Kukkudrill
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Position Of Swept Wings Relative To C Of G

Sun Mar 27, 2005 7:30 am

Straight-winged aircraft are built so that the thickest point of the wing, and the point of maximum lift, is aligned with the centre of gravity. Or that's my understanding at any rate. But what about swept wings? Is the wing aligned with the centre of gravity at the wing root, meaning that much of the wing area is behind the C of G, or is the wing set further forward to compensate for the sweep?

The B-52 has its wings set well forward of the main gear and the bomb bay, apparently in compensation for the sweep:


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Photo © Roberto Benetti



On the other hand, this Sabre appears to have the bulk of its wing area behind the main gear, suggesting that wing sweep does not influence the placement of the wing:


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Photo © Ken Cheung



The variable-sweep wing concept as applied to several military aircraft also suggests that sweep is not a factor when aligning the wing with the C of G, because if it were the wings would have to bodily shift forward when they are swept back and vice versa.

Can someone shed light on this puzzle for me?

Charles
Make the most of the available light ... a lesson of photography that applies to life
 
411A
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RE: Position Of Swept Wings Relative To C Of G

Sun Mar 27, 2005 9:09 am

In general terms, it has more to do with...

The length of the fuselage
The engine(s) placement...ie: with wing mounted in pods, or tail mounted.
The amount of fuel to be carred.
The authority of the tailplane/elevator assembly
The anticipated revenue payload

Take the B707 as an example.

Very powerful authority available from the horizontal stab/elevator.
Longer body (speaking here of the -320/-320B models), with large amounts of center tank fuel available, for long range flights.

When fully loaded for these longer range flights, large amounts of center tank fuel, together with a full passenger load, results in the CG being will forward.
After takeoff, due to structural considerations, during the climb, fuel is fed from the center tank to all 4 engines (due mostly to required wing bending relief (which, by the way is helped greatly by the engines being wing mounted in pods).
When the center tank is empty, the CG is now well aft.
Fuel usage is then tank to engine and as most of the fuel is well aft (swept wing) as the fuel is consumed, the CG moves forward once again.

Thus, a large horizontal tailplane is required, with adequate authority, to cope with these larger CG changes.

Then, when landing, that large tailplane is once again required to counteract the rather pronounced nose heavy tendency (pitchdown) of this particular model, as flaps are extended beyond 25 degrees.

Large heavy jet transports have large CG changes during flight, hence the very powerful powered horizontal stab fitted.
 
aeroweanie
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RE: Position Of Swept Wings Relative To C Of G

Sun Mar 27, 2005 9:20 am

Kukkudrill:

You need to read some aero books. Most of your assumptions are very wrong.

When you say "the thickest point of the wing" I don't know if you mean thickest in front view (the normal interpertation) or in top view. Whichever you mean, this location is independent of CG location. Similarly, the "point of maximum lift" is a spanwise location, so it has nothing to do with CG location.

You might note that the only aircraft that has wings that sweep completely (the pivot point being on the centerline) was the old Bell X-5 and for this aircraft, the wings did translate with sweep. Otherwise, all variable sweep aircraft have that wings pivot about an outboard location. The share of the lift carried by the fixed portion (and its contribution to the aircraft's longitudinal stability) helps eliminate the need for translating the wings.

On an aircraft, their is one particular place on the wing called the Mean Aerodynamic Chord. This location is found from integrating the distribution of chord squared against span. The longitudinal position of 25% of MAC is pretty close to where the CG falls, but the tail size and tail arm effect this too, due to longitudinal stability considerations. This is how wings are positioned in a simplistic view.
 
CosmicCruiser
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RE: Position Of Swept Wings Relative To C Of G

Sun Mar 27, 2005 9:39 am

The C.G. is a point but it has a span or envelope that it can fall into considering payload and fuel and be within the stable,controllable regime it was designed to operate in. Consider how much the CG must move when a plane burns 200,000 lbs. of fuel on a given flight. On most swept back winged a/c as fuel is burned the CG moves forward. It must stay within its designed limits. On the MD-11 that's the reason for the tail fuel tank. It "holds" fuel for most of the flight in order to keep the CG aft allowing the tail to carry part of the load thus providing some lift thus improving range/fuel econ.
 
OldAeroGuy
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RE: Position Of Swept Wings Relative To C Of G

Sun Mar 27, 2005 11:19 am

Quoting AeroWeanie (Reply 2):
On an aircraft, their is one particular place on the wing called the Mean Aerodynamic Chord. This location is found from integrating the distribution of chord squared against span. The longitudinal position of 25% of MAC is pretty close to where the CG falls, but the tail size and tail arm effect this too, due to longitudinal stability considerations. This is how wings are positioned in a simplistic view.

