# What is the effect of wingspan on wing stiffness?

In an article in aviationweek about flight testing the GE9X, this statement is made.

To reduce aeroelastic interaction between the testbed and the big engine, GE has also stiffened the wing by removing the 6-ft. tip extension developed for the standard -400 series. The reduced span of just over 195 ft. will reduce potential exposure to limit cycle oscillation and maintain an unrestricted test envelope.

How does removing the wingtip extension make the wing stiffer?

What is "limit cycle oscillation"?

• There is an aerodynamic force on the tip of the wing, which acts as a lever on the rest of the wing. Think of it this way, if you cut the wings in half, would you find it harder or easier to bend by grabbing the end and pulling? – Ron Beyer Nov 27 '17 at 19:29
• – fooot Nov 27 '17 at 23:26
• Your question takes for granted that the reduction in wingspan was the cause for the increase in "stiffness". I put stiffness in quotes, because Peter Kämpf has some reasonable doubts about stiffness having changed. He's also saying, that the article you quoted (I'm assuming he referred to this one) wasn't very well written. I can't comment on this, because I don't have access. – user7241 Dec 10 '17 at 8:52

Limit cycle oscillation is a fancy term for flutter with constant amplitude. The limit cycle is an attractor, meaning that the frequencies and amplitudes of a range of oscillations will converge to the limit cycle oscillation as time progresses. One example can be witnessed in this video.

By removing the wingtip, GE could raise the bending eigenfrequency of the wing, like you make a pendulum swing faster if you shorten it. Adding a heavier engine before certainly reduced the eigenfrequency, so the shortening was a way of compensating for the changed dynamic characteristics of the modified wing-engine combination.

Wingtip removal does not make the wing stiffer, only larger spar caps, a thicker spar or employing a stiffer spar material would. Stiffening the wing spar would raise its bending eigenfrequencies, and removal of the wing tip would do the same by different means. I guess the author wanted to express that bending frequencies were raised but picked the wrong explanation.

• Stiffness is defined in structural statics as applied force over displacement. This is identical to the definition of spring constant, which is used in dynamical problems for structures. So when they removed a part of the wingtip, they changed: a) The applied load, since they reduced wing planform area and possibly already added a heavier engine, b) changed the length of the wing, c) changed the moment arms of those forces about the wing root, d) changed the mass of the wing (and the moment arm of the resulting force of gravity). – user7241 Dec 9 '17 at 18:40
• They then confirmed that this raised the (damped or undamped) eigenfrequency of the wing. Assuming a mass-spring-damper equivalent system, they found that the spring constant had increased. Sounds like a valid thing to say. I don't know how the damping factor changed, if at all. – user7241 Dec 9 '17 at 18:43
• So I'm saying that it is ok to say that the stiffness has increased - if the mass change wasn't significant, since it's defined in terms of applied load and displacement. But I don't know if this can be solely attributed to the change in length. – user7241 Dec 9 '17 at 18:46
• @jjack: Wouldn't it be better if we define terms in clear and concise ways and then stick to that definition? They did not change stiffness: With the same load over the same surface, the short wing will show the same displacement as the longer wing. You weren't the author of that poor article by any chance? This would explain your contorted reasoning. – Peter Kämpf Dec 9 '17 at 21:41
• I gave the definition for stiffness. It is an indirect one, in terms of applied load over displacement. Also, which article are you referring to? The one linked by the OP? I don't have access to it. – user7241 Dec 10 '17 at 0:30

Stiffness is defined as the deflection resulting from a force load. An aircraft in straight steady flight has an upwards aerodynamic lift, bending the wing upwards. The longer the wing, the more the wingtip deflects as a result of a certain load. This is the reason why wings with a high aspect ratio bend a lot more.

Removing a bit of wing means that the wing area is reduced and that the aircraft flies with a higher AoA at a certain speed and altitude. It also results in a shorter moment arm for the bending forces, hence less deflection of the wing tip at the same load, hence a higher stiffness.

Wing stiffness is not only defined by the construction of the wing, but also by external influences. This link to @DeltaLima's answer to a similar question provides more background.

Limit cycle oscillation is a form of sustained flutter. From this website:

We discuss the origin of different kinds of limit cycle oscillations. Limit cycle is a trajectory for which energy of the system would be constant over a cycle - i.e. on an average there is no loss or gain of energy.