So I’m staying up way too late because I have found the most recent released report on the Columbia disaster (link here) and I’m curious about one part, which states that the crew (who were all likely deceased at this point) were in a “forebody [that] was rotating about all three axes at approximately 0.1 rev/sec and did not trim into a specific attitude.” I understand that they were trying to contrast this with the Challenger, where the crew cabin was basically intact and diving upon hitting the ocean, but I’m trying to get a human understanding of the forces, as it might relate to a car accident or something. Obviously, having the forces working on all three axes is tricky.
That sounds like an uncontrolled tumble, but at a relatively slow rate. By itself, I don’t think it would create any large G forces.
Watch this for a good understanding of what happened. It was a failure process that took a while and ended up in a uncontrolled tumble that resulted in a catastrophic burn up in the upper atmosphere.
Warning: Good but sad.
A question about basic physics: do objects really “tumble”- that is, rotate about more than one axis at a time? I thought that all rotational forces on an object added together into a vector that resulted in one axis/plane of rotation.
Here is an even better reconstruction of final events:
You thought correctly.
At a given instant in time, an object will be rotating around a specific axis. In the absence of external forces, the object will remain rotating around the same axis.
When the report says the shuttle was “rotating about all three axes,” I suspect it meant the rotation axis wasn’t perpendicular to any of the three primay axes that run back-front, left-right, and top-bottom. The resulting motion is visually confusing (try it yourself by flipping and twisting a book).
Bolding added.
But weren’t there external forces acting on it? Specifically, the atmosphere acting on the control surfaces, etc.? Couldn’t that disrupt the tidy rotation around one axis, causing it to tumble?
Yes, of course it could have. I’m not sure what the magnitude of the forces were, but it’s certainly possible the axis of rotation could have been changing over time (which is why I specified the part you bolded).
However, I’m inferring that the “all three axes” comment in the OP is a reference to simultaneous rotation about the three primary axes rather than a change of the rotational axis over time (not that both couldn’t happen, obviously, but the latter wasn’t reported).
Thanks everyone. Shagnasty, I started watching the second of your videos, and I think I’m going to wait to finish it until I’ve been awake for a while; don’t need to start the day sad.
I’m finding the report surprisingly easy to read, in spite of not having a background in the subject.
Bwuh.
What?
My head hurts now. If an object is both spinning and tumbling, how is that not rotating around more than one axis?
Depends on how you define “axis.”
We usually think of an object as having three *principal *axes, perpendicular to each other, running back-to-front, left-to-right, and top-to-bottom. The traditional roll, pitch, and yaw rotations are rotations about these three axes.
At any given time, the rotation of an object about its three axes can be added up to describe a rotation about one specific axis. However, that axis isn’t, in general, aligned with a *principal *axis.
I’m sort of envisioning one of those trainer things with the three concentric circles, each spinning different directions. I have no idea what they’re called.
It just doesn’t seem like .1/sec is very fast, and yet there was extensive damage to the crew - especially the upper bodies and heads, which were apparently not held as tightly to the seat. This is the part I’m having a hard time understanding. Was the cabin simply changing directions quickly?
I looked over the report this morning, although I didn’t read the entire thing. I remember it said that the crew module was tumbling at 0.1 revolutions per second, but depending on where each person was sitting in the crew module, they would experience more or less force (sitting further away from the center, there’d be higher torque due to a longer moment arm).
Also, 0.1rev/sec doesn’t sound too bad, but they were unconscious at that point. Their shoulder harnesses didn’t engage because they work on an inertial system (like car seat belts) where they don’t lock if there’s mainly side-to-side motion. So they were only restrained by their lap belts.
It would be like if you were a passenger in car accident where the car rolled over dozens of times, you only had a lapbelt on, and you were unconscious so you can’t brace yourself to prevent injury. Apparently the astronauts sustained a lots of injuries from this, including head injuries from their head banging around inside their helmets. Thank god they were unconscious.
I think this is the answer to the question I was trying to ask. (I’m not always at my clearest at two in the morning.) Thanks! And if anyone has anything else to add, go for it.
Understood, I think… can you help me visualize the single axis, in this case? I can see an axis in the end-over-end tumble, which would be vaguely around the left-right axis, even if isn’t exactly parallel, and I see another axis in the spinning, again vaguely around the vertical axis, but … motion around a single axis is described in 2 dimensional space, isn’t it? So how do you define a complex 3d motion like a spinning tumble in 2 dimensions? 
Is it that you mean you can define the motion with a single mathematical expression? Or is there something I’m still missing?
Bump?
For any constant rotation there will be an axis of rotation - a direction which is preserved. Points ‘spin about’ this axis, so the rotation is 2-dimensional in the sense that points remain on planes parallel to the axis.
