Monday, August 8, 2011

Falling for it

I've recently read some odd things and visited some odd websites while Googling to find out about the various aspects of falling. Free-falling in the sky, I mean - not falling out of my chair or down the stairs.

The first thing I was trying to find out was how long it would take you to splat into the earth falling from various heights, but I soon came across some other interesting questions from other readers of the various articles.

As to my first question, about how long it takes a person (or object) to fall to the earth from various heights, they started talking about physics right away so that sort of turned me off. All I really wanted to know was how long it would take an object to fall to earth from 20,000 feet, but could I get a straight answer? No. They kept talking about things like mass and resistance and attitude. I will admit to the attitude by then.

I realize that if I jump out of an airplane and go into a diving position I will fall faster than if I fall flat with my arms out like a skydiver. And I realize that a rock tied under an umbrella is probably going to fall a lot slower than a non-umbrellaed cannonball would, but I just wanted a general answer. Not possible, the Googled scientists said - need to know some factors first.

I remember Rocket Scientist telling me one time about terminal velocity, which I assumed referred to a child running through an airport. Anyway, the subject was sudden loss of cabin pressure and whether one would really get sucked out the airplane window like Goldfinger did. I think she said no, because the pressure would be lost too fast and wasn't that great of a differential in the first place, but if you were under several atmospheres of pressure or lack of pressure, like in a diving bell, then your bod would get pushed through the meat grinder pretty grossly.

Back to falling. What prompted this was me reading an old news story about two large airliners crashing over the Grand Canyon at 20,000 feet back in 1956. I was wondering how long it might have taken them to fall from that height to crash into Grand Canyon, and whether or not it would be a long enough fall for the passengers to have time to realize what had happened and what was about to happen to them, if you get my drift. I'm not insensitive to their terror, but inquiring minds want to know and I can't help them anymore by not asking anyway.

So, basically you get back to air resistance of the various parts of the still-intact parts of the airliners which contained the 200-some passengers (it was the largest loss of life of any airline accident up to that time.)

I'm guessing, and only guessing, that it took a least a couple of minutes. Must have seemed like an eternity to them. Neither of the planes were flyable and went straight down, crashing near each other, although one assumes engines or some of them were still running, they were screaming down to earth and not "gliding." The TWA super Connie had it's entire tail torn off, so you assume some passengers in free fall away from the plane, but the United DC-7 had half of one wing ripped off so maybe the pilot was able to keep the shiny side "up" rather than spiraling, but almost straight down. Can anyone improve upon my guess of "a couple minutes?"

The second question that came up (other than the normal questions of throwing cats and caterpillars out of upstairs windows) was about falling through the center of the earth. The deal was you drill a hole all the way through the earth and jump into it and fall out in China. And the question was how long would it take to make the trip. Everyone came up with between 12 and 14 minutes, which I thought was preposterous. Of course, you had to pretend a lot of things like you could breathe and there was no air friction and it wasn't hot at the center of the earth and things like that.

Nobody, none of the elementary school science teachers, came up with the answer I came up with, so I will present it to you here. They were concerned with mass and terminal velocity and diameter of the earth, and I was concerned with something they didn't even mention, which was gravity. I say, you would fall slower and slower and finally come to a stop at the center of the earth when the gravitational forces equalized. What's wrong with that idea? But nobody else mentioned gravity, so I must be wrong.

When I left the google thing, my mind kept on going, in free-fall, as it were. Like, what if you dropped two round lead balls out of an airplane, one the size of a marble and one the size of a small cannon ball. Pretend the airplane could come to a stop while you dropped them carefully. Pretend there was no wind to blow the lighter one sideways. Just think about mass. I say they would reach the ground at exactly the same time (if you pretend there was no air resistance. Sigh.) I say that the two objects of different weights (neglecting aerodynamics) would fall at exactly the same speed.

Speaking of terminal velocity. I think we were at one time. It turns out that an object doesn't just fall faster and faster until it reaches its terminal velocity and then continue at that speed until it hits the ground. Air being denser and denser the closer to the ground you are, the objects slow (slightly) down the closer they get to the ground. That's what they said. So you reach terminal velocity and then (still falling side by side?) you begin to slow down a bit. We are probably talking about less than a second here, but you know how scientists are.

I have finally convinced myself that if you are trapped in a falling elevator you will still be killed if you jump hard and high a split second before you crash. But I can't explain why. Sounds reasonable to me.


  1. Monday morning is not the time for these questions. I'll wait until the fog has lifted.

  2. Always a pleasure reading your posts. I don't have time to fully comment, but I will say two quick things: 1) I believe you are correct and you wouldn't fall through the earth- you stop at the center and 2) mythbusters did an episode of the jumping the instant before an elevator hits the ground.

