which was negligible a the top speeds of most piston-engined aircraft and trivial at the cruising speeds of even the fastest. Careful people will use an equivalent drag coefficient to account for the power used to drive those miraculous cooling fans nobody but the Germans found necessary; most popular authors do not.

Of course, differences in aircraft configuration, like setting of cowl (or radiator duct) flaps will change drag coefficient, as will random excrescences, like antennas, bomb shackles, and turrets, and holes, like those for waist gunners. So will bad rigging of landing gear doors, paint (camouflage paint tends to increase the skin friction component of the zero-lift drag).

I am not much interested in the 4th digit from the decimal point except as under 5 or over 5
The 3rd digit is where the significant difference is except for the P-51.
as you noted there are a host of small things that can affect the more precise figures.

However in the radial vs V-12 debate there are only a handful of fighters in which the radial engine got down to or close to the drag of the V-12 (or 24 cylinder engines) .

The only comparisons that are really valid are the ones where the same airframe was used with both types of engine.
Lagg3/La-5
P-36/P-40
Tempest II/ Tempest V
Ki 61/Ki 100
Fw190A/D

MiTasol said:

While this is true to a certain extent there is a belief in the military that they know everything about everything and that the designer and manufacturer of any product knows didley squat. The fact that the manufacturer was saying you are doing it wrong for our product should be listened to and acted on.

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And how! In the early 70s when I was in, the Navy's P-3 community was permeated with laid-off airline Electra pilots who'd come back in the service to wait out their furloughs. They were full of horror stories about how unforgiving the plane was at "slow" approach speeds and apparently got NATOPS rewritten to require much higher speeds. The consumption of tires and brakes and engine maintenance got seriously out of hand, and the Navy complained to Lockheed.
Well one day an old shriveled-looking civilian guy showed up at our local P-3 operator, VX-1, the Navy's ASW test and evaluation squadron, and said: "I'm from Lockheed. Just call me 'Fish'. I want all your P-3 qualified aircraft commanders and an airplane. We're going flying." Hours later, when they got back, a lot of white-faced Lieutenants and Lieutenant Commanders got off that plane and kissed the ground!
Apparently "Fish" was the test pilot in charge of the original Electra/P-3 flight test program, and he was being sent around to "do a Lindbergh" throughout the P-3 community. His little confidence building exercises in the P-3 shattered a lot of illusions and certainly ruffled a few feathers. Also led to a significant drop in tire, brake, and engine maintenance expense.
Cheers,
Wes

Young Hot Rocks - beware the grizzled vet that slithers into your nest and 'invites you for a check ride'..

Not to mention "old" hot rocks! He reportedly talked those pilots through repeated asymmetric thrust departures and recoveries BELOW 10,000 FEET without breaking his deadpan delivery and without stressing the aircraft. Tumbled the inertial system good, though! It was rumored that bird sat 36 hours out on the compass rose re-erecting the inertial.
Cheers,
Wes

I think it is fair to say best cruising speed depends on:
1) Configuration
2) Weight
3) External Stores / Armament
4) Range required
5) Altitude required

This assumes serviceable engines, props, and decent fuel.

Nice job, Greg: simple, succinct, and accurate!
Cheers,
Wes

B-29s could go hundreds of miles further carrying the same bombload by flying at low altitudes as opposed to high altitudes.
This is both counter intuitive (thin air should mean higher speed for same power) and contrary to airline experience (and others) but the B-29 when loaded burned an awful lot of fuel climbing.

For instance the Manual shows it taking 29 minuted to climb from 14,000ft to 25,000ft using 2000hp per engine. the plane covered 120 miles and burned 580 gallons of fuel. It took 21 minutes to reach 14,000ft. The 2400rpm/2000hp powered setting burned 91lbs of fuel per minute. Cutting power didn't help much as at 2350rpm the power was 1880hp/77lbs per minute but climb performance was estimated by using a weight 8000lbs more than the weight of the plane. Please note that going from 120,000lbs to 130,000lbs could add 20 minutes to the climb to 24,000ft using the 2400rpm power level.

There are a lot of manuals in the manual section. Those who are really interested in how the aircraft performed have a tremendous resource there.

Each plane reacted differently to the variables. But each one DID have an optimum cruising speed for any flyable configuration, and best L/D speed.

Optimum cruising speed when tanks were empty was best glide speed at that weight. Nothing new to a trained pilot.

I'm curious why the B-29 had better range at lower altitudes, and am surmising it was the high fuel consumption at typical climb power. But what about if they cruise-climbed at reduced power? It would be fun to research, but the time isn't there. Cheers.

Nice post, Shortround!

The climb chart is here:
B-29 Flight Manual Part 2.pdf

scroll to 2nd page.(page 103 of manual)
climb to 20,000ft using 2000hp per engine at 120,000lbs took 34-35 minutes while burning 91lbs a minute (3145lbs)
climb to 20,000ft using 1760lhp per engine at 120,000lbs took around 55 minutes burning 74lbs minute (4070lbs)

Granted the slower climb will cover more horizontal distance.
Chart also says to add 500lbs to the weight of the plane for every degree above the NACA standard day (59 degrees F ?) when figuring the climb performance. so taking off of a Pacific Island on a 90 degree day is like 15,500lbs to the plane on a NACA day.

B-29s may actually have climbed in stages on operations. some periods of level flight between climb stages to cool the engines and to burn off some fuel (weight) before climbing to the higher attack altitudes?