Elliptical wings
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Elliptical wings
Naughty me. In the TSR2 discussion the assertion was made that 'no heavy bomber was every produced with elliptical wings'. In a shameless creep of the thread, I responded with the He111. Another poster put up a plan of an He111 which showed that it was NOT elliptical - and the thread crept away. We all had our wrists gently smacked for threat creep, a fair cop, but it is an interesting topic so I thought I'd start a new thread to continue the discussion. And also explain why I volunteered the He 111.
Let's examine the elliptical plan briefly. As I think was already noted, Heinkel made a number of beautiful aircraft in the '30's with elliptical plan wings, including the He 77 and the He 119. I'm doing this from memory but I have a Heinkel book at home I can pick up the details from later. (Possibly not this evening as my wife might think it an inappropriate topic for the Feast of St. Valentine). I believe Heinkel got there before Mitchell with the Spitfire. And of course Heinkel also produced the beautiful He 100 racer and He 112 fighter, with wings which were close to elliptical if not actually so.
The point of my post in the TSR2 thread was that the early marks of He111, the airliners and the bombers up to, I think, the 'G' model, DID have a most elegent elliptical wing planform. So it was slightly a 'catch' answer. Interestingly this was changed to the simpler plan wing famous for the 'H' model and subsequent models, and this was the plan shown by the previous poster. I believe the reasoning behind this was that Heinkel saw advantages to the elliptical plan but as production built up they simplified the plan of the wing for ease of manufacture, resulting in the H and subsequent design. By mid-'30's standards the He 111 was pretty much a 'heavy' bomber so I think my assertion is broadly correct. Again, if I remember rightly, both the He77 and the He115 served in a limited way as bombers (torpedo in the case of the He115) in the Luftwaffe, but probably not very effectively and certainly not 'heavy'.
The change from elliptical to a simpler wing plan also happened with the Spitfire in the end, with the Mk 21 and the Spiteful having a simplified wing plan.
The advantage of the elliptical wing seems to have lain more in the thin section resulting from the very deep chord, rather that the plan as such. Can other posters confirm this? So was the fashion for elliptical wings just than, an aesthetically-driven 1930's design fashion, which inadvertently had a huge aerodynamic advantage. Hawker produced the Typhoon, and Westland the Welkin, both with enormously thick wing sections. Maybe if they'd followed the fashion for the ellipse those aircraft would have been more successful as fighters (ignoring the Typhooon's formidable effectiveness at low altitude and as a close support aircraft).
Another 1930's fashion in aircraft design which may be analagous was that for creating gull-winged gliders like the beautiful Minimoa, which did not have the aerodynamic advantages assumed? Slingsby also introduced gull-winged gliders, I think. I don't believe the gull-wing carried any aerodynamic advantage over the straight wing. So was this just a fashion too?
Surely both of these concepts, the elliptical plan and the gull-wing, could have been tested against conventional alternatives easily enough in wind-tunnels and shown to have no real advantage? Yet a designer as brilliant as Mitchell persisted with the elliptical wing, not least for his un-built 4 Merlin bomber as well as the Spitfire.
I'd be interested to see what other posters think about this. And anyone who introduces the TSR2 as an elliptically winged bomber will be well out of order...
Let's examine the elliptical plan briefly. As I think was already noted, Heinkel made a number of beautiful aircraft in the '30's with elliptical plan wings, including the He 77 and the He 119. I'm doing this from memory but I have a Heinkel book at home I can pick up the details from later. (Possibly not this evening as my wife might think it an inappropriate topic for the Feast of St. Valentine). I believe Heinkel got there before Mitchell with the Spitfire. And of course Heinkel also produced the beautiful He 100 racer and He 112 fighter, with wings which were close to elliptical if not actually so.