    I'll have to dust off my aerospace texts books to give an estimate on the time to free fall from 20,000 feet.

    Actually the last thing I will say is can ignore the horizontal velocity in your examples for a falling time estimate- especially if you are assuming no friction.

  3. The acceleration of gravity is approximately 32 ft/sec (yes, I know that off the top of my head). If we assume no other forces working (like air resistance), distance = 1/2xacceleration*[time]^2 (that's a constant acceleration thing per Newton).

    With Accleration=32 ft/s^2 and 20,000 feet, time would be about 35 seconds (NOT minutes).

    Not this would be simpler in SI units (6096 m with acceleration ~10/m/s) but the answer is about the same: 35 sec.

    So, now you know.

    If it takes longer (and it probably does), you know you should have been ignoring wind resistance. No one could have had more than 35 seconds though, since that's worst case.

  4. See, the whole reason for this post was to get someone to explain it to me in real people language.

    At least you used feet per second instead of some metric crap or angstrom units.

    I think it was more than 35 seconds. And someday I'll prove it. You just wait and watch.

  5. And I know 88 ft per second off the top of my head. From 5th grade. It has always stood me in good stead.

  6. Tell me again why 6096 m is simpler than 20,000 feet. I missed that.

  7. "Houston, this is United 46 heavy. Reporting 20,000 over."


    "What? WHAT???? Say that in meters!"

  8. "Say again?"

    Tower: "I can't divide 20,000 by 10 easily!"

    "Hmmmm. Why would you want to do that? Anyway, the answer would be 2,000 if you divided it by 10."


    "I don't think you can do it that way. Besides, I have an expensive government scientific calculator and you are just using you head. No one is going to believe you. Going to sleep now."

  9. Okay, so we won't neglect air resistance. So that comes out to 2 minutes. (.2 minutes times 10).

  10. You like Newtons too? We agree on something. Yummy.

  11. Ha--- i was looking forward to this, after seeing the post, I knew what was coming!

  12. @Stephanie-- I have to disagree with your "worst" case comment. Air resistance counteracts the acceleration of gravity and will add to the time. What you approximated was "fastest" case. I won't call it "best" case although you could argue that since you have less time to die of an exploding heart. Is that what you meant? No one will have less than 35 seconds.

    @ Relax Max- what exactly would you like explained? The calculation is relative simple when ignoring air resistance. Would you like a description of terminal velocity?

  13. Remember when we were kids and we all tried to dig a hole to China? How many kids do you see doing that today? None! The airlines got together and invented high-tech, mind numbing video games, made you have to walk pass the Hostess Ho-Ho's and Ding Dong's to get to said video games. Now children sit in front of their TV's getting fat and brain dead instead of digging that hole. I believe some poor sap in his childhood actually dug the hole to China, jumped in and it only took 15 minutes to emerge in a rice field. The government, the airlines and yes, the Hostess Snack Cake Company are in on this cover-up of the 15 minute jump to China. Follow the money, that's what I'm saying, follow the money.

  14. @Rocketscienist
    When I said "worst case" I meant least amount of time before they died. Which worked with "fastest case." But I did say it wrong; I should have said, "No one could have had LESS than 35 seconds though, since that's worst case." No wonder it threw you.

    I already explained terminal velocity and air resistance to RM. He's just giving us a hard time.

  15. And, technically speaking, my terminal velocity answer was on Ask Me Anything (Now Unlikely Otaku).

  16. From way back, when I was learning to jump out of things, I recall that a human being's terminal velocity, no matter how streamlined you try to get, tops out at about 162 mph. In the very highest altitude jump, Colonel Joe Kittinger fell in very thin air at a record speed of about 640 mph, but this would slow as air density increased.

    Might I suggest Max looks up characters such as Vesna Vulovic, Nicholas Alkemade, and Ivan Mikhailovich Chisov? All are survivors of high altitude feefall without parachute.
    Alkemade's story, I read as a teenager in the fifties. He was a tail gunner in a lancaster bomber, which was hit and on fire. His parachure was in the rear fuselage, burnt, and he had no hydraulics to crank the turret back and line up the door anyway. So rather than burn, he chose to jump, at 18,000ft, -and survived.
    The incident is fully documented. Vesna Vukovic holds the record, at some 30,000ft, but she 'rode' a large fragment of her plane down, thus never reaching full velocity. She was the only survivor, and was badly injured.

  17. Oh, by the way... in four hours time I'll be strapping myself into a 747 for a 5000 plus mile flight.
    Fingers crossed, I hope not to be your freefall research bunny.

