1

I've heard that higher aspect ratio wings (also lower chord length wings) are more stable and less maneuverable. Why is that?

Wyatt
  • 1,943
  • 1
  • 9
  • 24
  • The question in the title is different than the one in the text. Is your doubt more about wing pitching moment or airplane stability? – sophit Oct 05 '23 at 12:09
  • @sophit I kind of had 2 questions. Doesn’t the wings pitching moment relate to stability and maneuverability? – Wyatt Oct 05 '23 at 15:12
  • Wing pitching moment has no direct influence on stability and manoeuvrability is a quite broad terminology where wing pitching moment might or might not have an influence – sophit Oct 05 '23 at 15:34
  • @sophit ah okay thanks for the clarification – Wyatt Oct 05 '23 at 15:48
  • You're welcome. Some time ago I elaborated an answer about stability in pitch but I definitely need to streamline it a bit. I let you know when/if I'm done – sophit Oct 05 '23 at 16:14
  • Oh alright thanks for that! – Wyatt Oct 05 '23 at 16:18
  • Done, let me know if it is understandable – sophit Oct 06 '23 at 14:26

2 Answers2

3

Just as we non-dimensionalize wing lift coefficient as

$C_L=\frac{L}{q\,S}$

We non-dimensionalize wing pitching coefficient as

$C_M=\frac{M}{q\,S\,c}$

Where the chord provides the additional length unit to get a force to a moment. However, this also shows you how the forces and moments scale.

The moment on a wing is proportional to the pitching moment coefficient, ($C_M$), dynamic pressure ($q$), wing reference area ($S$), and wing reference chord ($c$).

$M=C_M\,q\,S\,c$

So, if you have two wings that are otherwise the same, then the one with the larger chord produces the larger moment.

The other thing to consider is that a wing does not act alone -- you should also consider the horizontal tail when considering an aircraft.

We usually non-dimensionalize the size of a horizontal tail using the horizontal tail volume coefficient...

$V_h=\frac{S_h\,l_h}{S_w\,c_w}$

Where the $h$ subscripts are for the horizontal tail and the $w$ subscripts are for the wing.

I.e. a horizontal tail's effectiveness is proportional to how big it is ($S_h$) and how far away it is ($l_h$ the tail moment arm). And inversely proportional to the wing's size and chord.

The wing terms are the terms that non-dimensionalize the wing's moment coefficient.

If you think about a horizontal tail's contribution to pitching moment as mostly due to lift over a moment arm, you will see that the $S_h$ comes from the lift of the tail and the $l_h$ is the tail moment arm.

Rob McDonald
  • 10,966
  • 1
  • 13
  • 34
  • thanks for your answer. One question that I'm not sure if you answered in you response : Does the chord length affect the pitch maneuverability of the plane? (you might've answered that in your response already but I didn't go to aeronautical engineering school so I didn't understand everything) Thanks! – Wyatt Oct 03 '23 at 23:38
  • Yes and no. We usually think about stability in terms of the static margin - as a fraction of the reference chord. So a 5% SM aircraft is much less stable than a 20% SM aircraft. However, if we dimensionalize those values to say 1ft and 4ft, then we think about changing the chord of the aircraft, we see that a smaller chord will make the same dimensional SM be a larger %SM. Consider a cargo aircraft that needs to tolerate changes in the center of gravity. Those would be scaled by the chord -- such that a small chord aircraft would be less tolerant of CG movement than a large chord one. – Rob McDonald Oct 03 '23 at 23:54
  • However, if we consider maneuverability via the tail volume coefficient -- which is a simple measure of the tail effectiveness. We see that cutting the wing chord in half (keeping everything else the same) would double the tail volume, making for a more sensitive and maneuverable aircraft. – Rob McDonald Oct 03 '23 at 23:56
  • thanks for that info. If the SM is the distance of the CM from the NP, how does that affect stability? I thought that the main judge of stability was the distance of the CP from the CM. Also, could you put the info you provided me in laymans terms, I don't know some of the terms used, and other things like that. Thanks again. – Wyatt Oct 04 '23 at 00:23
  • (forgot to notify, didn't know if you'd see my comment if I didn't, haven't used stack exchange for that long so I don't know much) – Wyatt Oct 04 '23 at 00:57
  • @Wyatt The CP changes with angle of attack, so it is not a useful point in terms of stability. The NP does not change with angle of attack. Your intuition about distance from CM applies to the NP. When an aircraft is trimmed (at some alpha), the elevator has been adjusted such that the CP is at the CM. – Rob McDonald Oct 04 '23 at 05:00
  • oh okay, makes sense. I saw this on a different question : “ The lower chord also reduces the wing's pitching moment, so a smaller tailplane can be employed, or the tail lever arm of the horizontal tail can be shortened.” Does that mean basically what you were saying, as the same dimensional SM is a larger % SM on a smaller chord wing? Also if a larger chord wing produces a larger moment, how do 2 planes that are the exact same, but the only difference being the smaller chord length of one, how are they more maneuverable (the one with smaller chord) like you said in a previous response. – Wyatt Oct 04 '23 at 17:01
1

Let's translate some of this to layman's terms

higher aspect wings contribute less to stability

The portion of the wing aft of the CG contributes to stability. It's torque consists of area × distance from CG. A wing with a longer chord will be more stable.

higher aspect wings are less maneuverable

Generally not because of higher stability, but because of lower G load tolerance (its easier to break a long thin stick compare with a short thick one).

Those who endeavor to increase aircraft fuel economy by increasing aspect ratio (airliners) should realize a larger, not smaller, tail may be needed to maintain the same stability characteristics as the previous iteration.

Robert DiGiovanni
  • 20,216
  • 2
  • 24
  • 73
  • Ah okay so high aspect wings are generally not more stable in pitch naturally? Edit : just re read your answer and saw the part about the section of wing behind the CG. Thanks! – Wyatt Oct 04 '23 at 18:25
  • @Wyatt you can check Cm data at airfoiltools.com. Profile of wing (degree of camber) can also affect stability, as well as (as you have noted) CG placement. – Robert DiGiovanni Oct 04 '23 at 18:47
  • One question though : does that mean that high chord length wings are more or less maneuverable than low chord wings? (Saw the part about more chord behind the cg but I wasn’t sure about maneuverability) edit : didn’t see your previous response until I commented this – Wyatt Oct 04 '23 at 18:56
  • @Wyatt you can make something more maneuverable by increasing the area of the control surface. Remember the distance from CG is far greater at the tail than at the wing trailing edge. Strength (G load limit) is the limiting factor, not chord length. Look at an F22 Raptor. – Robert DiGiovanni Oct 04 '23 at 19:40
  • Oh okay, makes sense. A question I had was say you had most of the wing forward of the CG (unstable), would a larger chord wing still be more stable than a smaller chord wing in that instance? – Wyatt Oct 04 '23 at 23:50
  • @Wyatt that will depend on the wing profile. The wind tunnel is your friend here, but applications of rear CG placement are rare. – Robert DiGiovanni Oct 05 '23 at 18:49
  • Ahh, okay makes sense. Thanks a lot! – Wyatt Oct 06 '23 at 15:24