The point of my post in the TSR2 thread was that the early marks of He111, the airliners and the bombers up to, I think, the 'G' model, DID have a most elegent elliptical wing planform. So it was slightly a 'catch' answer. Interestingly this was changed to the simpler plan wing famous for the 'H' model and subsequent models, and this was the plan shown by the previous poster. I believe the reasoning behind this was that Heinkel saw advantages to the elliptical plan but as production built up they simplified the plan of the wing for ease of manufacture, resulting in the H and subsequent design. By mid-'30's standards the He 111 was pretty much a 'heavy' bomber so I think my assertion is broadly correct. Again, if I remember rightly, both the He77 and the He115 served in a limited way as bombers (torpedo in the case of the He115) in the Luftwaffe, but probably not very effectively and certainly not 'heavy'.
The change from elliptical to a simpler wing plan also happened with the Spitfire in the end, with the Mk 21 and the Spiteful having a simplified wing plan.
The advantage of the elliptical wing seems to have lain more in the thin section resulting from the very deep chord, rather that the plan as such. Can other posters confirm this? So was the fashion for elliptical wings just than, an aesthetically-driven 1930's design fashion, which inadvertently had a huge aerodynamic advantage. Hawker produced the Typhoon, and Westland the Welkin, both with enormously thick wing sections. Maybe if they'd followed the fashion for the ellipse those aircraft would have been more successful as fighters (ignoring the Typhooon's formidable effectiveness at low altitude and as a close support aircraft).
Another 1930's fashion in aircraft design which may be analagous was that for creating gull-winged gliders like the beautiful Minimoa, which did not have the aerodynamic advantages assumed? Slingsby also introduced gull-winged gliders, I think. I don't believe the gull-wing carried any aerodynamic advantage over the straight wing. So was this just a fashion too?
Surely both of these concepts, the elliptical plan and the gull-wing, could have been tested against conventional alternatives easily enough in wind-tunnels and shown to have no real advantage? Yet a designer as brilliant as Mitchell persisted with the elliptical wing, not least for his un-built 4 Merlin bomber as well as the Spitfire.
I'd be interested to see what other posters think about this. And anyone who introduces the TSR2 as an elliptically winged bomber will be well out of order...
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Footloose
I think the elliptical plan provides a wing with a natural lift distrubition that reduces the effects of tip stall during high rate turns, a similar lift distrubition can be achieved through the use of wing twist and taper but I think that in the thirtys the first choice was to go for the design that looked right.
In a heavy bomber take off performance is important and again the need to avoid tip stall is important.
Can any ex spit crew confirm this?
I think the elliptical plan provides a wing with a natural lift distrubition that reduces the effects of tip stall during high rate turns, a similar lift distrubition can be achieved through the use of wing twist and taper but I think that in the thirtys the first choice was to go for the design that looked right.
In a heavy bomber take off performance is important and again the need to avoid tip stall is important.
Can any ex spit crew confirm this?
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This is a quote from Martin Simons' book on model aerodynamics, but I am reasonably sure it applies to full size as well.
"Mathematical analysis and experiment show that the only type of wing that will produce, at all speeds, constant downwash and load distribution exactly matching the area is one with elliptical planform distribution.
This is not quite the same thing as saying the wing should be a perfect ellipse. It may be so, but any other form which gives a chord at each point the same as a perfect ellipse will have the same effect.
The effective angle of attack everywhere is the same and the CL max is reached simultaneously along the entire span.
This follows from the equal distribution of load, area for area, of the wing."
There is more, mostly about tip stalling and the fuselage upsetting the lift distribution, and the paragraph ends by saying
"For these reasons the is best regarded as an ideal to be approached as closely as possible, rather than the best practical wing planform."
"Mathematical analysis and experiment show that the only type of wing that will produce, at all speeds, constant downwash and load distribution exactly matching the area is one with elliptical planform distribution.
This is not quite the same thing as saying the wing should be a perfect ellipse. It may be so, but any other form which gives a chord at each point the same as a perfect ellipse will have the same effect.
The effective angle of attack everywhere is the same and the CL max is reached simultaneously along the entire span.
This follows from the equal distribution of load, area for area, of the wing."
