More long-range Spitfires and daylight Bomber Command raids, with added nationalistic abuse (was: #1 Jet of World War II)

In article ,
Guy Alcala writes:
I'll step with some trepidation into Pete's territory here as he explains this
stuff far better than I do, but we've been keeping him busy doing calcs. The high
aspect ratio wing provides good L/D ratios, increasing range performance as well as
lift at low angles of attack. Here's how the a/c's aspect ratios stack up, from
low to high:

Stirling 6.72:1;. B-17, 7.58:1; Halifax (early) 7.81:1; Lancaster 8.02:1; Halifax
(late) 8.51:1; B-24, 11.55:1; B-29, 11.48:1.

As you can see, the B-24, designed a couple of years later than the British heavies
and five years or so after the B-17, has a much higher aspect ratio wing, and the
B-29 follows this practice. The wing area of the B-24 was considerably lower than
the others, for low drag. Good altitude performance requires some combination of
low wing-loading (high wing area for weight), engine thrust, and aspect ratio.

While the B-24 had good engine power at altitude and a high aspect ratio, it also
had high wing-loading compared to its contemporaries (not the B-29). It had better
altitude performance than the British a/c because of its engine supercharging, not
its wings. The B-17, with similar supercharging as the B-24 had a higher combat
and service ceiling, because although it had a moderate aspect ratio wing it also
had far lower wing-loading, and was able to fly slower. The B-24 cruised between
10-20 mph IAS faster than the B-17, but then it had to to be comfortable. The
crews hated having to fly in company with B-17s.

It's also easier to make lower aspect ratio wings of the same area stronger for the
same weight, because the stresses can be spread over a longer (and thicker) root,
which is one reason why a/c like the Stirling and B-17 have reputations for being
able to take lots of wing damage and survive, and why a/c like the B-24 had
opposite reps. However, the lower aspect ratio wing requires more area to get the
same lift at the same AoA, increasing drag.

A good job, Guy. If you don't mind, I'll dig a little deeper. into
some details.

The selection of Aspect Ratio and Wing Area are one of those tradeoff
deals. A high Aspect Ratio means that the Induced Drag (Drag due to
lift) is lower, for a given Lift Coefficient, and a low wing loading
means that the Coefficient of Lift can be lower. This is really
important at relatively low Equivalant Air Speeds, where the wing is
working hard to keep the airplane flying. As the speed goes up, the
Lift Coefficient decreases with the square of the speed, and the
Induced Drag coefficient drops with square of the lift coefficient, so
it decreases quite rapidly. Depending on what fraction of the total
drag is Induced Drag, Aspect Ratio might not be all that important.

I'll add the Stirling to the list, BTW. It should make an interesting
contrast to the Lancaster in terms of how the tradeoffs fall.

"Quest for Performance", L.K. Loftin, NASA History Office, 1985,
available online, has a quite good explanation and analysis of the
directions that designing high performance airplanes took through the
first 80 or so years. The data tables list the following values for
the various airplanes.

Airplane: Aspect Ratio Wing Loading Cruise Speed L/Dmax
B-17G 7.58 38.7 182 12.7
B-24J 11.55 53.4 215 12.9
B-29 11.50 69.1 253 16.8

Altitudes in cases would be 25,000', (Critical Altitude for the
turbosupercharged engines, in each case) and all speeds are True
Airspeed.

Note that the B-24 and B-29 have almost identical Aspect Ratios, but
the B-29 has a significantly higher wing loading. In general, this
means that the B-29 will have more induced drag than the B-24. But it
also cruises much faster. This is due to the lower total drag of the
airplane due to the much more streamlined shape.


--
Pete Stickney
A strong conviction that something must be done is the parent of many
bad measures. -- Daniel Webster