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# strongest wing tip vortices when slow, clean and heavy. BUT WHY?

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# strongest wing tip vortices when slow, clean and heavy. BUT WHY?

31st Oct 2009, 02:18

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Changing flap setting changes stalling speed because it changes the MAXIMUM lift coefficient. However, with plain and split flaps, changing flap setting doesn't change the instantaneous lift coefficient
Aaaaaaaaaah. But it does. Let us assume we are flying at a given speed with no flap extended. The wing will have an angle of attack of X° and be operating at a lift coefficient of Y. If you maintain the same speed and extend flap the angle of attack of that portion of the wing that is flapped is now (X+A)° with a corresponding increase in the lift coefficient. The unflapped portion of the wing, because the flapped portion is now producing a greater percentage of the required lift, has a reduced angle of attack and a lower lift coefficient and produces a reduced percentage of the total lift. As a pilot you notice the effect that when you lower flap you have to lower the nose to maintain the status quo. A diagram of the span loading of a flapped wing will show a discontinuity at the outboard end of the flap, compared to the smooth elliptical shape of an unflapped wing.
31st Oct 2009, 11:38

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G'day Brian! I'm sure you are aware that two different lift coefficients are defined. There is the aircraft lift coefficient C_L (capital C) based on the lift on the aircraft and the wing planform area; and there is also the section lift coefficient c_L (lower case c) based on two-dimensional flow around an airfoil section.

On 9 December on this thread you correctly stated that induced drag is proportional to the square of the coefficient of lift. That is a correct reference to the aircraft lift coefficient C_L. In your latest post you comment about the lift coefficient on the flapped part of the wing, and a different lift coefficient on the unflapped part of the wing. That is correct, but in your latest post you are referring to section lift coefficients.

In the well-known mathematical equation for induced drag coefficient, the reference to the square of the coefficient of lift is a reference to the aircraft lift coefficient.

Aircraft lift coefficient is defined by a mathematical equation which says C_L is equal to the lift divided by dynamic pressure and wing planform area. In my previous post I addressed this mathematical equation explicitly and in detail. You must admit your latest post comments about lift coefficient, but makes no attempt to address a mathematical equation. It is all subjective. We don't tackle mathematical equations by subjective prose.

(Section lift coefficient c_L is also defined by a mathematical equation.)

We are straying from the matter in question. My point is that the change in induced drag when trailing-edge flaps are extended can't be explained by a change in lift coefficient because changing flap setting (but changing nothing else) doesn't alter the aircraft lift coefficient (unless the flaps are area-changing Fowler flaps). What changes is the Oswald Efficiency Number (or Span Efficiency Factor) and this changes in such a way that extending partial-span flaps increases induced drag.

In your 9 December post you gave a web link to a NASA site that contains the formula for induced drag coefficient. There, in the denominator, is e, called the efficiency factor. That is the one I am calling Oswald Efficiency Number.

I am very happy to discuss mathematical formulae for induced drag, and lift coefficients, but we need to remember that mathematical formulae can't be solved by intuition or subjective assessments. Best regards.
31st Oct 2009, 14:25

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None of my business really, but it seems to this non-expert that some writers are confusing transient effects with a new stable configuration.

When lowering the flaps, instantaneously the momentum of the aircraft is maintained (no infinite force, so no immediate change in velocity – just accelerations that start). If the aircraft is kept pointing in the same direction, at the moment that the flaps are lowered:

1. Alpha at the inboard/flap section is immediately increased, if alpha is defined as the angle between the airflow and the chord from leading edge to (now lower) trailing edge. Hence inboard contribution of lift is transiently increased. If I do this in my glider, the immediate effect is to bounce it higher than it was, or reduce the rate of descent, very briefly – I can feel it happen. A sensitive accelerometer would display it as a transient effect.

2. Alpha at the outer/tip section is not changed instantly – airflow, attitude and wing section are not changed instantly.

What happens next depends on the pilot’s actions. If the nose is lowered to arrive at the same stable speed as before, after things settle down, alpha is higher inboard, lower outboard; overall Oswald efficiency (a term I had not heard before – thanks, D.) is lower as Dolphin says, and more energy is transferred to the atmosphere generally. The energy comes from more power expended or a greater rate of descent/expending more potential energy. Ultimately, that manifests itself as the vortices, as I understand it – the ultimate effect of a lift-producing wing passing through air is to add rotation, which appears as the vortices. More energy expended, stronger vortices. Unless someone has found a way round the laws of physics.