There is more, mostly about tip stalling and the fuselage upsetting the lift distribution, and the paragraph ends by saying
"For these reasons the is best regarded as an ideal to be approached as closely as possible, rather than the best practical wing planform."
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So was the fashion for elliptical wings just than, an aesthetically-driven 1930's design fashion, which inadvertently had a huge aerodynamic advantage. Hawker produced the Typhoon, and Westland the Welkin, both with enormously thick wing sections. Maybe if they'd followed the fashion for the ellipse those aircraft would have been more successful as fighters (ignoring the Typhooon's formidable effectiveness at low altitude and as a close support aircraft).
Lifiting-line theory, ascribed generally to Prandtl elsewhere than Britain, is still referred to as the Lanchester-Prandtl theory here, as Lanchester had produced a similar theory of lift well before this, with many intuitive insights published in his 'Aerodynamics', 1907. Prandtl and the German aerodynamicists were aware of this, indeed, much so than ourselves - as usual being somewhat tardy when it comes to pure theory - but it was Prandtl and his students that made it more accessible and gave it a useful engineering reality.
With Betz, Munk and others at Goettingen during WW I - the optimum distribution for minimum induced drag (a term only gradually coming into use then) was found to be that produced by an elliptical lift distribution (not necessarily planform). This comes about as a result of uniform downwash as would be produced by an infinitely long wing.
A generic integral solution for any wing chord planform and AoA was not easy, but Betz found one for a rectangular wing with constant AoA (gaining him his Ph.D, 1919). Trefftz (of the Trefftz-plane downwash theory) then applied Fouruer analysis to the solution in which form these theories are still used today.
Induced drag varies as the square of the lift coefficient. When flying very fast, Cl is low, induced drag is low. Conversely when slow and at high AoA, induced drag is high, also when pulling 'G', in fact anywheer near the stall it's important. Minimum drag speed is when induced drag and profile drag are equal, as they both vary with speed squared, but one inversely to the other.
Reginald Mitchell had taken good note of some of the inter-war Heinkels, especially the He70 and admired them. However when laying out the wing planform for the Spitfire, he wanted a fairly large root chord as well as maintaining this well outboard to give room for those machine-guns.
Drawing around the constraints, something pretty close to an ellipse came out, the chord changing very slowly to start with until well outboard.
He also chose a much thinner wing than his British contemporaries, possibly from experience with the Schneider Cup seaplane racers. He also chose about 2 deg. washout, in theory upsetting a perfect elliptical lift distribution but in practice creating a wing that was very resistant to tip-stalling (unless the gun-camera doors were left open, possibly showing how beautifully crafted everythig was).
Now, its easy when looking at induced drag to forget wing loading when comparing different aircraft. The Spitfire was given a generous wing area, so further reducing induced drag, the whole machine being balanced towards turning and climbing, rather than diving, yet just about held its own on level speed due to clean lines, a thin wing, and increasingly so as time went on, a powerful engine.
If it gained 5% Di through its planform (c.f. a good straight taper wing) and 5% through a lighter wing loading, even though just one part of the total drag, would become 10% of much the larger part when truning hard... you didn't have to push that larger wing as near the stall either. The Spitfire was never seriously challenged on its turning performace...
Where it fell down, and the P-51 made it clear, was cooling drag. Originally designed for evaporative cooling, that in retrospect never really looked a serious candidate for something being shot at, the subsequent radiator systems might be said to be almost 'tacked on'. Whereas, admittedly a good few years later the 'Mustang' designers took more than passing interest in what Meredith at Farnborough had suggested would be the best way to design a cooling duct, even possibly offsetting a fair portion of that drag, by expanding the heated air 'properly', especially at high altitude into cold air with the variable exit area duct... and the positioning of the P-51's dog-house was quite inspired at well - almost area ruling!
Possibly, de Havillands also made a fair stab at incorporating Meredith's ideas too in the Mosquito, certainly its sparkling performance indicated it wasn't beings seriously handicapped in that area.
