Why wing-loading isn't always the most important characteristic

[Stoney]

Just an example I discovered doing the stall testing on the 190 family...  It also shows an interesting phenomenon related to aspect ratio.  When testing the standard airframe 190s (A5, A8, D9), the wing-loading and how it affected stall speeds was intuitive--i.e. the higher the wing-loading, the higher the stall speed.  It surprised me to find that even though the Ta-152 has the lowest wing-loading of the 4 aircraft, it has the highest stall speed of the four tested.  Stall test results can be found here:

http://bbs.hitechcreations.com/smf/index.php/topic,287289.0.html

This is basically a function of its aspect ratio, where the Clmax is achieved at a much lower AoA compared to the other 190s.  Generally speaking, the higher the aspect ratio (or more precisely, the wing span), the lower the stall AoA will be.

[Stoney]

Another thing I found interesting:

Between the 190 series and the Ta-152, the 190s generate a higher Clstall in the clean configuration than the Ta-152.  They actually generate a higher Clstall than the Spit 5/9 (ignoring lift due to thrust and CG affects).

Using the stall speeds and other metrics collected during the tests:

Given the equation Clmax = L / q * S

Where:

Clmax = maximum lift coefficient
L = Lift (Weight)
q = Dynamic pressure (1/2*p*V^2)
S = Wing area

[Ardy123]

the higher the aspect ratio (or more precisely, the wing span), the lower the stall AoA will be.

I don't understand how AoA is related to wingspan. AoA is the angle the wind hits the wing correct? How is that impacted by wingspan? Obviously, wingspan relates to wing area but unless there was a 'twist' in the wing, wouldn't the AoA of a given wing be constant?

Also, the 'Lift' variable, I mean isn't that a function of the speed of the air and the AoA as it crosses the wing? ie the same wing with the same AoA moving at 50 mph produces less lift than if it were going 150 mph?

Thanks

[Stoney]

Excerpt from the USN Fixed Wing Performance, Flight Test Manual:



If wing area remains constant, an increase in aspect ratio is purely an increase in wing span. 

Lift variable in my equation isn't a variable--its fixed, given the plane's weight.  Lift = weight in unaccelerated flight. 

[Ardy123]

Stony thank you for the information, I am by no means trying to discredit you or argue, only trying to understand. so given a 'real' values.

FW 190 A8(accoridng to wikipedia)
wing span 10.50 m
wing area 18.30 m²
Weight  3,490 kg

clmax = 3,490 / ((1/2*p*V^2) *18.30

Whats p and V?

[Stoney]

Stony thank you for the information, I am by no means trying to discredit you or argue, only trying to understand. so given a 'real' values.

FW 190 A8(accoridng to wikipedia)
wing span 10.50 m
wing area 18.30 m²
Weight  3,490 kg

clmax = 3,490 / ((1/2*p*V^2) *18.30

Whats p and V?

(1/2*p*v^2) is the common expression for dynamic pressure, or rho (q).  So, in my formula Clmax = L / q*S, you have the weight of the aircraft divided by dynamic pressure * the wing area.  For dynamic pressure, the "p" = air density at the specified altitude in slugs(I used sea level since my stall speeds were all at sea level).  V is velocity in feet per second.  To get this, multiply mph X 1.467 to get fps.  Using this formula, you can determine the required lift coefficient for any condition of flight.  Its an approximation that will get you very close.  For example, if you wanted to find the required Cl at 20,000 feet and 385mph, you can plug in the air density for 20,000 feet, and 385*1.467 to get 564.8 fps.  Therefore rho (or "q", or dynamic pressure) would = .5 * .1267(air density at 20,000 feet in slugs) * (564.8)^2 or 20208.6.  Plug rho into the equation using your example and you have:

Cl = 3490 / 20208.6 * 34.4 (need area in ft^2) ~ .005.  This would be the required lift coefficient for the 190 at the weight you listed, flying at 20,000 feet and 385 mph.  If the required lift coefficient is higher than what the wing is capable of (Clstall), you could consider that condition of flight to be outside the envelope of the aircraft.

If you use the stall airspeed, you will find Clmax.  If you use any other airspeed, you will find required Cl at that condition.  Aircraft designers sometimes start with this formula in order to determine the wing-loading required to give them the desired landing speed.

[Ardy123]

Ok, thats very interesting, thanks! Now one last question, I hear a lot about NACA airfoils and how their shape will change the behaviors of the wing, including the lift and stall characteristics. The above equation did not take airfoil shape into effect at all, is there an extension to the listed equation that accounts for the airfoil shape? Also, doesn't the overall shape of the wing have an effect too (ie 37 degree sweep on wings for fighter jets, or diamond shape wings of the yak, etc..).

