Good point, the blackbird is analyzed as steady-state, and the skydiver is clearly a transient case. OTOH, it’s a fairly long transient:
-speed is in excess of 2000 MPH for 50 seconds. Assuming constant ambient temp of -72F during this time (a gross simplification), compression heating results in local temps in excess of 600F. The air is indeed pretty thin for most of that, though, so maybe you wouldn’t see much heat transfer to his suit’s skin in that time?
-peak speed of 2600 MPH (before decel begins) happens right around 100,000 feet altitude. Peak local temps would be over 1000F. Air is getting pretty dense here - thick enough to fly a blackbird - and so our skydiver might cook faster.
The decel will start as soon as there’s air. If there’s enough air at 100K to fly a plane, something in non-aerodynamic free-fall would slow way before then.
Yeah, the measurement would influence the outcome. Indeed Schrodinger’s ant would probably have a greater than 50% chance of walking away without being attached to the cell phone.
If I am standing on a cliff at 100K feet and jump off the edge, I must first accelerate to some non-zero velocity. I will fall some distance before beginning to decelerate.
Now try again, this time on top of a step ladder at 100, 010 feet. I’m still accelerating as I pass through 100K feet; decel still won’t begin for quite some time, not until I’m well below 100K feet…
Make my stepladder 100K feet tall, so now I’m actually standing at 200,000 feet. The “edge of space” is 330,000 feet, so presumably there is still air below that altitude. As before, I have to accelerate - even though there’s air - before I can begin decelerating.
If decel does not begin as soon as there’s air, when will I actually begin decelerating? Well, terminal velocity (the speed at which gravity and aero drag force are in balance) is a function of air density, and decreases with decreasing altitude. In a freefall, decel will begin only when one’s velocity is in excess of local terminal velocity. That point will depend on how fast the object is falling, and on its mass and shape, and on local air density. There’s nothing particularly magical about the 100K foot mark. If our jumper actually happens to begin decelerating around that point, have him try again, and this time replace his parachute with 100 pounds of lead; his decel will now begin at a lower altitude.
Very interesting. I was under the assumption that a skydiver dropped from rest (not orbit) from the “edge of space” would indeed reach a very high peak velocity, but not fast enough in dense enough air to make compression heating much of an issue.
It appears that I was incorrect. Our intrepid skydiver had better wear his/her asbestos underwear.
Really? That’s surprising, my guys have taken so many swan dives off my shoulders onto the hardwood floor by now I couldn’t even begin to count, and they just shake it off in 2 seconds. I was actually wondering if there was a similar thing at work with them as with the ants. I guess I better hold off on putting it to the test.
Oh snap, I figured anything that doesn’t deform would be about equally hard. Didn’t really think that one through. It’s only by the sheerest accident I’ve never dropped any of them in the (tiled) bathroom!
The gerbil deforms so much that it doesn’t matter whether it’s hitting tile or wood, but the difference matters if the item being dropped is something very rigid and brittle, like a porcelain salad bowl. Something like that can survive a fall from greater height if the floor is wood instead of ceramic tile.
This is untrue. You deform dramatically more than dirt or stone, but try falling off of a ladder onto each of them and see how you feel afterward. How hard the “rigid” floor is (wood vs tile for the gerbil) can make a very big difference.
The whole buttered cat levitation thing has always bothered me… It’s just sloppy logic. The basic premise is that instead of violating one of the two rules, we’ll just violate both, and that makes everything OK. If the cat hovers, then the cat does not land on its feet, and the toast does not land buttered-side down, since neither one lands at all. What’s needed is not a scenario where neither lands, but one where both do. For instance, the cat first makes contact with its feet, and then immediately thereafter rolls over onto its back.
