[meteorite-list] How Many Meteorites Fall?

Kelly Webb kelly@bhil.com
Sat, 09 Dec 2000 16:24:28 -0600


Dear List,

   Thought this would be of some interest to Listees. The news is good,
I think. More meteorites may fall to earth than is generally assumed,
always good news for hunters.
   I know I can always count on critiques, corrections if needed,
additions, amendments, and quibbles. All are welcome.

Sterling K. Webb

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               A NOVEL MEASURE OF METEORITIC FLUX
                       By Sterling K. Webb

METHODOLOGY:
    Beyond general interest in the particulars of meteoritic impact,
there is good reason to catalog cases in which meteorites have struck
such things as people, cars, buildings or ships.  Such cases provide an
opportunity to directly measure the total number of meteorites that fall
to earth every year by the method of collisional cross sections.
    It works like this: if we know that some specific area amounts to
one-millionth of the earth's total area, and that target area gets hit
by a meteorite once a decade on average, then it is easy to calculate
that the earth must be hit by a million meteorites per decade, or
100,000 meteorites per year.
    The most important aspect of the cross section method is that it
does not matter whether the target area is a single contiguous block or
consists of billions of patches randomly scattered over the planet. In
fact, using a number of widely distributed targets is likely to produce
more accurate results, because it provides a better sampling procedure.
    Take as an example the cases of meteorites striking human beings. We
know the size of a single potential target, the average human being. We
know the total number of humans on the planet for most historic eras.
The product of the population number times the size of an individual
human being constitutes the collisional cross section of humanity.
Comparing the cross section (target size) of humanity to the area of the
entire planetary surface and the rate of how often people are struck
provides a method for deriving a number for how many meteorites per year
fall over the planet as a whole.
    This method can be applied to meteorite hits on any class of objects
for which we can calculate a total cross section and for which we have
data. Another advantage of this method is that each calculation on a
class of targets is independent of the calculations involving any other
class of targets, allowing us to compare a number of independent
measures of meteorite flux.

HOW MANY METEORITES FALL EACH YEAR?
    Many years ago, Nininger estimated that 500 meteorites ranging from
100 grams to 10 kilograms in mass fell on land each year (approximately
2000 for the entire Earth). More recently, Canada's Meteor Observation
and Recovery Project estimated 23,930 meteorites per year as the
worldwide fall rate. I shall use this rate as a basis for comparison to
establish an expected frequency for impacts on people, dogs, cars,
buildings, and ships.

DATA USED:
    A table of 141 reported cases of meteorite impacts on people, dogs,
cars, buildings and ships can be found at the end of the thirteenth
chapter of John S. Lewis, Rain of Iron and Ice, Addison-Wesley, 1996. I
have taken that table as an initial trial database for just such an
analysis.
    Some of the cases cited are familiar and widely quoted and others
are much more poorly known. Usually these cases are treated only in an
anecdotal manner or as vaguely indicative (as if to say, enough
meteorites fall that once upon a time a dog was killed, or a car struck,
by a meteorite, for example). They are not treated by Lewis as
quantitative data, but they have that potential use.
    To analyze this list of events in a quantitative manner is a
procedure that depends on the completeness of the data for the accuracy
of its results. It should be understood that in this situation any
incompleteness in the data (omissions of events) makes the calculated
flux lower than it really is, so any additions to the data would raise
the value of the meteoritic flux.
    There is no evidence that Lewis intended his list to be either
complete or all-inclusive. In addition, there are probably accounts that
have yet to be discovered, events that went unreported or whose
reporting was discouraged, and events in which the meteoritic
explanation was never considered.
    Thus, it is important to stress that this analytical technique
establishes only a minimum value and does not constrain the maximum
value of the variable in question, how many meteorites fall to earth per
year.

