Area ruling in design

[Tuba Mirum]

I'm sure this question must have been asked before, but can't find a reference on PPRuNe.

I understand that an area-ruled design has advantages in the transonic and supersonic regimes. Could anyone enlighten me (ideally without university-level maths ) as to why this should be so? I think one aspect of this that confuses me is why a lateral extension of the cross-section at, say, the wing root should help the process when intuition says the airflow is following the long axis of the a/c - hope I'm making myself clear on this.

[Notso Fantastic]

From my elementary aerodynamics from 34 years ago, view the shape of the aeroplane as a series of cross section areas nose to tail. The graph of those areas should be as smooth as possible in a nice smooth mountain shape to minimise drag. Hence where the wing is, ideally the fuselage should 'waist' (impractical engineering wise). After the wing, some filleting should be used to smooth out the sudden drop in area (big fat wing root fairings or wing mounted area ruling structures-http://www.airliners.net/open.file/327737/M/). Those Convair 990 ones are called anti-shock structures, but I think it's the same thing.
Airliners don't allow such free expression with design as fighters, and it's with fighter design you very often see significant area ruling features. Don't know why , but it seems to work.

[gas path]

Notso's about on the money there. The cross sectional area ideally should remain the same except for a very gradual reduction before and after the wing. So the fuselage will be waisted at the area of the wing and tailplane. It's something to do with minimising form drag and the way the airflow behaves at transonic and supersonic speeds.
I think that they were called 'Kuchmann' pods??? (on the Convair 990) designed to delay the onset of the shockwave on the wing.

Bl00dy 'ell Notso I'm nearly as old as you.

[411A]

Older than you both...probably

The bits on the CV990 were called "speed bodies" (at the time, in the 'popular' press) and delayed onset of transonic flow.
Probably the best visable portion of 'area rule' structure can be noticed on the B747SP, at the back end.
'Coke bottle' shape personified.

[Jhieminga]

747SP Rear end

I wouldn't call the rear end of a 747 SP an example of area ruling. The reason for the indentation is (in my view) purely the result of the removal of a large part of the tapered afterbody of the aircraft when they designed the SP. The difference in width of the fuselage sections that then needed to be grafted together necessitated the indentation. The only other option would have been to redesign the entire tail section and Boeing obviously didn't want to pay the cost of that.

Ironically the 747 does posess a very good example of (probably not fully intentional) area ruling and its on the other side of the wing. The upper deck just slopes down to the normal fuselage height at the point where the wings start to sprout from the fuselage, this has the aforementioned effect of keeping the total cross section area more or less the same, or at least increasing it gradually.

[Notso Fantastic]

Bingo- the 747SP is probably one of the most identifiable examples of 'in your face' area ruling. Look at this Pan Am one:
http://www.airliners.net/open.file/347537/M/
That shaving under the fin is more than a nice big fat fin base (incidently the width of the base of the fin is 48"- not many people know that- or want to). This is where the wingtip area is running out and the fin/tailplane area is increasing, so to try and smooth out the profile slightly the fuselage has been shaved down. One of the favourite area ruling tricks is to vary the shape of a nice large wing-root fairing- Airbus A330/340 in particular:
http://www.airliners.net/open.file/351871/M/
They're not really usable space as they are outside the pressurised body- they are just flimsy fibreglass structures braced with surprisingly weak looking brackets.

[Tuba Mirum]

Thanks for the replies so far. It seems to me (please correct me if I've misunderstood) that the questions of what area ruling is, and the fact that it helps with transonic and supersonic flow, are well understood; but that the question of *why* area ruling works may be less well understood (cf Notso's comment in his first post). Is this a fair summary?

[Notso Fantastic]

Toobs- I don't think it's such a mystery. Think of a large body passing through air at high speed- the effects on the surrounding air. If it can compress fairly evenly and then expand again, it's not going to resist the passage of the body so much. Any deeper than that and you are into degree territory!

[Flight Safety]

Notso, I think the issue is a little more complicated than that, though you're on the right track.

In reference to the cross section profile mentioned above, you could think of an aircraft cross section this way.

Suppose you had a very large thin white screen and you mentally "passed" an aircraft through it on an axis perpendicular to the screen, so that the only thing that showed up on the screen, was the immediate cross section of the aircraft that happens to be in the "plane" of the screen. Suppose you could stop the "passage" of the aircraft through the screen at any point and measure the area of the aircraft's cross section.

Now think of the screen as representing a cross section of air that is being disturbed by the aircraft passing through it.

The air next to the "edge" of the aircraft's cross section, has to move "in" or "out", meaning "towards" or "away" from the center of the cross section as the aircraft passes through. BTW, this axis we're discussing represents the fuselage cross section, but the wing also has it's own central axis and cross section as well.

A fuselage design that has an abrupt change in cross section, causes a rapid acceleration of the surrounding air (and airflow) either "towards" or "away" from the cross section center, to either move out of the way or to fill the void (vacuum) created by the passage of the aircraft.