Imagine reaching your arm out (the axis of rotation) and firmly grabbing a spinning shaft. If you reach out straight to your side you do a somersault, if you reach straight up you do a pirouette, if you reach straight in front of you you do a cartwheel. Now reach somewhere other than one of these three primary axes. Say, 45 degrees between straight to your side and straight forward, and up a bit. You still rotate about, but it is much more ‘awkward’ because your body is not entirely on any single plane of rotation. Instead you get a ‘spinning tumble’ like a Cirque du Soleil acrobat on a ribbon.
If you want even more complex motion, change the axis of rotation while spinning. Adjust the direction you are holding your arm while you twirl about. As you do this, your motion is no longer described by a single rotation matrix, although your instantaneous rotation is still about a single axis. This complex spinning tumble can be defined by a series of axes of rotation (the directions which your arm moves through).
I think the main hangup with your visualization is that motion around a single axis is still 3d motion.
Rotational motion is analagous to translational motion, in that, even if it takes three parameters to describe the motion, the motion is still in one “direction” (or about one axis, in the rotational case).
Let’s step back and construct a thought experiment, starting with translational motion.
Imagine you have a cardboard box, nicely prismatic, with opposite sides parallel and all angles right angles–a standard cardboard box, in other words. Let’s also, if you like (this isn’t strictly necessary), imagine the length, width, and height are different.
Now imagine you have a gun. A BB gun, to make this thought experiment less dangerous. Place the muzzle of the BB gun at one corner of the box and carefully line it up so it’s pointing toward the very opposite corner, the point farthest away. (Asterisk to asterisk in the picture below)
*_______________
/ /|
/ / |
/ / |
/ / |
/______________/ |
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|______________|/
*
Now fire the gun. The BB will travel through the box, from corner to corner, in a straight line, right?
However, that straight line isn’t parallel to the length dimension, the width dimension, or the height dimension. If you think of the length, width, and height as the primary axes–X, Y, and Z–the BB is translating along all three axes at once.
Think about that a second. Even though the BB is travelling in a straight line (one dimension), the fact that it’s travelling through 3D space means we need three dimensions–three axes–to describe its motion.
NOW. Now, let’s jump to rotation. Back to the thought experiment box. You now have a box with, conveniently, two holes in opposite corners. Grab a dowel and stick it through the box from hole to hole, following the path of the BB.
Now spin the box around the dowel. The box is spinning around one particular axis (the dowel), right? But how do you *describe *that motion? In three dimensions, the motion is described as the sum of rotations around the X-axis, the Y-axis, and the Z-axis, in the same way as translation is described as the sum of the motion along the X-axis, the Y-axis, and the Z-axis.
If you watch the box closely, you’ll see that it really is “spinning” and “tumbling” and “rolling” all at once.
And it’s the same thing with the space shuttle, or a plane, or a car, or anything else. At any particular time, the object will be rotating about a particular axis, but that axis is not necessariy the same as a primary axis. In order to describe the rotational motion, we describe it as the sum of rotations around all three primary axes. The same as we do for translational motion.
Zut, why I raised the question in the first place: I imagined a situation in space where a tug has to grapple and de-spin derelicts and debris for recovery. I was thinking it would be extremely handy for an interstellar junk hauler to have something like a doppler radar that could scan a piece of tumbling debris, and have the computer figure out where it’s spin axis is. Then align the tug along one of the axises, match spin rate, grapple, and then de-spin.
I never made it past high school algebra, so I can’t tell if I’m asking the wrong question, or asking the right question and just not understanding you.
I get that if you take three frames of reference, (x, y, z) that are assumed to be 90 degrees opposed to eachother, you can use those three references to describe motion along an axis that doesn’t line up with one of them, as in your example above.
But to my literal brain, that doesn’t mean it’s rotating around those three axis, it just means its rotating through those three planes - right? It’s still rotating around one axis, just an axis that doesn’t correspond exactly with x, y, or z.
If we take your box, and place the dowel in the middle of two opposing faces (call them “top” and “bottom”, as opposed to left, right, front, and back), and spin it like a top on the point of that dowel, it’s rotating around one axis. In my head, anyway. Now, while it’s spinning, give it a whack on it’s underside. Because this is a though experiment, we can whack it in such a way that the force we apply will cause the box to begin rotating directly away from us, just as if it had a dowel through two opposed sides, as well as the top and bottom.
To me, the box is now rotating around two different axis. The original axis (the dowel through “top” and “bottom”, and another axis, which has its center in the “left” and “right” faces. It’s spinning and tumbling. Like a springboard diver, or a gymnast. Can we describe that motion using a single axis?
Am I even making sense? 