Using the concept of 25% MAC introduced by Aeroweanie, if you look at commercial airplanes, you'll find that most of them have a CG loadability range of 5% or greater MAC at the forward limit and 40% or less at the aft limit. Within this range, airplane handling and stability meets all regulatory requirements and airplane performance is as good or better than as described in the airplane flight manual.

Operators must load within this range and the CG must stay within the range as fuel is burned off during flight.

The landing gear position must be aft of the aft limit to keep the airplane from sitting on its tail.
Airplane design is easy, the difficulty is getting them to fly - Barnes Wallis
 
SlamClick
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RE: Position Of Swept Wings Relative To C Of G

Sun Mar 27, 2005 11:51 am

Just at a glance you can make an educated guess as to where the CG falls. It will be just forward of the main landing gear.

Why just forward? Because if it was 1 milimeter aft, the plane would fall on its tail.

Why not well forward? Because the elevator would not have enough authority to 'rotate' the plane to the takeoff attitude if it were too far forward. The arm from the elevator through the main gear to the CG is a lever, with the mains at the fulcrum. It has to be able to lift the entire weight of the plane around that fulcrum.

So if you can find the average or 'mean' location of the leading edge, and the average, or 'mean' location of the trailing edge, the distance from one to the other is 'mean aerodynamic chord' or MAC. MAC is 100% of itself. In my experience, most swept wing jets want to carry their load somewhere between about 10% and about 40% of MAC. (measured aft from LEMAC)
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aeroweanie
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RE: Position Of Swept Wings Relative To C Of G

Sun Mar 27, 2005 3:50 pm

Careful SlamClick - you described how to find the Mean Chord, not the Mean Aerodynamic Chord. The Mean Chord is the integral of chord over the span, divided by the span. The Mean Aerodynamic Chord is the integral of the chord squared over the span, divided by the span.

OldAeroGuy is quite right - most aircraft have loading ranges from about 5% MAC to about 40% MAC. The forward limit is established by the tail's ability to get the airplane to stall. At CGs ahead of the forward limit, the airplane can't be stalled. The aft limit is established by the CG point where neutral stability is experienced, with some buffer (usually about 10-20% MAC). For CGs ahead of the point of neutral stability, if the aircraft is disturbed in pitch, it will recover to its trimmed state. For CGs aft of the point of neutral stability, the aircraft will want to diverge from the trimmed state, if disturbed.
 
SlamClick
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RE: Position Of Swept Wings Relative To C Of G

Mon Mar 28, 2005 12:34 am

Quoting AeroWeanie (Reply 6):
The Mean Aerodynamic Chord is the integral of the chord squared over the span, divided by the span.

You are absolutely correct, mathematically. But if you just say 'chord' as you did, the next question is: Chord where? The wing is tapered also.

So without getting into the arithmetic I was just describing how one might find the sweet spot where the wing wants to carry its load.
Happiness is not seeing another trite Ste. Maarten photo all week long.
 
aeroweanie
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RE: Position Of Swept Wings Relative To C Of G

Mon Mar 28, 2005 4:56 am

Actually, I thought your explanation was a good layman's explanation, without getting too deeply into the details. I just wanted to note the distinction.

Getting too deeply into the details... Concerning my use of the word chord in: "The Mean Aerodynamic Chord is the integral of the chord squared over the span, divided by the span", as this is an integral, you are looking at the chord at each little increment of span you are using to approximate the integral.
 
Kukkudrill
Topic Author
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RE: Position Of Swept Wings Relative To C Of G

Mon Mar 28, 2005 9:08 pm

Thanks all for the replies. I have been confused but also illuminated!

AeroWeanie for what it's worth I meant the thickness of the wing profile when taken in chordwise cross-section (if that makes sense). All material on this subject that I've come across is either too basic or else too mathematical for me. If you're aware of a text which strikes a good balance for the layman, let me know.

Thanks again,
Charles
Make the most of the available light ... a lesson of photography that applies to life
 
aeroweanie
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RE: Position Of Swept Wings Relative To C Of G

Tue Mar 29, 2005 3:06 am

Kukkudrill:

I suspected that you meant thickness in top view. When I saw your nationality, I figured that there was a problem with English technical word meanings. I would have far worse problems trying to express myself in French!

For some good technical, but non- or easy-mathematical books, Darryl Stinton's books "The Anatomy of the Aeroplane", "The Design of the Aeroplane" and "Flying Qualities and Flight Testing of the Aeroplane" are all quite good. For the stability and control aspects, I recommend "Airplane Stability and Control; A History of the Technologies That Made Aviation Possible" by Abzug and Larrabee. Make sure you get the second edition, as the first edition is full of errors.

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