CofG and induced drag

[Soulman]

Can someone please explain why an aircraft flying at it's forward CofG limit has more induced drag than an aircraft flying at it's rear CofG limit?

Thanks in advance.

[Mark1234]

Simply put, in most 'normal' cases, the tailfeathers are supplying a *downward* force to keep everything straight and level.

The further forward the COG, the more downward force is required, plus a little extra from the mainplane to keep the whole affair at the same altitude, thus more induced drag.

[Chesty Morgan]

And an aft C of G will also reduce your stall speed and vice versa.

[Mohit_C]

An aft Center of Gravity will also reduce the static directional stability..

[Graybeard]

Is that induced drag, or parasitic drag?

Induced drag is fixed, regardless of speed, correct?

GB

[kenparry]

"Induced drag is fixed, regardless of speed, correct?

GB"

Well, no.

Induced drag is the drag produced as a consequence of generating lift. It is inversely proportional to speed squared - i.e. it is very large at low speeds and a lower proportion of total drag at high speeds. The subject has been addressed here many times. Try a search and ye shall find.

[barit1]

Wikipedia's (http://en.wikipedia.org/wiki/Induced_drag) explanation of induced drag is not bad.

[cwatters]

As well as the four forces lift, drag, thrust and weight there are also several torques acting on an aircraft that must be in balance to stop it pitching up/down. These act about the centre of gravity.

a) The Wing produces a nose down torque (A "pitching moment" not shown below).
b) The center of pressure isn't exactly on the CoG so that also produces a pitch down.
c) The tail produces a pitch up.

These must sum to zero or the aircraft rotates about the CoG. It's why a tail is needed in the first place.

Altering the CoG position effects b) so c) must be adjusted to compensate. As others have said the further aft the CoG the less downforce the tail must produce. The further forward the more down force the tail must produces and the more lift the wing must produce to keep overall lift and weight in balance. Increased lift = increased drag.


http://upload.wikimedia.org/wikipedia/commons/thumb/9/99/Longitudinal_aircraft_stability_10.svg/800px-Longitudinal_aircraft_stability_10.svg.png

On a canard (tail first aircraft) the foreplane ADDS to the overall lift produced..

http://upload.wikimedia.org/wikipedia/commons/thumb/4/4f/Longitudinal_stability_Canard.svg/800px-Longitudinal_stability_Canard.svg.png

[FE Hoppy]

I think your duck needs trimming mate!!

[airfoilmod]

That, at cruise, if I could shift the cg back toward the tail, the tail would have to produce a net "upforce" to balance (trim) the a/c? With the tail doing that, it would have to create more lift, correct? More drag also, but, the net effect with a loaded tail is a reduction in the wing's angle of attack? Thought so. So to reduce net a/c drag I could ask the tail to help lift, and save Fuel? Thought so.

AF

[kenparry]

airfoilmod:

If it was that simple, then of course Boeing and Airbus and uncle Tom Cobley and all would have done it years ago. The flaw in your idea is that with the C of G so far aft the aircraft would be unstable in pitch to the extent that it would be unflyable without an autostab. That device would be critical to the safety of the flight regime, so it would need at least triple redundancy...................... and so we go on.

[Intruder]

That MIGHT work if you have fly-by-wire controls that can deal with a marginally stable or unstable airplane. Load the airplane to the most aft allowed CG, but no further aft.

[FE Hoppy]

As long as the CG is ahead of the neutral point then you still have positive stability. The neutral point is not the centre of lift of the main plane but of the entire aircraft.

Of course the amount of stability required is set by the certification standard so military aircraft can be designed with neutral or negative stability and use FBW systems to make them flyable by a mere mortal pilot. He does get the option of a martin baker arrival though in case the systems fail.

[airfoilmod]

FE Hoppy, you are on the money. Any dynamic balanced mass will tend to follow an existing path, the problem is control input, rate of change and lateral stability. An x plane @ Edwards flew with ailerons on the leading edges of the wings. No mortal, (and few current computers) could keep up with Delta roll. There is nothing untoward about shifting the cg aft (generally by adjusting fuel use) and pushing ND trim to add lift and drag to the tailplane, lowering the AOA of the a/c and its overall induced drag, which saves aforementioned fuel.

[chornedsnorkack]

Look at it this way: the drag is at its minimum when both main wing and horizontal stabilizer have exact same AoA which is the best L/D AoA for both. But this has neutral stability: if you pitch up from best L/D AoA to stall AoA, both wings reach stall AoA at the same time and the plane mushes down without dropping nose and recovering from stall. A plane is stable when the rear wing has lower AoA: when the forward wing stalls and drops, the rear wing is not yet stalled and so the nose drops. If the rear wing has higher AoA then the plane is negatively stable, and the rear wing stalls first, dropping the tail and pushing the front wing into stall.