If the nose is not lowered, after things settle down a new phase of flight is entered with possibly different speed, certainly different alphas at tip and inboard, and the maths is too complicated for me to summarise. (But anyway, when flying, I can’t tell the induced drag – it is total drag that produces effects that the pilot sees.)

Chris N.
31st Oct 2009, 17:33

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With plain flaps and split flaps, changing flap setting changes none of these things - no change in weight, load factor, indicated airspeed or wing planform area. Consequently changing flap setting doesn't change instantaneous lift coefficient. In the minute or two after changing flap setting there is usually a significant change in airspeed that brings about an equally significant change in lift coefficient, but it is the change in airspeed doing that, not the change in flap setting
G'day D. Call me a dullard but I'm having trouble getting my head around this little bit. On flap retraction the immediate aircraft reaction is to reduce its rate of climb - read a loss of lift, on flap extension the immediate reaction of the aircraft is to balloon - read increase in lift (as I see it). In the lift formula the only thing that is changing to bring about these effects (once again as I see it) is a change in CL.

As I understood it CL = lift coefficient and cl (both lower case) the section coefficient. Should the section l be a capital as per your last?

While we have you D as an expert to hand, can you give a definitive explanation as to the reasons why a swept wing (eg Boeing 707 or like) stalls at much higher angles of attack than a straight wing.

Thanks D, and standing by to be educated.
31st Oct 2009, 18:48

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Slow, clean and heavy. Make it easy I will try.

Wing needs to produce required lift, which it will do, I think Slow holds the simple key, wing moving slow allows more time for higher pressure air under the wing to find lower pressure air on top of the wing.

An easy to think of it could be, keep slowing the wing to zero speed and have magic higher pressure air under the wing, this hi pressure air would have all the time in the world to slip over the wing tip and find the low px air.

Well at least that's what I though I read many many years ago.

Anyone have an easy way to explaine why heavy aircraft glide further than lighter aircraft ? (engines switched off)
31st Oct 2009, 20:09

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and even when you have equations it still requires verification I've seen the most elegant math make fools of engineering teams when the actual data was in

Dolphin51 obviously knows what the hell he's talking about,...

but let me say this again aerodynamics is an EMPIRICAL/EXPERIMENTAL science based upon experiment,... real life data on airfoil sections for designers is available in 'Theory of wing sections' by Abbott and Von Doenhoff--this is a BASIC [foundational] text on the subject it has much data and some theoretical treament on high lift devices

also I don't remember the exact name of the authors but there's ananother text ' Aircraft performance, stability and control' the further expands on the subject---

not too bad to get in the right mind set with Hurt either

the reason I like Davies so much is that although he was a TP and spoke engineering' the reason why his text was so effecdtive was because he could translate the abstractions of certification into plain pilot 'Horse Hooey',...I mean he spoke just enough horse hooey to get the stuff that matters WRT to stick and rudder,...pilots are not supposed to be too smart anyway

PA

Last edited by Pugilistic Animus; 31st Oct 2009 at 20:20.
31st Oct 2009, 20:46

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This question always puzzled me.

The engineer has to know what he says, of course. But let me explain my "theory".

I always thought that induced drag (the one responsible for the wake turbulence) for a given lift depended on how this lift was was distributed on the wing planform. If most of it was in the root, like in airplanes with long span, or with eliptical planform, or with some taper ratio, then induced drag was less. Because the "leakage" of air at the wingtips was less.

All wings (or all I know, at least) have flaps in the root area and ailerons near the tips. If we maintaing the flight path after extending flaps, lift will be the same (after the ballooning) but lift distribution will be now more concentrated in the root, therefore reducing induced drag. This makes sense, Doesn't it?

But then, why don't we keep the flaps down all the way as he suggests?

Because when flying at high speeds parasite drag is the problem, not induced drag. And with the flaps down we have lots of parasite drag. This makes sense, too.