CROSS SECTIONS AND MEAN-TIME-TO-IMPACT:
    Taking the area of the Earth to be 5.1 x 10^8 km^2 and the
meteorite flux to be 23,930 yr^-1, this yields the assumed collisional
cross section of the earth to be 21,360 km^2 yr^-1. This rate means that
one meteorite per year falls on an area of 21,320 square kilometers. The
inverse function of this value is how long we have to wait for a
meteorite to fall on a standard area, or the mean time to impact: 21,360
yr km^-2. To put this flux into perspective, if you owned a house with a
half-acre yard, you would have to wait 10,552,000 years for a meteorite
to fall in your front or back yard or on your roof! (On average, that
is; it could happen tomorrow.)

TARGET CROSS SECTIONS:
    I have taken the collisional cross section of any target to
be its profile when viewed from a 45-degree elevation and from a
orientation of 45 degrees from its orthogonal axes, thus averaging all
the possible directions a meteorite could come from. In the case of
human beings, whether standing up or fully recumbent, this results in an
individual cross section of 0.4 m^2. The cross section of an automobile
is more than an order of magnitude greater: 6.25 m^2. (This value for
cars is self-compensatory for changes in the proportions of U.S. autos
from the 1920's to today by virtue of the fact that older vehicles are
taller but narrower and newer ones are lower but wider.)

IMPACTS ON HUMAN TARGETS:
    The total collisional cross section of humanity is:

DATE            CROSS SECTION     MEAN TIME TO IMPACT  (population)
                                   (@23,930 yr^-1)
====            =============     ===================  ============
in 1630 A.D.      200.0 km^2      mean time  106.9 yr  (half billion)
in 1830 A.D.      400.0 km^2      mean time   53.4 yr  (1 billion)
in 1930 A.D.      800.0 km^2      mean time   26.6 yr  (2 billion)
in 1960 A.D.     1200.0 km^2      mean time   17.8 yr  (3 billion)
in 2000 A.D.     2400.0 km^2      mean time    8.9 yr  (6 billion)

    The assumed flux of 23,930 meteorites per year would predict 1.1
human impacts for the fifty year span between 1825 to 1875, 1.25 impacts
for the fifty years 1875-1925, and 2.25 impacts for the 1925 to 1975
period.
    The actual data for human impacts is as follows:

PERIOD      CASES     DEATHS    INJURIES    TOTAL     % EXPECTATION
======      =====     ======    ========    =====     =============
1825-1875:  4 cases   2 deaths  3 injuries  5 total   364% by cases
1875-1925:  4 cases   9 deaths  1 injury   10 total   333% by cases
1925-1975:  5 cases   1 death  32 injuries 33 total* 1470% by persons
(* 28 injuries, no deaths, in one shower - 1946)

    As you can see, the incidence suggests a meteoritic flux is at least
three to four times greater than the assumed value, or 71,790 to 95,720
meteorites per year. That flux corresponds to a terrestrial cross
section of 5340 km^2 yr^-1 to 7120 km^2 yr^-1.

A RESERVATION:
    One problem of interpreting the human impact rate is the fact
that all human populations create structures with which they are closely
associated, spending 35% to 90% of their time under shelter. This causes
an overlap of the human target population with the structure target
population. This may confuse the results in this way.
    If a human being is inside a building which is struck by a meteorite
and the collapse of the building causes the death of the person but the
meteorite never actually touches the victim, is it fair to count that
death as being directly caused by meteoritic impact? (The cross section
method requires that each target population be considered separately.)
    One case in the 1825-1875 period and one case in the 1875-1925
period are just such cases. If they were to be eliminated from the
analysis, the implied meteoritic flux drops to around 52,000 to 65,000
meteorites per year. However, in both these cases, we do not know from
the source whether the victim was struck or not. There are many more
cases of persons untouched in a room struck by meteorites, however.
    In the one case of a combined building and person hit in the
1925-1975 period, the meteorite multiply perforated the building but
managed to strike (non fatally) the target human. So, it counts.
    In strictest terms, this method should be applied to the number of
persons physically contacted by meteorites. This would yield results of
5, 8, and 15 times the expected rate, 100,000 to 300,000 meteorites per
year. But, of course, we know that most of these cases of multiple
injury are caused by multiple objects in the same shower, fragments of
the same entering object, so it hardly seems "fair" to count each human
struck, although that is what the method demands.