  18. @A. - It's not early morning any more. You are still strangely silent. :) (Like I should be, but you know me.)

    @Rocketscientist - Thank you. At least I can understand you. Unlike SOME people I might mention. :)

    @Jeff King - It's not me. It's that Stephanie woman.

    @Rocketscientist - declining on the terminal velocity explanation. Thanks. Unless it involves Newtons.

    @Stephanie Barr - Thanks for the link to your old Ask Me Anything blog. Nobody will be going to your new Japanese thing willingly, so the link will be helpful. :)

    Say, here's a thought - change the title of the blog to "TeachingAdvancedAlgebraInAncientSanskrit." You will get more hits and a LOT more comments. :) :) :) :) :) :) (Translation: Bwahahahahahahahahaha!!!)

    Unlikely indeed. Otahwaku or otherwise.

  19. What exactly do I want explained?

  20. Sue! Is that really you? Finally, someone I can understand! And sometimes even relate to.

    Yet, oddly, I don't. What are you on? The Ho-Hos? Your comment shows evidence of a distinct sugar high. Just sayin'.

    ::eyes narrowing suspiciously now::

    Yet, you ARE the first person on this blog to ever make me publicly admit to digging deep holes. ooooEEEEEoooo.

    Incidentally, I posted a tip on the Pub blog recently about a REALLY good source of side income that doesn't require writing. After you do what I say there and become ordained, then I am almost finished with my "Weird Occupations That Really Work" series, and I think the one on "How to be the Pope" might interest you.** But you have to sign up first on the other blog ore else you won't be able to legally perform marriages..

    I've gone on again, haven't I? Sorry.

    **If you choose to sign up to become Pope, you will have to cut your hair even shorter and start using a man's name. And I don't mean Boy Named Sue.

  21. @Soubriquet - ::yawns:: Those formulas are only good if you freefall over Yorkshire. Wake up and smell the hybiscuits, man!

    And if you think I am going to believe someone survived a freefall from those heights, you had better think again. Just because I am an American doesn't mean you can just say ANYTHING and I will believe it! Holy Haddock!

    "The incident is fully documented." Right. By Lady Thatcher yesterday under FULL medication, maybe.

    I can say these things to you because right now you are on a 747 winging your way away from God's favorite hemisphere, and you can't hear me. And when you land, you will have nothing to look forward to but more riots and yob firebombers. There, now I've said it. You had better just turn around and come back to Texas where it's safe and get yourself a real gun is my advice.

  22. Relax Max I will go over and read your post on side incomes that don't require writing but I have to tell you my online writing instructor told me to watch out for people like you. I believe she referred to you as a Dream Crusher.

    My middle son was a Pope for Halloween one year, so I already have the outfit.

  23. @Sue - Well, I never said you should stop writing. I'm sure the woman you are paying to teach you to write will never say stop either. :) But I am not a Dream Crusher, and I hope you write forever and ever. Amen.

    Now a word or two about Pope etiquette, as you apparently haven't read the book. First of all, it is usually the elder son who has dibs on the white robes for halloween, but your foh paw will be be overlooked. Note also that you MUST be ordained first and have begun to do marriages before you even THINK about being Pope, even of just Ohio.

    Having done this, however, you will be free to start cashing in on the big bucks by staging official visits to mall openings and such. I don't think I will tell you yet about the blessing stipends or the big hat discounts.

    Please keep writing. I'm sure she meant "Dream Catcher."

  24. You may rest reassured that even though I was sitting in an exit row, I resisted the urge to throw the handle on the door at 40'000 feet and measure the time it takes to reach the ground in freefall, on behalf of Relax-Max Blogging Inc.
    My more intellectual researching has given me a time to impact of three minutes and four seconds.
    That was based, apparently on air-force research that gave a terminal velocity of only 123 miles per hour. It's hard to find a definitive answer. At 40,000 ft, without oxygen, you'll be unconscious in seven seconds.
    So any plans for a neat, spread-stable parachutist's position will be irrelevant. You're fairly unlikey to regain consciousness in the short time before the splat.
    I love those stewardess theatricals, with exit information, and how to use the oxy-masks, and lifebelts.
    it's carefully designed to pretend that you'll survive. Which we really know is unlikely. Still, I do have one friend who survived two air crashes in one day (the rescue helicopter blew its gearbox out at 150 feet), so i know there are always going to be a few exceptions to those who succumb to probability.