What do you think, guys?
31st Oct 2009, 20:56

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boundary layer control and aspect ratio is also important WRT to your question,...much too complex for detail on PPRuNe

or wiki
1st Nov 2009, 13:55

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I agree that tackling a practical problem with a mathematical approach can be challenging. The following might clarify things.
We want to determine the effect on aircraft lift coefficient when trailing edge flaps are moved, but nothing else changes except those things that have to change such as angle of attack and engine thrust. So we imagine this thought experiment. An aircraft is flying straight and level at 150 knots IAS with flaps retracted. Aircraft weight is 10,000 pounds and wing area is 250 square feet. To find aircraft lift coefficient we divide 10,000 by half the standard density of air and the square of 150 and the wing area, 250. (The result is 0.525)
Next we imagine plain flaps have been extended but the aircraft is still flying straight and level at 150 knots. To find the aircraft lift coefficient we divide 10,000 by half the standard density of air and the square of 150 and the wing area, 250. (Again, the result is 0.525 so we conclude that with plain flaps, changing flap setting has no effect on aircraft lift coefficient.)
I agree that in real life, as the flaps are running angle of attack will change and there will be a departure from level flight, the pilot will have to increase thrust to maintain 150, and he will have to re-trim. But most importantly, the above calculations show that after all those transient effects have died away and the aircraft has returned to level flight at 150 knots, the aircraft lift coefficient will be the same as it was prior to initiating the change in flap setting.
Changing flap setting might change induced drag and the strength of trailing vortices but that won’t be because of any significant change in aircraft lift coefficient because we have convinced ourselves that aircraft lift coefficient is independent, or almost independent, of flap setting. We need to look elsewhere to find an explanation for the change in induced drag.
Your question about stalling angles of swept-wing versus straight-wing aircraft is a good one. I will put my thoughts in a separate post on this thread.
1st Nov 2009, 14:24

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To flap or not to flap, that's the question for Mr Vortex

I fly simple aircraft such as gliders and L-19 towplanes.
It is my experience that more lift needed to be provided by slower airflow, using a clean wing, is one source for vortex increase at the tips.
When lowering flaps, the wing's AOA decreases at a given airspeed, hence the wings are at less AOA producing less vortex. However, the airflow around the flap tips will now become the large vortex generators.
I follow other L-19's closely on final and have experience strong roll tendencies of my aircraft when flying through another L-19's vortex.( created by its use of full landing flap.)
Mind; the lowering of flaps at a given airspeed and AOA requires an increase in power setting to overcome the added drag OR the aircraft nose needs to be lowered to overcome the added drag i.e. steepen the glide path, which is exactly what the pilot needs to land in a given space at the slowest safe speed.
I am not very scientific with this explanation, but it helps me understand the operation of aircraft.
1st Nov 2009, 17:39

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just to add the chordwise load distribution over flapped wing sections was given special treatment by Julian Allen in a paper titled " calculation of chordwise load distribution over airfoil sections with plain split or serially hinged trailing edged flaps". NACA report 634,1938

just as an aside in engineering the way certain comparisons in terms of 'efficiency are made' is to compare an ideal [or simplified] theoretical condition to the real condition as mentioned above this simpliedied section is basically a simple flap compared to the real flap this is the flap chord ratio and it is this ration that is the 'efficiency factor mentioned in one of the above post,...so how does one do so?

well the equations are too cumbersome for here but basically when design ing the section,...data from other designs is used,...so that makes these questions well within the realm of experiemtnal engineering would not everyone agree

Munk's integrals have also proven useful in this area
1st Nov 2009, 22:43

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G'day D, I awoke this morning with an inspired "I know what he's talking about". Remarkable how we (I) can become fixated on looking at something from one particular view point - and be wrong. Sorry to have put you to an extensive post when a good slap about the ears would have sufficed. Thanks.
1st Nov 2009, 23:24

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Joetom

Heavier aircraft (of the same type) glide further than lighter aircraft as they start with a higher total energy. (potential due to mass and altitude, kinetic due to mass and velocity....assuming different masses but identical starting altitudes and speeds)

I leave the experts to demonstrate the mathematics.
1st Nov 2009, 23:30

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Reply to Brian Abraham re swept-wing aircraft

G’day Brian. You asked why a swept-wing aircraft stalls at a higher angle of attack than one with a straight wing. I think the best answer is that an aircraft with a lower aspect ratio appears to stall with a higher angle of attack than an aircraft with a higher aspect ratio.

Every fixed-wing aircraft flies in the downwash induced by its own trailing vortices. If the downwash in the vicinity of an aircraft is 10 knots and the aircraft is flying level at 100 knots true airspeed that shows the atmosphere appears to be descending towards the aircraft at a gradient of one in one ten. Ten percent or six degrees. If the wing of this aircraft needs an angle of attack of twelve degrees the angle between the wing and the horizon will be eighteen degrees, not twelve. The effective angle of attack is twelve degrees, but the induced angle of attack is six degrees, so the geometric angle of attack is eighteen degrees.

