Aviation Archive

Friday, June 9, 2017

What Would Happn if Everybody on an Airliner Jumped at the Same Time?

Vomit CometI recently came across the Quora question, If everybody on a Boeing 747 jumped at the same time, what would happen to the plane?. The first answer I read was spectacularly wrong, and most of the others were either guesses, jokes, or just generalities without much substance. So, I did what any good engineer would do and calculated it. Here's what I wrote.


In general - not much is going to happen if everybody on a 747 jumps at the same time. Just from a big picture view - there is no major change to the external forces acting on the aircraft/passenger system. So, you would expect the combined center of gravity to continue along the same path. And since most people can't jump very high, and the aircraft weighs substantially more than the passengers, the aircraft isn't going to be affected much at all.

In general, when the passengers jump, they'll push the aircraft down slightly, in proportion to their own mass and how far they jumped up. Then, since the lift didn't go away on the aircraft, the lift will first slow down the aircraft's slight descent, then cause the aircraft to start to climb again as the passengers start to fall.

But we don't have to just hand-wave an answer. We've got equations - we can calculate what will happen. So, I made a super simple model of this, with one mass to represent the aircraft, and another to represent the passengers*.

According to Wikipedia, a 747-400ER can hold 660 passengers, and has max takeoff weight of 910,000 lbs. According to FAA Advisory Circular 120-27E, average adult passenger weight in the winter, including "a 16-pound allowance for personal items and carry-on bags" is 195 lbs. Assuming the plane is full of adults, and that they're not going to be holding their carry-ons when they jump, that's 179 lbs per passenger, or a total of 118,140 lbs for all the passengers combined. That leaves 791,860 lbs for the aircraft itself.

For the forces, I assumed that the passengers jumping would be applying a constant force 2x their weight for 0.2 seconds. For the lift on the 747, I assumed that it would remain unchanged. Granted, there will be a small change in angle of attack (not pitch) due to the changes in vertical velocity, but I assumed it would be negligible.

So, what actually happens? This:

Δh vs. t

For passengers jumping ~1.3 ft into the air, the airframe itself will dip ~0.2 ft (2.4 in). Unsurprisingly - that's the same ratio as passenger weight to aircraft weight (confirming that the combined center of gravity does indeed continue on the same path unaltered). As the passengers reach the apex of their leap, the 747 reaches the bottom of its dip, and they quickly come back in contact again in less than a second.

I did skip out on what happens when they come back in contact, since I only did a super simple model and didn't really feel like spending a lot of time on it. They won't come smacking into each other. Rather, it'll probably be something like a mirror image of the jump, where the passengers flex their legs as they land to cushion the coming back together.

And of course, if you change up the assumptions, this will all change accordingly, but this puts the whole thing into perspective, showing the magnitudes and general behavior.


*Here's a fuller description of the simple model, attempting to put it terms that most people can understand. Like I said, I broke the system up into 2 bodies - one for the 747, and one for the passengers. Here's a diagram of the forces acting on each body (insert joke about spherical cows here):

Free Body Diagram

Note first of all that I'm only looking at forces in the vertical direction, since that's the only thing changing in this problem. Thrust and drag are staying constant, so the speed of the aircraft isn't going to change. Next, note that thanks to Newton's Third Law, we know that the force the passengers are pushing down on the 747 is the same magnitude but in the opposite direction as the force that the 747 is pushing up on the passengers. That's the magenta arrow on each body. Finally, note that that's the only force that changes during the entire problem. The weight of the aircraft is essentially constant. The weight of the passengers is essentially constant. And like I already explained up above, I assumed that the lift remained constant. So, here are graphs of what those forces look like, with an additional solid curve showing the net forces on each body (or the summation of forces, designated with the Σ label):

Forces on 747

Forces on Pax

Note that just before the jump, everything was in equilibrium, with no net forces. As the passengers jumped, they pushed down on the plane. Once they were in the air, that force, Fy_pax_to_747, went to zero, and then only lift and gravity were acting on the 747, and only gravity was acting on the passengers.