I'm sure things were improved in the later Marks of Griffon Spitfire, when serious intercooler heat energy also had to be dissipated, as 440mph and a climb to 40,000 ft in just over 10 minutes was still state of the art in 1946
NB. When cruising at very high altitude, it's possible a P-51 would be deriving up to half its forward thrust from exhaust energy and cooling, or so it has been said !
Naughty me, I've gone off topic... maybe to draw out that elliptical wings and induced drag are just one part of an overall package. The FW-190 didn't have them and took a lot of beating in the air... another superb package!
The main reason the elliptical wing form was superceded is that it took so much to build it, almost all the panels had to be individually stretched in three dimensions. It was said of the Spitfire that it took 100,000 man hours to produce one aircraft. Of course now it could be done in Carbon fibre just as fast and easily as any other wing shape but in 1938 there was only sheet aluminium.
If you look at a diagram of airflow separation at stall for various wing shapes you will see that in the elliptical wing the initial airflow separation is evenly distributed along the trailing edge, the tapered wing is close, ( but no banana) and plank wings have a relatively poor pattern. Hence the outstanding handling, (I am commenting on reported qualities, regrettably I have not had the privilege.) Also in the compromise, cost versus speed, cost, for a racing airplane (Schneider Trophy) was the low priority and speed was the high priority, so even a couple of miles an hour given by an elliptical wing versus the extra cost of producing it was acceptable. With hind sight, perhaps, in aluminium construction the elliptical wing would not have been the ideal choice for a warplane, but then we'd never have had the prettiest airplane ever built.
If you want a simple analogy look at the Sherman vs the |Tiger. The Tiger was magnificent but the easier manufacture of the Sherman meant that the Sherman could overwhelm the Tiger with sheer numbers.
As engines became more powerful and other strategies were developed the difference between elliptical and tapered, or even plank, wings became less important but in the 1930s, for a racing aircraft, drag was the critical factor and the elliptical wing was it.
If you look at a diagram of airflow separation at stall for various wing shapes you will see that in the elliptical wing the initial airflow separation is evenly distributed along the trailing edge, the tapered wing is close, ( but no banana) and plank wings have a relatively poor pattern. Hence the outstanding handling, (I am commenting on reported qualities, regrettably I have not had the privilege.) Also in the compromise, cost versus speed, cost, for a racing airplane (Schneider Trophy) was the low priority and speed was the high priority, so even a couple of miles an hour given by an elliptical wing versus the extra cost of producing it was acceptable. With hind sight, perhaps, in aluminium construction the elliptical wing would not have been the ideal choice for a warplane, but then we'd never have had the prettiest airplane ever built.
If you want a simple analogy look at the Sherman vs the |Tiger. The Tiger was magnificent but the easier manufacture of the Sherman meant that the Sherman could overwhelm the Tiger with sheer numbers.
As engines became more powerful and other strategies were developed the difference between elliptical and tapered, or even plank, wings became less important but in the 1930s, for a racing aircraft, drag was the critical factor and the elliptical wing was it.
Manufacture
Spitfire - 13,000 manhours per airframe
Hurricane- 5,000 manhours per airframe
Me109 - 4,000 manhours per airframe
Restore
Spitfire - 12,000 manhours
Hurricane- 30,000 manhours
This explains why there are far more Spits flying now than Hurris!!
Spitfire - 13,000 manhours per airframe
Hurricane- 5,000 manhours per airframe
Me109 - 4,000 manhours per airframe
Restore
Spitfire - 12,000 manhours
Hurricane- 30,000 manhours
This explains why there are far more Spits flying now than Hurris!!
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Thanks Low'n,
I thought that Spitfire figure was an order of magnitude out
Nice to know the comparisons too.
.. and I'm not even sure those Supermarine racing seaplanes had truly elliptical wings either - at those speeds induced drag pales into insignifiance
I thought that Spitfire figure was an order of magnitude out
Nice to know the comparisons too.
.. and I'm not even sure those Supermarine racing seaplanes had truly elliptical wings either - at those speeds induced drag pales into insignifiance
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I'm not even sure those Supermarine racing seaplanes had truly elliptical wings either