[WMLute]

OMG!

I almost understood that!

[Charge]

"Now one last question, I hear a lot about NACA airfoils and how their shape will change the behaviors of the wing, including the lift and stall characteristics. The above equation did not take airfoil shape into effect at all, is there an extension to the listed equation that accounts for the airfoil shape?"

That is a good question Ardy and I have been wondering exactly the same.

I think that the problem lies in the definition of Cl or CL depending on if we consider 2D or 3D lift characteristics since they provide approximations which are adequate for most uses. Ok there is alpha and according to airfoil data we know the limit at certain Reynolds number which determines the flow speed around the airfoil but I have understood that Re is not the speed itself i.e. Mach number.

http://en.wikipedia.org/wiki/Lift_%28force%29

http://en.wikipedia.org/wiki/Lift_coefficient

http://en.wikipedia.org/wiki/Lifting-line_theory

http://en.wikipedia.org/wiki/Reynolds_number

http://en.wikipedia.org/wiki/Mach_number

So where exactly does the airfoil geometry plug in? Calculating the general CL of a wing at certain alpha can it be just counted in as a modifier to result if wing profile characteristics are known?

http://en.wikipedia.org/wiki/File:Lift_curve.svg

I think that one of the competitors of Aces High is using some kind of a general lift curve for their FM since the maximum alpha is same for all their aircraft. If the airfoil data is counted in all along the calculation would it be too complicated calculation to run in real time?

-C+

[Wmaker]

Ok, thats very interesting, thanks! Now one last question, I hear a lot about NACA airfoils and how their shape will change the behaviors of the wing, including the lift and stall characteristics. The above equation did not take airfoil shape into effect at all, is there an extension to the listed equation that accounts for the airfoil shape? Also, doesn't the overall shape of the wing have an effect too (ie 37 degree sweep on wings for fighter jets, or diamond shape wings of the yak, etc..).

The Cl of an aircraft is normally very close to the Cl value(s) of its wing profile in power off condition. So the Cl-value of an aircraft that comes out of the equation is very much dependent of the airfoil(s) that particular plane uses.

For example using AH 190A-8's stall speeds and weights from Stoney's testing (4245kg/172km/h) you get a Clmax value of ~1.6 which is very close to the Clmax values of NACA 23000-series airfoils which Fw190 used.

[PJ_Godzilla]

Ok, thats very interesting, thanks! Now one last question, I hear a lot about NACA airfoils and how their shape will change the behaviors of the wing, including the lift and stall characteristics. The above equation did not take airfoil shape into effect at all, is there an extension to the listed equation that accounts for the airfoil shape? Also, doesn't the overall shape of the wing have an effect too (ie 37 degree sweep on wings for fighter jets, or diamond shape wings of the yak, etc..).

If I understand your question, I'd offer that, if you look, for example, at Stoney's plot above, you'll see that Cl = f(alpha) and that that function changes, airfoil to airfoil (2D) and 3d wing to 3d wing (as he shows here for varying aspect ratio) . If you're interested, take a look at, for example, Abbott and Von Doenhoff - it's a classic text on airfoil sections and plots out the cl versus alpha characteristics for many common 2d airfoils. My understanding of the development of most of these plots is that they're empirically derived (i.e., from test). Conceivably, you could "virtually" test 'em now, given CFD but A&vD predates computers as we know them.

And yes, the overall shape dramatically affects the wing characteristics. Consider, for example, cross-flow on swept wings causing higher relative velocities locally or the impact of elliptical planforms on drag and trailing vortex formation. 

Speaking, as we were, of aspect ratio, one of the upsides of high AR is low induced drag - and this is related to Stoney's point, imj. Since induced drag is the "dragward" component of lift, and since a high AR wing produces more lift at lower relative AofA, his plot makes good sense. High AR planes tend to climb like demons for this reason - they can make lots of lift without making lots of induced drag - and THAT in turns, is corroborated, as expected, by our own AH Ta-152. The downside? Well, it gives it up in stall sooner too.

[bozon]

Speaking, as we were, of aspect ratio, one of the upsides of high AR is low induced drag...

Sort of. High aspect ratio lowers the effect of wingtip turbulence. This vortex around the wingtip transport air from below the wing plane to above it and lowers the effective lift (lower CL). To produce the same lift, higher AoA is required and this builds more induced drag. At the same time, the lower pressure difference due to the vortex delays the stall and the wing can be pushed to higher AoA.