Next, we use Newton's second law, F=ma, to figure out the accelerations on the bodies. Since the force of the passengers jumping was modeled so simply as a constant force for 0.2 seconds, and all other forces were constant, the accelerations also all turned out to be constant.

a vs. t

For a constant acceleration, it's easy to calculate velocity, using the formula V2 = V1 + a*Δt. That produces accelerations over time that look like:

V vs. t

Finally, I used the velocities to calculate how far the bodies moved. I actually broke it up into 0.001 second increments, and did this linearly, with the simple formula h2 = h1 + V*Δt. That's not exactly accurate when velocity isn't constant. There are more exact formulas you can use, but when you break it up into such short segments, you're going to be very, very close. And with Excel, it's very easy to do this brute force approach. And doing that gave the graph I already showed up above, but which I'll repeat again here for completeness:

Δh vs. t

Image Source: NASA by way of Business Insider

Saturday, December 17, 2016

Happy Wright Brothers Day

Wright Brothers' First Flight, December 17, 1903

113 years ago today, the Wright brothers became the first humans to truly fulfill the dream of flight. You can read what I wrote about the significance of this from my Wright Brother's Day, 2007 entry. On a related note, you could read my entry, Flying, from a few years ago, where I marvel at just how cool it really is to be able to fly.

(Yes, this entry is recycled. I only have my iPhone today, so I'm not up for typing a long original entry. But I still couldn't let the day go unmentioned.)

Thursday, December 17, 2015

Happy Wright Brothers' Day, 2015

Wright Brothers' First Flight, December 17, 1903

On this day in 1903, the Wright brothers became the first people to achieve a dream of humanity for thousands and thousands of years - flying. Yes, their legend is a little overhyped in some circles. There were aviation pioneers who had preceded them, and contemporaries working on the problem at the same time who would have figured it out eventually, but the Wrights were the first. Moreover, with their systematic approach and especially with their focus on control, they were years ahead of everyone else. When they gave their first public demonstrations in France in 1908 (they'd spent that intervening time improving their flying machines), crowds were awestruck.

To quote myself from a previous entry, "Flying has become so common place today that we take it for granted. People complain about the cramped seats, the long lines to get through security, the bad food (if you even get any) on flights. But just remember how long people have dreamt of flight, for how long people looked to the skies wanting to emulate the birds. Flying used to be the stuff of myth and legends, reserved for the gods. Now, we can all get in an airplane, and soar above the clouds. It really is something special."

So as you go about your business today, take a moment to look up and find an airplane, and marvel a little at the achievement.

For more aviation-themed information on this site, you could browse the Aviation Archive on the blog, or check out the Aviation Section of my static pages. Or you could jump to some of the highlighted pages I've listed below.

Related Entries/Pages:

Previous Wright Brothers Day Entries:

Wednesday, December 17, 2014

Did Gustave Whitehead Beat the Wright Brothers as the First To Fly

Woodcut of Whitehead's Flying MachineIn honor of Wright Brothers' Day, I figured I'd address a topic concerning their reputation as the first people to fly. There's a bit of a movement to try to bestow that honor on a different man - Gustave Whitehead.

Whitehead (born Weißkopf, but he changed his name when he moved to America) was an early aviation pioneer who built several unsuccessful flying machines. However, there are claims that he was successful on a few occasions prior to the Wright Brothers. These claims mostly come from a handful of sources - Whitehead's own claims, eye-witness accounts, and a report from the newspaper, the Bridgeport Herald. There's also a newly discovered photo supposedly showing Whitehead in the air. This photo was enough to convince Jane's All the World's Aircraft to officially recognize Whitehead as the first to fly, and for Connecticut to pass a bill proclaiming Whitehead as the first.

The problem is that none of these sources of evidence are particularly reliable. Whitehead himself could hardly be considered an unbiased party, so his claims can only be taken with a grain of salt without independent evidence to back it up.

There are numerous eyewitness accounts of Whitehead making flights. These do help the case, but they're still not ironclad proof. Eyewitness accounts are notoriously unreliable. Just this morning I received my weekly eSkeptic newsletter, with the subject this time being about just how unreliable eyewitness testimony can be (in this case, prompted by the Michael Brown affair in Ferguson). That article has many good examples, but one of my favorites that it didn't include was the Challenger Study (or a similar 911 study). When people were interviewed the day after the Challenger tragedy, they gave an account of where they were and what they were doing when they learned about the explosion. But in a follow-up interview a year later, even though the memories still seemed vivid and real, they had changed, sometimes in very big ways (e.g. hearing about it from classmates vs. watching it live). In the case of Whitehead, most of the affidavits from eyewitnesses are from decades later - more than enough time for memories to become warped.

The local newspaper in Bridgeport published an article about Whitehead and one of his supposed flights. There's some conjecture over how serious the article might have been, but the most damning aspect of it is Whitehead's account of the flight. Speaking as a private pilot and an aerospace engineer, this is not the type of description you'd expect for somebody's first time flying any aircraft, let alone a primitive airplane designed when there was less understanding of controls and stability. Read this passage about his climbout, and how Whitehead did nothing to level his climb, but just rode it out with the machine taking care of it.