As an aircraft approaches transonic speeds, an abrupt change in cross section can cause the local airflow to go supersonic as it reacts to the abrupt change in cross section. The local shock waves created by this causes shock drag (i.e. transonic drag), and it can get very pronounced if the aircraft tries to go any faster.

A design that is carefully "area ruled" can delay the onset of transonic drag as it flies faster and faster, by delaying the onset of these local shock waves created by any abrupt changes in cross section.

The wing cross section (or profile) is a different animal in regards to transonic drag, and I know even this explanation is somewhat oversimplified. I'm not an expert here, so any corrections are welcome.

[Notso Fantastic]

So would you say the CV990 wing fairings are area ruling in practice then?

[Flight Safety]

I'm not very familiar with the Convair designs, but they could be.

Looking at the CV990 in the link above, makes me wonder why airliner designers often choose to put the flap track mechanisms on the outside of the wing. I wonder if the flap track fairings are designed to serve a dual purpose, both to contain flap track hardware and to provide some area ruling.

[Tuba Mirum]

I think I'm beginning to see the light here a bit, FS. What I find particularly interesting is the implication in your post (if I've picked it up correctly) that the fuselage and wing cross-sections may need to be considered separately. To take it to its logical extreme, would it be valid, for example, to consider the cross-section of a pair of wing tip-tanks in assessing the "area-ruledness" of a design? In other words, would the presence of those tip-tanks (assuming they were designed as permanent fixtures) need to affect the shape of things at the fuselage/wing root? Is there, perhaps, a threshold separation distance beyond which components of the total cross-section should be considered as separate entities rather than as parts of the same overall entity?

Hoping, as usual, that I'm making myself clear in spite of my lack of exposure to the relevant disciplines.

[Flight Safety]

TM, the term "area ruling" normally applies only to the slipstream airflow along the longitudinal axis of the fuselage and wings. The wings (root to tip) are in fact taken into consideration when calculating the slipstream cross section.

Maybe I should've left out the comment about the wing and its cross section when discussing "area ruling". The wing has an axis perpendicular to the fuselage axis, and it has its own cross section called the airfoil profile. This is really a completely different area of optimizing shape for delaying the onset of transonic drag. Super critical wings have airfoil profiles (i.e cross sections) that manage the acceleration of airflow over the surfaces of the wing, to delay the creation of local supersonic airflow, and the subsequent creation of shock drag. The design work on the wing cross section exists in at least 2 parts, namely to create a shape that both generates lift, while still managing the speed of the local airflow.

In the case of "area ruling" the slipstream airflow down the fuselage, the idea is to manage the airflow to delay the creation of local supersonic airflow, usually without the emphasis on creating lift at the same time (whether lift is actually considered would depend on the airframe's intended purpose).

The 2 design processes (area ruling and super critical wings) have in common the desire to delay local supersonic airflow, but have a lot of different goals otherwise.

I think I might have confused things by mentioning the wing cross section in the previous post. But I decided to mention it because the wing cross section does contribute to the overall frontal area (and thus the longitudinal cross section) when doing "area ruling" design work. Again, go back to the illustration in my previous post to see how the wing contributes.

[Tuba Mirum]

FS, I'm happy now that I understand the concept well enough from a layman's POV. What I think I was worried about all along was the idea that in some way the *whole* cross-section of the a/c contributed to the area calculation, and I couldn't quite see how that worked in the case of a/c components widely separated laterally. Whatever the issues regarding wing profiles (and I think it's more a case of me confusing the issue here rather than you ) it seems clear to me that my worry was groundless, and that calculations concerning wings can in general be kept separate from calculations involving the fuselage. (Probably best at this point to resist any temptation to correct this view, provided it's not complete balderdash!)
Thanks for your help. I may come back some time with a query on another of the many things I have trouble with in aviation theory .

[Flight Safety]

TM, I could add a brief discussion of swept wings just to make things more interesting.

Swept wings (as used on modern airliners) help to delay the onsite of local shock waves (transonic drag) in 2 ways.

First, to the airflow passing over the wing, the wing appears to have a greater cord than it actually does, since the air passes over it at an angle. To the airflow, the airfoil profile appears to be longer and more gradual, thus the changes in speed of the airflow over the wing are not as sharp, delaying the onsite of sonic flow.

Second, the swept wing also contributes to a more gradual change in the area ruling. Going back to the illustration I used earlier, there's a big difference between the entire leading edge of the wing suddenly showing up in the cross section as you move down the fuselage, and the leading edge gradually showing up in the cross section as you move down. The swept wing both enters into the area rule cross section and exits the area rule cross section much more gradually than a straight wing. This more gradual change in cross section contributes to good area ruling and a delay in the onset of sonic flow.

[Keith.Williams.]

