# Why does a lower chord length reduce the pitching moment?

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

• The question in the title is different than the one in the text. Is your doubt more about wing pitching moment or airplane stability? Oct 5, 2023 at 12:09
• @sophit I kind of had 2 questions. Doesn’t the wings pitching moment relate to stability and maneuverability? Oct 5, 2023 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 Oct 5, 2023 at 15:34
• @sophit ah okay thanks for the clarification Oct 5, 2023 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 Oct 5, 2023 at 16:14

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.

• 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! Oct 3, 2023 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. Oct 3, 2023 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. Oct 3, 2023 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. Oct 4, 2023 at 0:23
• (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) Oct 4, 2023 at 0:57

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.

• 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! Oct 4, 2023 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. Oct 4, 2023 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 Oct 4, 2023 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. Oct 4, 2023 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? Oct 4, 2023 at 23:50