The Physics of Why Airplane Wings Oscillate in Turbulence

 

When I fly, I like to get a window seat. This is a poor option if you plan on going to the toilet, but it’s great if you like to look at stuff.  I think that’s a fair trade off.

In a recent flight, I had a nice view of the wing. It’s pretty cool to realize how much the wing oscillates—especially when the aircraft enters some turbulence. Check it out.

There are two questions I think of looking at this oscillation. First, how large is the amplitude of oscillation? Second, why do the wings oscillate? Here are the answers.

Amplitude of Oscillation

It’s clear that the end of the wing is moving up and down some. But perhaps it’s not so clear the distance it moves—especially since this video was recorded without a tripod (it was just me with my phone). Fortunately, I can use Tracker Video Analysis and set the coordinate axis to some other spot on the aircraft that I will assume to be stationary. Next I can measure the relative location of the end of the wing with respect to this reference frame. Of course, the only thing I will need is something to determine the scale of the motion. I can use this site to get the size of the winglet on the end of a Boeing 737 (8 feet 2 inches). Now I’m ready.

Here is just part of the motion of the wing. I recorded the video in slow motion mode so that it is in 240 frames per second.

There’s clearly some noise in this data, but it’s good enough for now. I suspect there are errors introduced when I made slight adjustments to the orientation of the coordinate axis. If I tilt the x-axis just a little bit, a point very far away can have its y-value change significantly. In the later part of the data collection, I tried to have fewer adjustments to the angle of this axis and the data looks a bit smoother.

Even though the data’s not perfect, it’s still useful. First, let’s look at the amplitude of the oscillation. Towards the end of the plot, the data is fairly smooth. At a time of around 1 second, the position of the wing (I used the “dot” in the Southwest.com on the winglet) is at 1.4 meters. Slightly later it is up to 1.5 meters. That is an oscillation amplitude of 10 cm (just under 4 inches). So, the wing does indeed oscillate.

Actually, I can also get an estimation of the frequency of the oscillation. It looks like it takes about 0.3 seconds to go from one minimum position to the next. With a period of 0.3 seconds, the frequency would be 3.33 Hz. That’s just for fun.

But Why Does it Oscillate?

First, the wing is a spring. Really all materials act like a spring. When you push on them, they bend—even if it’s just a little bit. The more you push on something, the more it bends. Here is a very simple demonstration. Place a meter stick so that it hangs over a table and then add a mass.



Notice that the meter stick bends? The more mass you put on it, the more it would bend. Really, this is just like an aircraft wing.

But why does it oscillate? Let’s imagine that there is an aircraft flying at a constant speed and altitude. We can represent the forces on the aircraft with a diagram.



Since the aircraft is moving at a constant velocity, the net force in the vertical direction must be zero (there are also horizontal forces—thrust and drag). But now, the airplane enters a region of the atmosphere with a higher density air (or something like that) and this produces more lift. Now the aircraft is no longer in equilibrium. This causes two things to happen. First, a greater lift force means that the wings will bend more. Second, a greater lift force makes the plane accelerate upwards and perhaps also causes some stuff to rattle around inside the aircraft (like you).

Of course the plane doesn’t continue to accelerate upwards. It soon reaches air with a different density and stops its vertical acceleration with reduced lift. But wait! The wings were bent upwards due to the greater lift. Well, now they have to bend back down. This is the source of the oscillation. Here you can see a similar thing with a mass and a rubber band.



Pulling up harder on the rubber band makes the mass accelerate up. When I decrease the pulling force, the mass stops accelerating up—but now you get a bit of an oscillation. The wing is a lot like the rubber band in that the oscillation is damped and doesn’t continue for a long time. This is the way you want it.

So, yes—the wings bend and yes, they are supposed to do that. Carry on and drink your soda and eat your peanuts as you enjoy your flight.