The way to get positive stability is to get the CoG ahead of its rear limit (where the stability is neutral) so that the front wing carries more of the weight and rear wing carries less or actually pushes down - but since the wings are not at their best L/D AoA then, this adds drag.

[airfoilmod]

Long moment arm, lighter stick. Not heavier. With the cg closer to the tail, and a short moment arm, the stick force is increased, (reversed), making the a/c theoretically more frisky in Pitch. (It is).

[Brian Abraham]

Long moment arm, lighter stick. Not heavier. With the cg closer to the tail, and a short moment arm, the stick force is increased
Other way about. Stick force per "G" reduces as the C of G moves aft, which is what makes for the frisky and exciting times - if not your death.

[airfoilmod]

the greater the distance between the elevators and cg, the less energy it takes to change pitch, advantage empennage. The shorter the distance, the more energy it takes to change pitch. However, with aft cg, it isn't changing altitude (climbing), instead it is loading the airframe, mushing. The difference is in the available "weight" of the a/c closer to the tail, which "aids" the pitch up. Specifically, loading the tail, depriving the a/c of lateral stability. A more correct cg loads the wings. Instead of "trimming the airframe", the tail carries load as the center of lift is moved aft, producing the instability. I'm sticking with that. (As cg inches aft, "balancing" pitch forces is more difficult. The a/c is easy to pitch up, more difficult to lower the nose, etc.) AF

[Mark1234]

You're both right (sortof). You're talking about different moment arms!

I believe what sky captain meant is that with a forward COG there is a long(er) moment arm between the COP and the COG, so the stick force is higher to keep everything in balance (the length of the empenage not generally being variable).

Back to my original post, while it's *possible* for there to be download on the tail, in the general, conventional, non-canard civilian aeroplane, it's pretty much guaranteed that there will be an upload. Yes, the aeroplane COP is behind the main wing COP, but the COG's rarely allowed that close that it really matters.

[airfoilmod]

Stick force (Pitch) simply put, describes the authority required to rotate the mass around its cg. Brian mentions "G" and pitch force lessening as cg moves aft. It 's true, if one wants to pitch up. It is increasingly more difficult to Pitch the nose down as cg travels aft. The reason is clear: with more weight (Inertia) near the Tail, the elevators must perform more work to resist gravity. Do I miss your point?

Addressing the original question? An unaccelerated a/c flies straight and level with all forces balanced (cwatters). Let's try to reduce drag. Assuming the cg is at a point that allows aft movement, and any change isn't other than benign, move the cg aft some small amount. To compensate for the resultant Pitch up (and increase in AoA) lets trim the tail (elevators) and bring the nose back down. We will note with satisfaction that the added drag of the trim (increased lift @ tail), has reduced the AoA of the Wings. This slight reduction in OVERALL drag is the payoff in lower fuel burn rate.

If we have gotten too enthusiastic with aft cg, eventually the elevators will be unable to keep the nose down, and that's the final outcome. The picture is clearer with a discussion of tailless a/c, and how challenging flying that critter is.

[Mark1234]

Do I miss your point
Somewhat :) - you seem to be the only person posting from the point of an extremely aft COG

I can't argue with what you say - all perfectly correct as far as I understand, but also perfectly irrelevant to a legally loaded civil aircraft of 'conventional' disposition.. where there's going to be a nose down couple, opposed by the tail feathers.

As to the original question, why a fwd COG increases induced drag, I think it's been answered many times over. So long as you start with the reasonable assumption that the COG is ahead of the neutral point.

[airfoilmod]

Right. fwd cg difficult to raise the nose; aft cg difficult to lower it, all related to the distance of the cg from the tail. The key is the discrepancy in up or down authority, as the cg moves in relation to the control surface necessary to rotate the mass. The tail is necessary to balance the airframe. Disregard the cg. Think of the Lever. The cg is the fulcrum. Nose and tail are either end, move the fulcrum and gain an "advantage". The warning to everyone is this: when the force necessary to move the nose up or down differs by more than a little bit, you are having cg issues.

AF

Mark - The difference in cg isn't so important as the Physics when it changes. I'm the only one?

[Mark1234]

OK, at least now I understand where we're misunderstanding each other....

The CG is NOT the fulcrum. The neutral point is. It's possibly just a frame of reference thing, but..

[airfoilmod]

My bad. Uncle

[Brian Abraham]

I'm not entering into the discussion other than to give some references by which anyone interested may gain some insight.
http://www.flightlab.net/pdf/5_LongitudinalStaticStability.pdf
http://www.flightlab.net/pdf/6_LongitudinalManeuveringStability.pdf
http://www.flightlab.net/pdf/7_LongitudinalDynamicStability.pdf
To sum for those who have little interest in going further,

Conventional handling qualities require that the aircraft c.g. lie ahead of the stick-free static neutral point. If c.g. lies on the neutral point stick forces are zero. If c.g. moves behind the neutral point, control forces reverse. A pull force becomes necessary to hold the aircraft in a dive; a push force becomes necessary in a climb.