Wing Loading: You keep using that term....

[sprstdlyscottsmn]

... I do not think it means what you think it means.

Hello everyone. We recently had a poster who seemed to think that wing loading was the end all be all and we also frequently have posters who try to modify wing loading based on body lift. These things get under my skin so I am starting this thread as both a way to get this off my chest and to maybe, just maybe, educate a few people who want to know better.

Wing Loading: What is it?

Wing loading is the weight of an aircraft divided by the reference wing area (the one you can easily find in any open source). It is used as an idea of how "heavy" an aircraft is but it does not tell the whole story. Not for a wing+tube (F-104) or for a flying wing (B-2). Let's discuss why: Stability, total lifting surface, total lift coefficient.


Stability: Why more is worse

Stability is complex and is not static. I will happily go into this at length at another time. For now we will say that stability is the tendency to lower the nose if a gust increases AoA momentarily. It means the center of lift (total, not just the wing) is behind the center of gravity.

In order to balance the pitching moment a download (negative lift) is applied to the tail (not discussing canards at the moment). This means in level flight the total lift of a plane is equal to Weight-Tail Load+compensation for tail load. A stable tail means not all the lift the plane is making is fighting gravity, some of it is just there for balance. The tail loads and compensation for tail loads both create additional drag, called trim drag.

It was recently discussed that under a max G turn at high speed an F-111 had a tail load equal to 20% of the net lift, meaning net lift +20% is what the rest of the plane had to generate. That means that a total of 140% of the net lift was being generated, 120% up, 20% down. This would mean trim drag would be on the order of 96% of the standard "Induced Drag". This is an extreme case.

In effect, sometimes not all lift made by a plane/wing is usable to turn the plane. When a plane is in an unstable condition then a lifting force is generated by the tail. When this occurs all the lift of the aircraft is used to turn/fight gravity and trim drag is effectively zero. The stability of a plane changes with fuel and payload and also changes with angle of attack, so even a stable design can reach an unstable condition and vice versa.


Total Lifting Surface: Never add "Body Area"

It is fairly common knowledge at this point that the body of a fighter makes lift. This is as true of any airplane, and I do mean any airplane, only the total contribution is different. Now, on to "widebodies."

People often point to the tunnel design of the F-14, MiG-29, and Su-27 as the best for generating lift stating that the tunnel "increases the wing area". They then use this info to adjust the Wing Loading (remember Wing Loading? This is a thread about Wing Loading) by as much as 40%. This is sometimes countered by statements than even the F-16 can get 40% of its lift from the body under the right conditions, or the IDFAF F-15 that flew home on one wing.

Obviously the wing (as defined by the part protruding from the fuselage) does not produce all the lift. The protruding wing area however is not the reference wing area stated in open source documentation or used in Wing Loading calculations. Roughly 40% of the Ref Wing Area is in the fuselage of nearly every fighter made from the F-14 onward (Isn't it funny how so many sources say the body adds 40% to the lifting area?).

Clearly this buried wing area does not have the same aero properties as the exposed wing. It will have a different lift curve, drag curve, moment, critical angle of attack, critical Mach, etc. The Ref Wing Area works because it ends up averaging out everything within a reasonable margin. How?


Total Lift Coefficient: Where everything comes together.

Let's say the Ref Wing Area is 10, just for easy math. 3 on each wing and 4 in the body. Now let's say with the shape of the wing and the high lift devices allow for the exposed wing to generate a CLmax of 2. This does NOT mean our total LIFT AREA is 20 (Cl 2 * RWA 10). It means the contribution of the exposed wing is 12 (CL 2 * eWA [2*3]). The body of the aircraft has a total area (not including exposed wing) of 15. At the angle of attack where the wing hits CLmax the body is only up to a CL of 0.5. This contributes 7.5 units of lift. The total lift of the aircraft is 19.5 units. This comes to a Ref Wing Area CL of 1.95 (units of lift divided by Ref Wing Area). Induced drag is a function of CL^2 (We'll just call it 3.8 right now).

If we increase the angle of attack the main wing begins to lose CL, let's say it's down to 1.5 for 15 units of lift. The body however is up to a CL of 0.7 for 10.5. Now our total lift is up to 25.5 units! However since the main wing has stalled and the body has a worse L/D than the wing (this will always be the case) you are making so much more drag than you were before. So now, even though our component CLs are 1.5 and 0.7 our Ref Wing Area CL is 2.55 with a corresponding ref induced drag of 6.5. Didn't I say we would have more drag?

Hey look, the body lift happens to be just about 40% of the total lift under this condition.