I agree with much of what has been said above, but cannot agree with the idea that area rule has nothing to do with the wings. This is simply not true.

The aim of area ruling is to reduce transonic drag by delaying the formation of shock waves (increasing MCRIT) and by reducing the intensity of the shock waves when they eventually form. To understand how this is achieved it is necessary to look at what causes shock waves.

The local speed of sound (LSS) is the speed at which pressure changes move through the air. When a series of pressure changes move upstream through an airflow, their velocity relative to space is reduced by an amount equal to the velocity of the airflow.

If the pressure changes reach a point where the airflow velocity is equal to the LSS, the speed of the waves relative to space is reduced to zero. This causes the changes to pile up on each other at the point where the air velocity is LSS. In this condition the values of all of the changes are added together to create an instantaneous larger pressure change.

If the pressure changes were decreases in pressure the effect would be a sudden decrease in pressure. This would not from a shock wave. If however the changes were increases in pressure, the piling up of succeeding changes would cause an instantaneous increase in pressure. This sudden increase in pressure is a shock wave. Air passing through a shock wave is decelerated and its temperature increases. This increase in temperature cause a loss of total pressure energy in the airflow. The overall effect of this process is increased (wave) drag, whcih adds to the total drag of the aircraft.

The important thing to note in this sequence is that shock waves and the resulting wave drag occur when pressure INCREASES meet sonic or supersonic airflow. Pressure decreases meeting such airflows cause no such problems. So to reduce wave drag we must reduce pressure increases around the aircraft.

The second point to note is that shockwaves cannot form if the airflow velocity is less than LSS. As an aircraft moves forward, the air must move aside to let it pass. This causes the flow accelerate around areas of surface curvature. The local air velocity at any point on the aircraft is equal to the TAS of the aircraft plus whatever acceleration has been caused by the structure. So to achieve the greatest TAS without any airflows reaching LSS, we must minimise the acceleration rates of the air around the aircraft.

The accelerations are proportional to the rate of change of cross section of the aircraft, so minimum accalerations require minimum rates of change of cross section. So by reducing the rate of cross sectional area, the area ruling process increases the TAS at which the first shockwaves form. This delays the onset of wave drag until the aircarft has reached a higher TAS.

But the process does not stop there. Broadening the fuselage ahead and behind the wing roots, and narrowing it at the wing roots, fin roots and tailplane roots, reduces the rates of pressure increase and hence shock wave intensity in these areas. To understand this we need to look at what the air is doing as the aircraft passes.

Air which is moved aside to allow the aircraft to pass, must move into space which is already filled with other air. The overall effect is that the air is compressed and its static pressure increases.
If a lot of air is pushed aside, the increase in pressure and hence shock wave intensity will be large. These stong shock waves will cause a lot of wave drag.

But narrowing the fuselage at the wing roots, provides additional space for the air to move into. This reduces the overall increase in pressure and the resulting shock wave intensity. These weaker shock waves produce less wave drag. So by varying the fuselage cross section to match the position and cross sections of the wings, fin and tailplane, wave drag is delayed and reduced.

Although this process has been used in many aircraft, it was particularly evident in the old Northrop F5. Not only was the fuselage waisted, but also the wing tip fuel tanks. It is an indication of the effectiveness of this process that many such aircraft types performed better with external tanks fitted than without them.

Supercritical wings can be said to be an extension of area ruling. In this case the formation of shock waves is delayed and the accelerations over the wings, shock wave intensity and wave drag are all reduced by reducing the camber of the upper surfaces.

[WOK]

For a classic illustration of almost all that has been written about here look up a picture of a Blackburn Buccaneer - possibly the most obviously area-ruled shape to make holes in the sky.

[Flight Safety]

KW, I never said that the wings play no part in area ruling, they certainly do. I only said that working on wing profiles to delay transonic drag has additional goals.

I loved you're explanation otherwise.

[Keith.Williams.]

You are quite correct FS.

But I did not say that you said that wings play no part in ........ (let's not go there it will get very boring).

But if you look at the post made by Tuba Mirum at 1702 on the 16th, it is quite clear that this is how he/she was interpreting your comments. Because this interpretation misses the whole point of area ruling, I felt that it needed to be corrected.

In many aircraft designs, the arrival of the wings in the hole in our vertical slice of air represents the greatest and most abrupt single change of cross sectional area. The benefits of area ruling will therefore be greatest if we take this fact into account when designing the overall shape of our aircraft.

WOK, The Buccaneer was indeed a good example of area ruling. I believe that it was also another example of an aircraft where the drag was lower with the external (slipper) tanks fitted than without.

[Tuba Mirum]

Keith, I hope you won't castigate FS for my own faulty understanding. It's clear to me now that I didn't read his post closely enough.

Your own post has fully answered my original query: at this point, I am in danger of thinking I understand something about aerodynamics, which will never do!

Thanks to all for your patience with a benighted non-pilot.