  25. oops. That time was from 40,000, not 20,000ft.
    Halve it and you won't be far wrong.
    Terminal velocity is reached in about 15 seconds.
    Forward velocity of the plane has NO effect on the rate of fall, it only determines the distance you travel horizontally, which willbe... um not a lot, because you'll decelerate rapidly in your forward motion due to air resistance, whilst accellerating downward. Bomb-aimers tables must, I'm sure, be available on the interweb. it's a fairly simple bit of three dimensional geometry.
    Which I'd be unable to do in the time even the worst bomb-aimer would be allowed.

  26. @Me dear safely-returned-Soubriquet:

    I would have felt really badly if you had jumped out at 40,000 feet (can't really say how many meters that is) just to time the fall for my curiosity, even if divided by two. I will carefully consider your statement (which seems to echo that of the Rocket Scientist) about initial sideways momentum being irrelevant to falling time. I'm still digesting that in my sorry 4th grade educated brain. Perhaps I will consult with Adullamite for final verification. And I am also discounting the wind resistance of your wide open blood curdling screaming mouth and wildly flapping arms. (Reflexively so, since unconscious by now.) However, I share your mirth at the flight attendants telling us that our seat cushions can be used as "flotation devices in the unlikely event..." that we are forced to dive screaming and praying into the ocean. Frankly - and here I speak the sober truth - if it ever happens and I am sitting in the seat next to you, you may have my "flotation device" as well as your own. As God is my witness you will never see me splashing in the ocean with my face buried in an airline seat cushion which millions of "Fat Bastard"-cloned curry-eating kilt-wearing Scotsmen have farted into over the years. If we go down in the Hudson, I'll just strike out for shore. If we go down in the Pacific, I'm sure we will all be shark bait long before the saltwater washes the seat cushion clean enough for me to hug. Just saying.

  27. If you shoot a rifle horizontally, and drop a similar bullet at the same time, one will have made it a lot further away by the time both hit the ground, simultaneously.
    Well, to be exact, the shot bullet might stay up a millisecond longer. the Rocket Scientist could probably tell you how much muzzle velocity you'd need to get it into a stable orbit, five feet up above the mythically perfectly flat planet. that is, if there were no atmosphere. if there were an atmosphere, your impossibly high muzzle velocity would lead to a rapidly melted and boiled, and evaporated bullet.

  28. I'm sorry. It sounds almost plausible, I must admit. But I'm still going to have to speak with Adullamite, he being my go-to expert on things that fall a lot.

  29. Maybe I am mistaken about falling things expert. Adullamite may be my expert on people who think the earth is flat.

    Or whether the gizzard of a bagpipe explodes at 40,000 feet making a terrible wailing death gasp. Now I'm unsure altogether. He is an expert at many things, though.

    A poser.

    Perhaps you could try a safer experiment for me than jumping out of a plane with a stopwatch that I could retrieve on impact. Perhaps, instead, you could stand in the bed of a doooooooly going 88 feet per second and jump in the air? I know you'd have no fear, but - just in case - maybe you could stand close to the cab when you jumped. You may be a really high jumper. I will be the one shooting the rifle.

  30. "...impossibly high muzzle velocity would lead to a rapidly melted and boiled, and evaporated bullet.""

    many people have said that on this blog, none has returned with any evaporated bullet evidence. And that once included Algore the global warming scientist.

    See... you are probably thinking that right now that I am merely being argume... argumenta...



  31. Wait! I get it now. You have been talking about the laws os physics in ENGLAND! Now I get it.

  32. I just shot a bullet toward you.
    If you continue blogging, you'll know I was right, it either fell to earth or evaporated.

    Or I'm a lousy shot. but that's not true. I have a medal somewhere that proves otherwise. mind you, i won over forty years ago. before i needed bifocals.

  33. God, they just found that rat-faced little blogger turd dog shot! The bullet was in pristine condition with no signes of falling or melting. No harm done, unfortunately, because it struck turd-dog in the head.

    Thank God for 'Bamacare- he'll only have to pay for...
    all of it.

    The police have no leads but they are looking for clues. They theorize the bullet came from the east or some other direction. Right now they are at Dunkin Donuts looking for more clues in their coffee.

    Max is doing his Pope blessing imitation with one paw upraised, going "Father forgive him for he knows not what he did." Or something like that.

  34. I probably won't keep you updated since dufus looks like he is going to live.

  35. Send donations to:

    Relax Max Recovery Fund
    C/O Vicar Ezra
    Sheep Springs Station 31
    Alice Springs, NT

    "We will take responsibility if you send cash. No risk."

  36. Damn. I was aiming for his tiny, wrinkled little heart. Bullet must have been pushed a smidgen off course by the coriolis effect.

    Still, his insurance company will be using that cheap new microsurgery operated by a guy called Dilip from a call-centre in Calcutta. Maybe the connection will get dropped.



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