This is why total lift coefficients are so important if you want to estimate agility. I use the term Lift Loading for dividing the weight of the aircraft by the units of lift I described above (CL times Ref Wing Area). The problem is total lift coefficients are not easy to find. You need to look up research papers with wind tunnel data of whole aircraft models or flight test data. If the data is given in stall speed then you need to know the equations and how to balance the units in order to get the CL. Then you need to remember that the greater the difference between Wing Loading and Lift Loading the greater the induced drag will be meaning Sustained (Ps=0) turns are that much harder.

I have intentionally written this on a low level so that it does not take an engineering degree to understand it. There will always be small nuances and corner cases but in general what I have written should hold up.

Okay I think I am done now.

[botsing]

Thank you for this vital part of information!

I learned something new today.

[sprstdlyscottsmn]

I am theoretically done with the original post.

[vanshilar]

What about the effect of wing sweep and aspect ratio on wing loading with regards to using it as a proxy for maneuverability? My understanding (which may be wrong) is that delta wings inherently has to have lower wing loading to achieve the same level of maneuverability (due to the wing sweep angle and/or the low aspect ratio or something along those lines) -- which is why Eurocanards (Rafale and Typhoon in particular) have very low wing loading. Yet the wing loading is held up as evidence that they're more maneuverable than everything else, since their wing loading is lower than even the F-22's. And the Mirage 2000 has even lower wing loading than the Eurocanards (obviously even more maneuverable!).

[count_to_10]

What about the effect of wing sweep and aspect ratio on wing loading with regards to using it as a proxy for maneuverability? My understanding (which may be wrong) is that delta wings inherently has to have lower wing loading to achieve the same level of maneuverability (due to the wing sweep angle and/or the low aspect ratio or something along those lines) -- which is why Eurocanards (Rafale and Typhoon in particular) have very low wing loading. Yet the wing loading is held up as evidence that they're more maneuverable than everything else, since their wing loading is lower than even the F-22's. And the Mirage 2000 has even lower wing loading than the Eurocanards (obviously even more maneuverable!).

The short answer is that "wing loading" was only ever an approximation, even for "winged cylinder" aircraft, and doesn't really work as a proxy for maneuverability.

[sprstdlyscottsmn]

Right. The issue with Deltas is that they have a lot of area (good wing loading) but a very long (high max AoA) and flat lift curve slope (poor CL at any given angle of attack). This is why they tend to have one good pull in them as they bleed off all their airspeed from the induced drag.

[linkomart]

Nice thread...
The issue with deltas is not so much the leading edge sweep, more the poor aspect ratio. The fact that the leading edge is swept a lot means that there is a leading edge vortex attached to the wing at high angles of attack that gives a low pressure zone above the wing, contributing to a high cl. The downside to that is that the cd goes up proportionally more, giving a higher drag. So for instant turn performance it is ok, but the sustained turn suffers a bit.

my 5 cent.

PS
tail load.. have to get back on that subject.
DS

[sprstdlyscottsmn]

I didn't call it out specifically, but it would have been part of the Total Lift section.

[linkomart]

I didn't call it out specifically, but it would have been part of the Total Lift section.

eh, sorry, do you by it mean the tail lift or the aspect ratio?
I realize you didn't go in to detail about the subject, if you do that it would fill books... and it has been done. Anyway, nice thread.

Right. The issue with Deltas is that they have a lot of area (good wing loading) but a very long (high max AoA) and flat lift curve slope (poor CL at any given angle of attack). This is why they tend to have one good pull in them as they bleed off all their airspeed from the induced drag.

Agree


Best regards

[sprstdlyscottsmn]

I was meaning tail lift. Leading edge sweep will flatten the lift slope. So will low aspect ratio. Deltas get a double dose. You are right that volumes could be, and have been, written on the intricacies of lift.

[F-16ADF]

Here is part of the problem.


The pro Grumman/F-14 poster (I will refer to as G....y). I assume we are discussing the prior F-14D vs F-15E thread. Is listening to the words from Mike Ciminera at 16:45.

Listen to Ciminera's words very carefully:

https://www.youtube.com/watch?v=SsUCixAeZ0A

Ciminera (who in fact was a Grumman Aerospace Engineer for many, many decades) does say that its (F-14) wing loading was more "like 44-48lbs/sq ft."

He shows this chart:

http://i19.photobucket.com/albums/b169/ ... ngarea.jpg


Mr. Ciminera is in fact adding 443 to the normal reference area of 565sq ft.

So my point is, people like G....y (and F-14 fanboys aka "Grummanites") will simply always defer to Ciminera's words from the video. I have tried to argue this point over the years with Grummanites. And their usual response is/was: Ciminera was a Grumman Aerospace Engineer for many years, are you smarter than him?"

And there are many other sources that do tend to point out the combined 1008sq ft. number.

