[meteorite-list] Terminal velocity of small falling objects

From: Mark Miconi <mam602_at_meteoritecentral.com>
Date: Thu Apr 22 10:08:26 2004
Message-ID: <002801c25cd0$03004ee0$54b60344_at_ph.cox.net>

By the way...I was the poster that said simple ballastics and that comes
from many years of competing in rifle and handgun events. Your math did not
take into consideration or show the "Foot Pounds" of energy that the object
would retain. At 200 meters through a pair of 7 power binoculars it is
possible to see a 240 grain 44 caliber pistol bullet fly in to and strike a
mettalic ram target. The target weighs on the order of 30-40 pounds and the
bullet will knock it over if hit properly.

Here in Phoenix that young girl that was killed by a 240gr 44 caliber slug
was a couple of miles from the shooter. In court the experts deduced that
the bullet was fired at near vertical into the air, it reached apogee and
began its decent. Even though it was tumbling and had reached whatever
terminal velocity you wish to calculate for it, it retained enough foot
pounds of energy to penetrate her skin, skull and brain with enough retained
energy that when it stopped and that energy was dissipated in her brain it
killed her instantly in mid conversation with her best friend on the phone.
In her memory we named the law...."Megans Law" for her and it is now a
felony with a mandatory sentence for anyone convicted of discharging a
weapon into the air.

I stand by my statement as do others on this list that even a piece of
meteorite travelling at the speeds you calculated would do enough physical
damage to warrant a visit to a doctor, if not a hospital, expecially for a
young child.

Mark Miconi
Phoenix AZ
----- Original Message -----
From: Piper R.W. Hollier <piper_at_xs4all.nl>
To: <meteorite-list_at_meteoritecentral.com>
Sent: Saturday, September 14, 2002 12:59 PM
Subject: [meteorite-list] Terminal velocity of small falling objects


> Hello Tom, Tom, Shaun, Dave, Ron, and list,
>
> > As I said before, simple ballistics made it impossible, the girls foot
would
> > have been damaged and in need of a hospital.
>
> 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.
>
> 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.
>
> 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.
>
> 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 velocity.
>
> How small does a meteorite need to be to not be dangerous?
>
> The magnitude of the terminal velocity depends on a number of things:
>
> 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.
>
> 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.
>
> 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.
>
> 4. The shape of the falling object.
>
> 5. The rigidity of the falling object.
>
> 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.
>
> There is a convenient web page where one can simply plug in the relevant
> values and have a computer do the calculation:
>
> http://www.processassociates.com/process/separate/termvel.htm
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> 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.
>
> Best wishes to all,
>
> Piper
>
> 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.
>
>
>
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Received on Sun 15 Sep 2002 11:53:18 AM PDT