When the ship had reached a height of about forty or fifty feet I began to wonder how much higher it would go. But just about that time I observed that she was sailing along easily and not raising any higher.

But this paragraph is the one that really struck me.

And while my brain was whirling with these new sensations of delight I saw ahead a clump of trees that the machine was pointed straight for. I knew that I must in some way steer around those trees or raise above them. I was a hundred yards distant from them and I knew that I could not clear them by raising higher, and also that I had no means of steering around them by using the machinery. Then like a flash a plan to escape the trees came to mind. I had watched the birds when turned out of a straight course to avoid something ahead. They changed their bodies from a horizontal plane to one slightly diagonal to the horizontal. To turn to the left the bird would lower its left wing or side of its body. The machine ought to obey the same principle and when within about fifty yards of the clump of trees I shifted my weight to the left side of the machine. It swung over a little and began to turn from the straight course. And we sailed around the trees as easy as it was to sail straight ahead.

Are we really to believe that Whitehead took off in an airplane without having given any thought beforehand to how he was to control it? It's absurd to imagine that such a flight would be successful, or would have been the leisurely affair that Whitehead described. And as the commentary in the article I linked to describes, the inferred speeds from this flight are impossibly slow. It's just not a plausible scenario.

Now it's time to examine what's actually my favorite part of this 'controversy' - the photographic evidence. There were some press reports that a photo of Whitehead in flight had been on display at the first exhibition of the Aero Club of America in 1906. Noone has been able to find this photo, but a Whitehead advocate, John Brown, thinks he's found evidence of it. The evidence comes from this photo of the exibition:

First exhibition of the Aero Club of America, January, 1906

The box and arrow were added by someone else to show the area of interest to Whitehead supporters. Brown took that region and enlarged it by several thousand percent to get this supposed image of Whitehead in flight:

Alleged photo of Gustave Whitehead in Flight

Brown has a lengthy article describing his analysis of the photo. He also has a description of it on the homepage of Gustave-Whitehead.com, that includes this side by side comparison of the photo to what he thinks it represents.

John Brown's Interpretation of Alleged Whitehead Flight Photo

Now, that's a pretty fanciful interpretation. And Brown appears to be very confident in his analysis despite the obvious lack of detail. But thankfully, we don't have to just wave this off as too vague to be meaningful. Carroll F. Gray has dug into this claim (and many others). Gray has pretty conclusively demonstrated that this photo is not of one of Whitehead's machines, but is rather a glider built by a John J. Montgomery. As much as I would like to steal some of Gray's photos to show in this post, he's put in so much effort that he deserves the visitors at his site. So, in case you missed the link before, here it is again, Update # 5: The Photographs - Whitehead Aloft They Are Not. I highly recommend visiting that page. Even if it's not Whitehead in the air, it's very interesting how Gray was able to track down this scene from such a blurry image and definitively identify the actual scene it's depicting.

Aside from all these poor lines of evidence put forward by the Whitehead advocates, it also helps to take a step back and look at the big picture. The Wright Brothers made their first flight in 1903. They learned their lessons from that flight, went through a few more iterations of flying machines, and by 1908 were giving public demonstations that amazed audiences (though it should be noted that by 1908, there were others flying - just not nearly as well as the Wrights). Whitehead supposedly made his first flight a year or two before the Wright brothers, and then... what? Other than that one questionable article (and many papers that picked up that single story), Whitehead never made headlines with any public flights. He never even built an airplane that could fly after that. How does someone go from being the first in flight to not being able to make another working airplane, despite several attempts?

There's really no good, strong evidence to back up the claim that Gustave Whitehead was the first person to successfully fly an airplane, and there are actually a few indicators that it never happened (like his account of the flight). I think it's possible (though still not backed up with evidece) that he did have some success, maybe even making a vehicle capable of hopping into the air and staying aloft for a few seconds. But the honor of the first in flight still belongs to the Wright Brothers.


I came across several interesting articles on these issues (some of which I might have already linked to above).

More Info:

Image Source: Wikipedia

Happy Wright Brothers' Day, 2014

Wright Brothers' First Flight, December 17, 1903

On December 17th, 1903, the Wright Brothers became the first to achieve something people had dreamt about for centuries - flying. Granted, the Wrights weren't lone geniuses working in a vaccuum. There were many pioneers before them whose work they built upon, and many contemporaries working on the problem who would have figured it out eventually. But the Wright Brothers were the first, and their systematic approach and especially their focus on controllability put them years ahead of anyone else, and fulling deserving of that honor (even if their later patent wars might have hurt the fledgling industry).

So when you're out and about today, glance up at the skies, and if you spot an airplane, marvel a little bit at what an accomplishment it is.

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Selling Out