The downwash and induced angle of attack are what tilts the lift vector backwards so that part of the lift is actually drag – that part of the drag called induced drag. The higher the induced drag the higher the induced angle of attack. Induced drag is highest at slow speeds and on aircraft with a low aspect ratio.

Perhaps the lowest aspect ratio of any manned aircraft is seen on the Anglo-French Concorde with an AR of only 1.5. At low speeds the induced angle of attack on the Concorde causes it to fly so nose-high that the pilots have an inadequate view of the airspace ahead. This is especially true when approaching to land and the pilots need to have the runway in view. The designers of the Concorde gave it a drooping nose so that the pilots had an adequate view in spite of the extreme nose-high attitude. It was the same in the Fairey Delta 2 research aircraft which had a drooping nose.

Delta-wing combat aircraft have an exaggerated nose-high attitude during takeoff and landing because of their low aspect ratio wing.

The spanwise lift distribution of a swept-wing aircraft is far from elliptical, especially at low speeds so its effective aspect ratio is significantly less than its geometric aspect ratio. (Oswald Efficiency Number is much less than one.) As a result, swept wings also appear to have an unusually high angle of attack when flying slowly. In fact, their angle of attack is not unusual but the strong downwash means the angle between the wing and the horizon is significantly greater than the angle between the wing and the approaching air.
2nd Nov 2009, 01:22

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My goodness... phew...

If we're sticking to the original question, I think ahramin had it best covered quite a while back.. my answer would be much the same as his. The Slow and heavy bit is easy of course, vorticity function of Cl ^2

Somebody said this of those authors quoting also CLEAN as a condition..
Perhaps the authors of 90-23F know something that aerodynamicists don’t. Aerodynamicists would be willing to accept the knew knowledge if only the authors would divulge what it is.
This is matter of QUALITY Vs QUANTITY as ahramin said I think...

Due to non-elliptic distribution, the TOTAL vorticity will almost certianly be highest with flaps extended (perhaps even with Fowlers extending without deflection, which also upsets the elliptical distribution)

BUT, that DIRTY voriticity will not all be wound up fractionally inboard of the wingtip, as it would for a nominally elliptical distribution*

So the upset(ting) potential may well be less, when in a dirty configuration, with strong trailing vortices but several of them across the span, dumping at points where there are significant steps in chordwise circulation (which is what creates lift).

* A straight taper wing of sensible (>7) AR and of nominally constant section and a wee bit of washout, does as someone stated, produce a spanwise lift-distribution quite close to elliptical, maybe close to 0.9 efficiency factor.

- The Spitfire Wing -

The story goes that this was not made elliptical due to the so-called 'ideal' lift distribution (an expensive production challenge anyway, as Vickers found out). It was originally sketched by RJ Mitchell, around the constraints he had to work with...
Span
Area
Thickness (Spit was always a thin wing, )
Guns- 8 of them within the above three constraints...meant that he had to keep the chord wide well outboard

The consequence was that he opted for a nominally elliptical planform to fit everything in, was accused of copying the Heinkel He70, certainly admired its aerodynamic smoothness, but his colleagues denied it had significantly influenced the Spitfire's layout.
Physical constraints had determined the Spirfire's wing (Mitchell was known as a good down to earth practical, not a fanciful or too theoretical engineer). Of course, he was aware that this planform wouldn't do any harm to it's maneouvring drag and so it also proved, whatever came near or bettered it at various stages in it's fighting life, it always could turn inside them, and at a similar power output, outclimb them in steady state (non-zoom) conditions.
Even the last of the line, the Griffon powered Seafires could climb to 40,000 feet faster than almost anything piston powered, certainly getting up there quicker than a Sea Fury (10 minutes from memory). In fact it could go on to about 50,000 & 51,500 wasn't unknown in the tropics! That was 10 years after it first flew too...quite a sustained development programme that that original elliptical wing (strengthened immensely torsional stiffness) made possible. The main spar was an absolutely unique design... (thin wing, had to be a bit special)

Thus, however highly thelater P51 is rated, the Spit was always to its last operational days, the better pure interceptor, exactly what it had been designed to do in 1935/6... and the 'accident' of the elliptical wing may have helped a bit.

