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Wolfgang, et al
The aircraft MAC (also called neutral point) relative to CG is the key to evaluating aircraft longitudinal stability. This is independent of whether the tail is providing an up or down force (either can be stable). Longitudinal stability is defined by the reaction of the entire airframe to a disturbance from equilibrium. The size, location and pitching moment characteristics of each component factors in (wing, tail, fuselage etc.). Evaluating the behavior of just the wing is not sufficient to describe the response of the aircraft as a whole and certainly not to quantify the response. Actually, a wing section alone will be unstable as the pitching moment is negative. It is stable when inverted - flying wings have negative camber for this reason.
A stable aircraft must have a positive pitching moment when in equilibrium. In order to be stable, the pitching moment coefficient must have a negative slope with increasing angle of attack. This provides an increasing opposing moment to an increasing disturbance.
A larger tail increases the response when a disturbance occurs. It is a function of the larger area producing more restoring force for any given angular disturbance. The size of the horizontal stabilizer feeds into a quantity called the tail volume ratio - a unit-less measure of relating tail area to wing area and wing mean wing chord to distance to the horizontal stabilizer. More area or a longer tail increase the effectiveness in terms of stability.
The neutral point is fixed by the configuration of the aircraft. Only configuration changes will move the neutral point. Lowering the flaps, for example, changes the airfoil, relative incidence angles, pitching moment of the wing and so on. In all configurations the neutral point must remain well behind the CG. 10% of the mean chord length is a good starting minimum. Once the neutral point is known, the incidence angles and CG can be set. What will fall out is the trim airspeed. That is, in equilibrium the aircraft will seek out a specific angle of attack and the corresponding airspeed. One can play around with different combinations of incidence angles and CG locations to achieve both a stable aircraft and minimum trim drag at any desired airspeed.
hope that helps,
Chris
Chris Zavatson
N91CZ
360std
From: Wolfgang <Wolfgang@MiCom.net>
To: lml@lancaironline.net
Sent: Wed, July 14, 2010 10:37:18 AM
Subject: [LML] Re: Small tail, MK II tail, CG range
I'm not familiar with MAC as applied to the entire airframe, can you elaborate? I think there may be a problem with that idea since the tail is typically providing a down force which would move the "airframe MAC" to the front, not the rear.
Wolfgang
----- Original Message -----
Sent: Tuesday, July 13, 2010 8:35 PM
Subject: Re: [LML] Small tail, MK II tail, CG range
Wolfgang, et al,
<<Any more to the rear and you get negative stability at cruise and a larger tail doesn't help much with that anyway.>>
A larger tail moves the MAC rearward allowing the CG to move farther aft while maintaining the same level of stability.
There has been a lot of discussion about Cm. We need to be careful to distinguish between the Cm for the wing, tail and total aircraft. It is the later that is critical to stability and this is where the larger tail influences the situation. The large tail moves the MAC to the rear approx. 1.5 inches. For the same CG, the more rearward MAC produces a greater restoring force if the plane is disturbed from level flight. The practical benefit for us is that it allows a lot more baggage to be thrown the rear of the plane before suffering stability problems. You pointed out the other benefit of increased control authority at slow speed with full flaps.
Chris Zavatson
N91CZ
360std
From: Wolfgang <Wolfgang@MiCom.net>
To: lml@lancaironline.net
Sent: Tue, July 13, 2010 2:51:23 AM
Subject: [LML] Small tail, MK II tail, CG range
The quest continues.
I'm checking further into the data on these questions and am coming to question the need for a larger tail. I'm not sure a larger tail by itself will solve the problem. After doing some static and in flight measurements, it looks like the tail authority is not a big problem, if a problem at all.
Static measurements of N31161 have shown "vanilla" parameters. 2.5º incidence between the wing root at full reflex and the tail and a 1.3º washout. Put the flaps at 0º and you get an additional AoA of 1.8º at the root for a total incidence of 4.3º . . . . not radical at all.
What is interesting is the POH (Dec. 1994 pg. VI-3) gives the CG range as 24.5" to 30.3" aft of the rear face of the fire wall and the MAC at 15% to 20%
. . . well . . . no . . . that range is more like a MAC range of 15% to 30% - - - a good range made touchy only by the small size of the air frame.
After going over the plan view kit drawings, I come up with a CG range of 23-1/4" to 29-1/4" for a MAC range of 15% to 30%
That range is about 1-1/4" forward of the book and fits better with first hand flight experience.
Any more to the rear and you get negative stability at cruise and a larger tail doesn't help much with that anyway.
Negative stability makes pitch control a real chore. As Scott K. has indicated, going to 0º flaps helps under that loading condition.
Too far forward and landing becomes "interesting". A larger tail can help there . . . or don't use as much flaps.
I think understanding these conditions can help everyone.
. . . The quest continues . . . Comments welcome.
Wolfgang
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The LNC2 uses the NLF(1)-0215F airfoil. A lot can be found by doing a Google search on that number.
More detail can be found by going to Google for "NASA Technical Paper 1865".
I have not taken the time to reverse engineer the CG range of the LNC2 but let me offer some observations.
The airfoil used has long been touted as "the greatest thing since sliced bread" for General Aviation and it definitely has some advantages. But it's not new. Compare this airfoil to the P-51 airfoil and you will see some close similarities. The LNC2 being composite construction instead of aluminum lets the airfoil show more of it's theoretical advantages.
It's a laminar shape with a good drag bucket. That bucket can be made to move to the lower Cl (lift coefficient) ranges with reflex allowing noticeably lower drag at higher cruise speeds. Along with reflex, the Cm (moment coefficient) goes positive, the center of lift of the wing travels forward giving a nose up force requiring down trim. This is in addition to the usual nose up force that goes with most all airfoils at high speed before considering flaps.
With down flap, the drag bucket will move to higher Cl's making slower flight more efficient. And, of course, the Cm goes negative giving a nose down force requiring up trim.
. . . and appropriate variations in-between . . .
So, the rear CG limit is determined by high speed flight and available control authority,
and the forward CG is determined by low speed / landing flight and available control authority.
What is becoming clear here is that the center of lift does quite a bit of traveling fore and aft which is exaggerated by allowing negative or "cruise" flaps. Since you can't shift the CG during flight, you need a large amount of pitch authority from the tail to cover that range of lift travel.
You have two choices in the LNC2, live with the limitations or install a larger tail to give that extra pitch authority.
. . . A larger tail area can also help with abnormal attitude recovery.
Wolfgang |
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