IMPACTS ON BUILDINGS:
    Here is the raw data:
DATES          TOTAL HITS     MULTIPLE HITS (Year)
=====          ==========     ====================
1800-1849           9              2 (1803)
1850-1899           6                --
1900-1909           3                --
1910-1919           6                --
1920-1929           1                --
1930-1939           7              2,2 (1936, 1938)
1940-1949           3              2 (1949)
1950-1959           6              2 (1950)
1960-1969          10              2,4 (1961, 1969)
1970-1979           6              2,2 (1971, 1973)
1980-1989          11              2,2,3 (1988, 1989, 1984)

    I have found as yet no reliable way of estimating the structural
cross section of the world's buildings. The U.S.A. contains about 38,000
km^2 of human structures, but this density cannot be extrapolated to the
world as a whole. For that reason, I cannot apply the cross section
method to this data.
    The data shows a constant and slowly rising, but highly variable,
trend which suggests incomplete reporting and a lack of detection and
attention. The cause of the dip in the rate for the 1940's is easily
explained; at a time when Rotterdam was rendered to ashes and Dresden
was turned into the backside of the Moon, who would notice a smallish
meteorite impact?
    The population of meteorites is sorted according to a power law,
meaning that there many more small objects than large ones. Nearly all
of the building impact reports are fairly dramatic in nature,
suggesting that only the most substantial impactors are detected. The
actual impact rate for our population of meteorites may be 5 to 10 times
greater than these data show, but without a good estimate of the total
cross section of structures, it's impossible to say.

IMPACTS ON CARS:
Total collisional cross section of U.S. Automobiles (Vehicle data
from The Statistical Abstract of the United States, various years)

DATE          CROSS SECTION    Mean Time to Impact
====          =============    ===================
1940            260 km^2           82.2 yrs
1950            306 km^2           69.8 yrs
1960            386 km^2           55.3 yrs
1970            503 km^2           42.5 yrs
1980            654 km^2           32.7 yrs
1990            880 km^2           24.3 yrs
2000           1040 km^2           20.5 yrs

    The assumed flux of 23,930 meteorites per year would predict 1.65 to
1.75 impacts on U.S. automobiles in this past century. The actual rate
is four impacts: in 1938, 1950, 1977, and 1992.
    The data is less contaminated by the association of the targets
with human shelters (only one car was hit while in a garage). Further,
since Americans are quite sensitive to and observant of damage to their
cars, the chances of under-reporting is less than with buildings. I
believe this to be the "cleanest" set of data.
    The data for U.S. automobiles is 250% of expectation, again
suggesting a flux of 59,825 meteorites per year, or a terrestrial
collisional cross section of 8528 km^2 yr^-1.
    In all these cases, the impactor was in excess of 1 kilogram.
This suggests, again, that smaller impactors may have been unreported. A
slow moving 100 gram stone that whanged into an eighteen wheeler
barreling down the interstate might provoke no response greater than
"dam kids!" (while a fast moving 10 kilogram stone would certainly
produce more spectacular results).

IMPACTS ON SHIPS:
    There are a fair number of reports of ships hit, sailors killed,
and marine near misses. It is impossible to easily produce a cross
section for a target population that ranges in size from modern
super-tankers hundreds of meters long to dories and skiffs two meters
long, particularly over historic periods. The fact that there are any
marine reports is suggestive but not quantifiable without a reliable
cross section measurement.
    One might consider the case of a medium sized modern ocean-going
vessel of 100 meters in length with a 20 meter beam (and equal height),
displacing about 15,000 tons. At a fall rate of 23,930 meteorites per
year, a fleet of 7000 such vessels could expect to cruise the seas of
the world nonstop from the time of the ancient Greeks until today before
accumulating a 50-50 chance of a single meteorite impact!
    Contrast that rate with the occurrence of two impacts on ships
within 18 months (in 1936-38) or the impact of two substantial fireballs
in Fortune Bay, Newfoundland, within one month's time. I could calculate
how far off expectation that is, but I don't think my calculator has
that many zero's.