Oops! Have I strayed somewhat

Last edited by HarryMann; 2nd Nov 2009 at 02:23.
2nd Nov 2009, 13:35

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D - I think you have left out the effect of vortex lift? If you are straying into Concorde/FD2/HP17 territory then is it not established that a very large part of the lift generation on very low aspect ratio wings is from vortex rather than 'classical' aerodynamics? I was always taught that it was vortex lift which continued flow attachment and 'lift' well past normal angles.
2nd Nov 2009, 22:51

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c=wing chord

cl = section lift coefficent

alpha [i]=downwash angle in degrees at span wise position 'y' measured from the center along dy

AoA e = effective aoa [as described by in HTBJ] =Alpha-alphi

effective Aoa at is a function of cl

skipping a few setps we finally have [to just scratch the surface]

alphae =alpha -180/pi*b/2pi*int[d/dy(cl*c?4b)dy/y1-y],b/2,-b/2]

solving this equation for your chosen sections will determine both down wash and span wise distribution

a mathmatical explaination of Dolphin1's eloquent post

as far a the vortex effect on general circulation [as BOAC mentions] I'm not gerttin on that bus
2nd Nov 2009, 23:09

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repaat for edit

I'm trying to edit slightly the above post, but the computer wont let me nor can I delete it as a copy

c=wing chord

cl = section lift coefficent

alpha [i]=downwash angle in degrees at span wise position 'y' measured from the center along dy

AoA e = effective aoa [as described by in HTBJ] =Alpha-alphi

effective Aoa at is a function of cl

skipping a few steps we finally have [to just scratch the surface]

alphae =alpha -180/pi*b/2pi*int[d/dy(cl*c/4b)dy/y1-y],b/2,-b/2]

solving this equation for your chosen sections will determine both down wash and span wise distribution

a mathematical explaination of Dolphin51's eloquent post

as far as the vortex effect on general circulation, in supersonic/non-ideal flows [as BOAC mentions] well I'm not gettin on that bus

PA
3rd Nov 2009, 01:59

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D - I think you have left out the effect of vortex lift? If you are straying into Concorde/FD2/HP17 territory then is it not established that a very large part of the lift generation on very low aspect ratio wings is from vortex rather than 'classical' aerodynamics? I was always taught that it was vortex lift which continued flow attachment and 'lift' well past normal angles.
It is, due to the low AR and sweep, and 'controlled' in Concorde's case by a very clever Ogive planform and cunningly cambered leading edge (tricks learnt on the Fairey delta, Vulcan and Lightning, and TSR2 (of course!)

The LCS (Lift Curve Slope), normally 2 Pi (radians) for an infinite AR (2D) wing, deteriorates in a consistent manner with reduction of AR. Due to large amounts of 3D flow, the stall becomes mushy, very draggy and indeterminate as top-surface flow and thus overall circulation breaks down, Clmax usually suffers.. think Lockheed Starfighter (the widow-maker!)

But with sweep, lots of it, and the appropriate l.e shapes, that 3D flow can be controlled and utilised..Think of the lift-line being rotated backwards so the ciurculation takes place alomg a more fore-aft than spanwise axis... massive vortices develop as incidence increases, and whilst drag goes up massively too, Clmax's are maintained without flaps, once the vortex is stabilised...

One of the bonuses of the delta wing is the vortex sheet
which attaches itself at low speeds and high angles of attack.
It increases lift, it is claimed, by about 30 per cent and by
as much as 60 per cent in the ground cushion on landing.
By rounding the wing tips and extending the root fillets (thus
producing the "gothic" plan-form) this vortex sheet can be
made to stay attached up to and beyond the stall.
One downside is being on the back-side of the drag-curve, induced drag is high, and when slowing even more, increases dramatically! Of course, cart down helps.

Last edited by HarryMann; 3rd Nov 2009 at 02:27.
3rd Nov 2009, 07:41

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I just love that lower picture, HM! So illustrative. Any idea what alpha that is, and what the 'white' ?vortex? is which appears to start 'nowhere'?

Being well out of touch with modern aerodynamics like the ogive, has the 'stall' been re-defined for these shapes? Obviously there is no clear point where flow 'separates' since it is pretty well 'separated' at most angles and the classic 'nose-drop' and sudden onset of sink rate are no longer there. Do you know what the trigger is for the ultimate breakdown of the 'attached' vortex?