I’m sure you’ve all heard about the airplane that ditched in the Hudson last week. (Just 30 blocks from my office!) When it happened, after we found out more about what caused the plane to ditch, I wondered how long it would take before the 911 Truthers came up with a conspiracy theory about it.
Not long. Via SkepticBlog comes news of a conspiracy theorist claiming that the ditching doesn’t make any sense. Brian Dunning at SkepticBlog does a good
job explaining what’s so stupid about this, but there were two things about
it that I thought were particularly interesting from the point of view of a math and computer science geek.
First, as long-time readers know, one of the things that I’ve harped on many times is just how bad we are at understanding numbers and scale. The conspiracy theorist provides a great example of this. He asks:
Also in this picture are dozens and dozens of “survivors”… it’s hard to count because the picture is so fuzzy and distant (a common theme… distant and fuzzy pics). How can more than 20 people stand on a wing and not collapse it?
How can 20 people stand on the wing of a plane and not have it snap off?
How does a plane fly? The aerodynamic shape of the wing creates a differential in air pressure between the bottom and top of the wing, which produces lift. What that means is that the air flowing over the wings pushes the wings up, and the wings lift the airplane. The wings are capable of lifting the entire airplane: all of the people on the plane, the metal hull, cargo, engines, fuel. The weight of a completely empty A320 (the type of plane in this crash) is 42 metric tons, or just a little under 100,000 pounds. Fully loaded (fuel, passengers, and cargo), it’s something over 60 metric tons – or about 130,000 pounds.
The wings of the plane routinely lift 60 metric tons. The force on the wings at takeoff is equivalent to a dramatically higher static load than that. And the wings are built and tested with a large safety margin to
be able to withstand significantly higher forces than they’d ever encounter in real circumstances.
How much do 100 people standing on a wing weigh? Assume an average of 200 pounds each – which is almost certainly much too high – and you’re looking
at around 20,000 pounds.
Of course, there’s a different standing on the wings. The upward force of lift is uniformly distributed over the wings. In the pictures, people are pretty well distributed – they’re not bunched towards the end. But even if they were, the weight of the people on the wing wouldn’t be enough to break it. After all – in routine operating conditions, the lift is uniform. In turbulent conditions, you get huge torquing forces on the wings. When’s the last time you heard of an airplane’s wing snapping off in turbulence?
And all of that is ignoring the fact that the plane was, at the time, floating on water. The water was supporting the wings – meaning that the wings could handle even more weight.
The idea that people standing on the wings of a plane floating on the water should have broken the wings is just ridiculous, when you consider how
their weight compares to the kinds of forces that the wing routinely encounters.
The second thing comes from a totally different direction, and involves
image manipulation. Our conspiracy theorist believe that the photographs of the plane have been heavily photoshopped.
Basically, because when you zoom in on the photos, you can see extreme
pixellation along the edges of the plane. When you edit an image, particularly if you’re not particularly good at it, you get edge artifacts – that is, pixellated jags where you joined two images together.
Once again, though, we hit an issue where understanding what scale
means leads to errors.
One of the causes of the artifacts in photoshop is the fact that the
resolution of the boundary of the region that you cut and pasted doesn’t match
the resolution of the actual image – so you get artifacts. The jags are
always there in the image. But they become more visible, because the
resolution mismatch brought along some pixels from the original context of the
clipped section, and those contrast more against context into which you’ve
inserted the clipped section. Photoshopping didn’t create the jags;
it just made them more visible. The other cause of artifacts in photoshopped images is resolution mismatch – the resolution of the source image doesn’t match the resolution of the image into which it’s clipped – so when you look at the boundary, you can artifacts produced by that mismatch.
Take a normal digital image, and scale it up, and you’ll see those jagged
artifacts exactly the same way that you would in a bad photoshop. The image
is, ultimately, pixellated. When you get to a high enough scale, you’ll see
jagged artifacts of that pixellation. Those artifacts will be more visible in places where there’s more contrast between the colors on either side of the boundary. Like, say, the contrast of the airline logo against the white background of the airplane’s hull.