At high speeds level flight, the AoA is typically rather low and the effect of wingtip turbulence is less significant. Planes that need to maximize speed are typically designed with low aspect ratio wings (there are also other considerations). Good example is the Mirage 3/5/2000. With the short delta wings it cannot turn worth a damn, but it has a gentle stall and can "mush" into the turns at high AoA. It also has a very high top speed and rate of roll.

Wing profile matters. If you strap two doors of some size to a fuselage you can get any "wingloading" you want but it will not even get off the ground. High aspect ratio wings have a problem with the stalls, especially with some profiles as the whole wings suddenly stalls at once. Therefore sometimes the profile changes along the wing and sometime the wing has a twist to it - as far as I know this is the case with the spitfires. The idea is to lower the angle of attack at the outer wing at the ailerons section. The stall then develops gradually from the wing root outward and is much more gentle. It also leaves the ailerons effective even though part of the wing is in stall and significantly lowers the risk of snap stall. The price is the the wings produce less lift than what one might expect from its area (call it lower CL). It also has more drag at any AoA. So again wing-load is not the whole picture.

[PJ_Godzilla]

Sort of. High aspect ratio lowers the effect of wingtip turbulence.

Therefore sometimes the profile changes along the wing and sometime the wing has a twist to it - as far as I know this is the case with the spitfires. The idea is to lower the angle of attack at the outer wing at the ailerons section. The stall then develops gradually from the wing root outward and is much more gentle. It also leaves the ailerons effective even though part of the wing is in stall and significantly lowers the risk of snap stall. The price is the the wings produce less lift than what one might expect from its area (call it lower CL). It also has more drag at any AoA. So again wing-load is not the whole picture.

Agreed, Your second para here clearly refers to washout - of both the aero and geometric variety. The FW appears to have actually had some "wash-in", per Stoney's (another thread) sourcing of the sections inboard and outboard on the venerable Focke...

As for wingtip vortices, I'd contend that, independent of AR, you can eliminate them altogether with an elliptical lift distribution. That's why I find your initial point cryptic since the AR dictates nothing about the pressure discontinuity at the tip - other than that it's likely to be a small-chord section, the way it's generally executed. But I find this distinction practical, as opposed to abstract and general, since a counter, as I 've stated, is readily available. 

[bustr]

In WW2 was the organic 3D shape of the wing targeted at a mission role or was it a choice by the designer to first achieve a unique performance specification then as circumstances unfolded in battel the mission roles? The Russian fighters all seem to have similar wing shapes to the yak9 and Lavotchkin or the 109 and 190 series have straight tapers. But then the U.S. and Britain had a mixture from elliptical to shapes like the Russians and germans. 

Is this a chicken or an egg question?

[Stoney]

In WW2 was the organic 3D shape of the wing targeted at a mission role or was it a choice by the designer to first achieve a unique performance specification then as circumstances unfolded in battel the mission roles? The Russian fighters all seem to have similar wing shapes to the yak9 and Lavotchkin or the 109 and 190 series have straight tapers. But then the U.S. and Britain had a mixture from elliptical to shapes like the Russians and germans. 

Is this a chicken or an egg question?

Bustr, its a good question.  Basically, designers of the era did not have the full knowledge of aerodynamics we do now.  Remember that WWII started only 35 years after the Wright Bros. first flew.  A lot of the knowledge of planform, airfoil, wing sweep, and aspect ratio and how they impacted the efficiency of the wing, weren't really known.  There was a lot of "almost" knowledge out there as a result of designers simply regurgitating NACA testing and documents, but, for example, Supermarine probably didn't consider that the washout they introduced to control tip-stall was both (a) contradicted by the airfoil thickness taper, and (b) only good for making the wing draggy as hell.  Had they known a little more, they would have realized that an elliptical lift distribution can be approximated in ways that are much more cost effective than a true "elliptical" wing. 

IMO, the two most important "aerodynamic" advances of the war were the design of the P-51D, which broke the mold, from an aerodynamic perspective, of the WWII fighter, and the Me-262.  Obviously the Germans had figured out how important transonic considerations were for jets.  Compare it to its peers in England and the U.S. who were still building "straight" winged jets.  Another example can be seen in wingtip designs.  Almost all early WWII aircraft had highly rounded wing tips, which were designed in the erroneous belief that they "mocked" elliptical shapes, and therefor, had lower drag.  Had they had more wind tunnel data, you would have seen more straight wing tips that would have been more efficient, earlier.

We have the benefit of analyzing all of this stuff with 20/20 hindsight.  At the time, all of these designs were considered by their manufacturers as "state of the art".