[meteorite-list] Terminal velocity of small falling objects
From: James_TOM Knudson <peregrineflier_at_meteoritecentral.com>
Date: Thu Apr 22 10:08:25 2004 Message-ID: <F71Bs6Oz44RPHInQUtj0000900e_at_hotmail.com> <html><div style='background-color:'><DIV> <P><BR><BR></P> <DIV> <DIV></DIV> <P><BR><BR></P></DIV> <DIV></DIV> <DIV></DIV></DIV> <P>Hello, I don't know if this post is in regards to the post I posted about the girl getting hit by the meteorite, but it sure sounds like it. I do not think a small meteorite would necessarily hurt a person! The hole weight X velocity thing! She stated that she noticed the falling meteorite at about roof level. I know the velocity of a small falling rock from "miles up" has to be to fast for some one to "notice" it falling from roof level! It sounds to me that she noticed it at the top of its apogee, about roof level after it was thrown at her! You through a small rock at least 120mph and try to see it! I don't agree with your terminal velocity thing ether : ) A 16 lb bowling ball might reach terminal velocity and stay at that speed, But, a 2 lb female Peregrine Falcon will reach terminal velocity with out flapping and then keep accelerating as long as it's aerodynamics' allow some where over 200mph. <BR>Thanks, Tom</P> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>From: "Piper R.W. Hollier" <PIPER_at_XS4ALL.NL> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>To: meteorite-list_at_meteoritecentral.com <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>Subject: [meteorite-list] Terminal velocity of small falling objects <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>Date: Sat, 14 Sep 2002 21:59:45 +0200 <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>Hello Tom, Tom, Shaun, Dave, Ron, and list, <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>> As I said before, simple ballistics made it impossible, the girls foot would <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>> have been damaged and in need of a hospital. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>Ron, I DON'T agree with this statement made by an unnamed contributor, nor with several other similar statements. My disagreement is based not on "simple" ballistics, but on "mathematical" ballistics, that is, taking known formulas and plugging in reasonable input values and seeing what comes out. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>I will make an amateur attempt here to contribute something about the physics of small meteorite falls. Like many other phenomena where most humans have little or no first-hand experience, some people may develop intuitive notions about the subject which are rather inconsistent with the laws of physics. The sensationalist bent of the media doesn't help much. I am a firm believer in "doing the math". Calculations based on known formulae are arguably not as good as making experimental measurements, but are still considerably better than seat-of-the-pants guesswork. Somebody please correct me if my logic or my math are off track in the following analysis. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>An object dropped and allowed to fall through the lower atmosphere does not continue to accelerate indefinitely. There will instead be an upper boundary on the velocity at which it falls, called the "terminal velocity". At the terminal velocity, the downward force cause by gravitational attraction between the object and the earth (the "weight" of the object) is exactly balanced by the upward force of the aerodynamic drag of the object's passage through the atmosphere. When these two forces are in balance there will be no further acceleration and the object will maintain an essentially constant downward velocity. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>For a sky diver the terminal velocity is about 53 meters per second, or 120 mph. There is only significant acceleration during the first 10 seconds or so of fall. After that, the onrushing air pushes the person up just as hard as the earth pulls him or her down, and the fall velocity levels off. Animals smaller than sky divers have a lower terminal velocity -- in the case of small insects it can be much less than 1 mph. This is part of the reason why bugs, lizards, tree frogs, and even small mammals can fall out of tall trees, hit the ground, and usually simply walk away unharmed, while a human would be seriously injured by a fall from the same height. Terminal velocity is also the reason that a small meteorite can fall "for miles", hit a person, animal, car, or building and do little or no damage. Small meteorites will in most cases have lost all of their cosmic velocity at a considerable distance above the ground, and the fall velocity upon reaching the ground is the aerodynamic terminal velocit y. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>How small does a meteorite need to be to not be dangerous? <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>The magnitude of the terminal velocity depends on a number of things: <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>1. The density and viscosity of air. The exact values of these at sea level depend on barometric pressure, temperature, and humidity, but for the purposes of rough calculations can be assumed to be about 1.222 kg per cubic meter density and 1.73 x 10^-5 newton-seconds per square meter viscosity on a typical pleasant afternoon in Northallerton. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>2. The density of the falling object. This is typically 3.25 to 3.90 grams per cubic centimeter for ordinary chondrites and about 8 grams per cubic centimeter for irons. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>3. The size of the falling object. Use a ruler or make an estimate from a photo. The meteorite in the Northallerton photo looks like it is about one inch (2.5 cm) in diameter. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>4. The shape of the falling object. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>5. The rigidity of the falling object. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>If one makes the simplifying assumptions that the object is spherical and rigid, the calculation of terminal velocity is rather straightforward. These are not unreasonable approximations when making rough calculations for falling meteorites. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>There is a convenient web page where one can simply plug in the relevant values and have a computer do the calculation: <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>http://www.processassociates.com/process/separate/termvel.htm <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>If we assume a small meteorite with a typical chondritic density of 3.65 grams per cubic centimeter and a diameter of 2.5 cm (roughly one inch), we come up with a terminal velocity of about 46.8 meters per second, or roughly 105 mph. This meteorite would weigh about 29.8 grams, or roughly one ounce. The question of how much damage a hard one-ounce object traveling at 105 mph might do upon striking a human being is left to the reader's own judgment and intuition. Personally I think it would hurt a lot but would not necessarily require a trip to the emergency room, much less the morgue. This is far from a "speeding bullet" velocity. It is not a lot faster than a fast ball pitch and the object is a lot lighter than a baseball -- batters routinely survive getting hit with a fast ball. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>An iron meteorite of the same diameter with a density of 7.9 grams per cubic centimeter would weigh about 65 grams, or about 2.3 ounces. The terminal velocity would be about 69 meters per second, or roughly 155 mph. I would not want to be in the way, but getting hit by even this falling object would probably cause a lot less damage than a gunshot at close range. Short of a hit on the top of the head, this is probably a survivable encounter in most cases. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>Somewhat counter-intuitively, it doesn't really matter whether these meteorites had been falling through the air "from miles up" or only a few hundred meters. Once the velocity approaches terminal velocity, which happens in just a few seconds for small objects, there is no significant further acceleration. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>The 3 gram chondrite fragment which hit the boy at Mbale would have been falling at approximately 33 meters per second, or about 73 mph. Once again, I think it would have been painful if it had hit him directly, but accounts stating that his life was saved because the meteorite was slowed down by hitting a tree before striking him seem sensationalistic to me. Falling stones that weigh only three grams are just not a big danger, regardless of what height they fall from. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>The Sylacauga, Alabama stone which fell through a house in 1954, hitting a woman and severely bruising her, weighed a very substantial 3.9 kg (8.6 pounds). This is another situation entirely compared to small stones weighing an ounce or less. Calculation of the fall velocity is left as an exercise for the reader. If several layers of house construction hadn't slowed the rock down, she would almost certainly have qualified for a very unique epitaph on her gravestone. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>Best wishes to all, <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>Piper <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>PS -- BTW, I don't doubt in the least that it is dangerous, irresponsible, and idiotic to amuse oneself by shooting a gun into the air in populated areas. <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>______________________________________________ <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>Meteorite-list mailing list <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>Meteorite-list_at_meteoritecentral.com <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV>http://www.pairlist.net/mailman/listinfo/meteorite-list <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV> <DIV></DIV></div><br clear=all><hr>Join the world’s largest e-mail service with MSN Hotmail. <a href='http://g.msn.com/1HM1ENUS/c157??PI=44364'>Click Here</a><br></html> Received on Sat 14 Sep 2002 07:16:34 PM PDT |
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