IN-JOKE:
    I have not been able to calculate a collisional cross section for
the dog population of the planet.

CONCLUSIONS:
    This analysis suggests that the actual meteoritic flux is much
greater than what is currently assumed (23,930 meteorites per year). The
data implies a better fit with a meteoritic flux of 60,000 to 100,000
meteorites per year at a minimum.

DATA RELIABILITY:
    There is, and always will be, reservations about the accuracy or
authenticity of historical reporting of events attributed to
meteoritic activity, but it worth noting that to reduce the flux
implied by these reports to a value of 23,930 meteorites per year
would require throwing out half to two thirds of the data, which I would
regard as unreasonable.
    There is a rough similarity between the results of the analyses of
the data for human impacts worldwide and the more restricted set of data
on impacts on U.S. automobiles in that the estimated fall rates from the
two sets of data overlap. Since the two calculations are not dependent,
it would seem unlikely that this correlation is fortuitous.
    That the data is potentially incomplete implies that the true
meteoritic flux may well be higher than the minimum that this analysis
suggests.

POSTSCRIPT: ADDITIONAL DATA?
    As always, more data is needed. Additional cases represent a more
comprehensive data set, and each would substantially increase the
calculated rate of fall. Obviously, every potential case for inclusion
in the data could (and would) be disputed by some and accepted by
others. What is required to reach a level of acceptable reliability?
    So, I have restricted my analysis here to a data set compiled by
someone other than myself and previously published (i.e., Lewis), so as
to avoid the possibility of biasing the results by adding to the data
incidents not all vetted by the same source, but there are other
reports.
    I have been able to find newspaper accounts of a car struck on May
10, 1961, in Minnesota, and a number of impact injury cases, none of
which are included in Lewis' list.
    The best of these human impact cases took place on November 6, 1951,
in Bremerton, Washington; a man's arm was seriously injured (burned) in
his hotel room by an impacting object which set portions of the room
afire. The incident was witnessed from across the street by a policeman
(who was writing a parking ticket at the time); he saw a fiery streak
cross the sky, streak into the hotel room window, and explode. You could
hardly ask for a better documented case: a cop as a witness to the fall,
a verified fire investigation report, and a medical treatment report
from the hospital at the Navy shipyard where the victim was treated.
Yet, in this case, a meteoritic explanation seems never to have been
suggested at any time, presumably because the impactor was never found
(or recognized). However, there are undoubtedly those for whom the
absence of the rock would make the report unreliable (or at least,
indeterminate).
    How many more cases are there?



Copyright 2000
Sterling K. Webb
(kelly@bhil.com)
November 30, 2000


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    NOTE: Thanks and kudos to E. L. Jones for a great piece of work
investigating a recent purported meteorite strike on an automobile and
saving me from re-calculating a whole section! Still, the odds favor
another car hit in the next couple of decades.
    NOTE2: Uses of the technique. Example: Wyoming, with over 250,000
km^2, should get hit with between 12 and 40 meteorites per year,
depending on the flux you assume. They're out there, Dave! If the fall
rate was 30 per year for Wyoming, then since the ice went away 10,000
years ago, there would have been 300,000 falls, or about 1 per square km
(247 acres). 247 acres is a front yard in Wyoming, isn't it?
    NOTE3: If you want to reply or respond to this post, save
wear'n'tear on the servers. Don't append this entire text, just type in
the subject line "Re: How Many Meteorites Fall?" to your message.