That is why in my responses to him I adjusted my numbers to correspond to his belief of what he thinks wing area is. And of course he will ALWAYS say Mr. Ciminera (again, a well seasoned Grumman Aerospace Engineer) is right and everyone on F-16.net is full of BS.

The same can be said of Commander Robert L. Shaw's (he is an Aerospace Engineer and flew the F-14 for many years) book on pg. 139:

"This G capability reflects the maximum lift to weight ratio of the fighter, which depends to a great extent on the ratio of aircraft weight to total wing area, commonly called the "wing loading." As explained in the Appendix, wing loading alone can be misleading in this regard if one fighter has a more efficient wing for producing lift, possibly as a result of maneuvering slats or flaps. The way in which wing loading is calculated provides a further complication as illustrated in Figure 4-1 (he exhibits the same F-14 chart that Ciminera did in the video). The wing loading of the F-14 fighter shown here might be stated conventionally as 97lbs/sq ft, based on the shaded area in the left hand silhouette. The very broad fuselage of this aircraft, however, provides a large proportion of the total lift, particularly at very high AOA, so a more realistic value of wing loading 54lbs/ sq ft. might be based on the area shaded in the right hand silhouette."


Also, Rear Admiral Gilchrist's (he was an AE/consultant and naval aviator (F-8/F-14))book about the F-14 says basically the same thing (pg.29).

So technically all three men here are not using the traditional reference area of 565 sq ft. (wingtip to wingtip) of the F-14 (wings at 22 degrees) in their calculations. They are factoring in the portion below the "traditional" reference area (bottom portion of the pancake + nacelle shelves) and the portion above the "traditional" reference area (top portion of the pancake + highly swept strakes that terminate at VG intakes) to factor in an additional 443 sq ft into the equation for to what they refer to as "wing area" now equating 1008 sq ft (wrong or right).


Quite frankly I do not understand why these people do this? However, who am I to criticize them.




Books such as "Flight Theory and Aerodynamics" pg 63 states that "wing area S, is the plan surface area, including the area covered by the fuselage." and Klaus Huenecke says on pg. 37 of his book: "The wing area S is the projection of the wing on the x-y plane." And again according to "Introduction to Aeronautics" pg. 114 "The wing span B is measured from wing tip to wing tip (line goes through the fuselage)."


However, wing loading by itself is relatively inconsequential without knowing the total lift of the aircraft (CL). The Lift Coefficient takes into account all lifting areas whose sum equals total lift.

pg.128 of Introduction to Aeronautics: "...It (normal planform) is a poor approximation for fighter aircraft configurations like the F-16 and F-22, for which the strakes and wide fuselage contributes a very significant part of the aircraft's total lift."

pg. 125 states: "The strake also increases the total lifting area (intense low pressure field at high alpha), but it is usually not included in the reference planform area."

Again as the book says on pg. 113 "Other components beside the wing contribute to an aircraft's lift. The lift contributions of the aircraft's fuselage, control surfaces, high lift devices, strakes, etc. all must be considered to predict an aircraft's lifting capability accurately. The aircraft's maximum lift coefficient is one of the governing factors in an aircraft's instantaneous turn capability, landing speed and distance, and takeoff speed and distance."

And:

"The drag of all aircraft components must also be included when estimating whole aircraft drag. The variation of an aircraft's drag coefficient with its lift coefficient is called the aircraft's drag polar. The drag polar is the key information about an aircraft needed to estimate most types of aircraft performance. Aircraft maximum speed, rate, and angle of clime, range, and endurance depend so heavily on an aircraft's drag polar that a 1% change in drag can make a huge difference in a jet fighter's combat effectiveness."


As I earlier said, try telling this (and wing area vs total lift) to people such as G....y or those (Grummanites) on other sites. Or try explaining to them that while the total lift of the Tomcat and Eagle are, yes, both substantial.... They both also exhibit fair amounts of subsequent drag (remember those giant boxy VG intakes)....

One great attribute of the F-16, I believe, lies in its low drag design.

[sprstdlyscottsmn]

F-16adf, You get it. What even those Grumman engineers are leaving out int their statements is that the Lift characteristics of the wings, pancake, nose, intakes, nacelles, and stabs all have their own component. The pancake, being more airfoil shaped, is better per unit area than the nacelles. So while something like the Eagle does not have anything as efficient as the pancake its body does have better lift properties than the nacelles of the Tomcat. So it still averages out fairly well, but again as you noted this is all covered in total lift coefficient.

You indeed mentioned the thread, and poster, that drove me nuts. I started this thread to kind of scream at the aether.

[rheonomic]

I'll note that there was a lot of research done in the early-mid 90s on metrics to compare different fighter aircraft; search for "fighter agility metrics", e.g. this dissertation (PDF).