Why does a lower chord length reduce the pitching moment?

Question

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

Answer 1

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.

Answer 2

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.