| Update from Bob Warren on pi and
e
Note: This letter originally appeared in "Backscatter"
on 21 April 2006. However, the formatting of e
pi/4 in three equations was lost when the
letter was saved as a text file rather than an HTML file.
I apologize to Bob Warren for this error. Editor.
Editor,
I'm pleased to see that you included my pi and e article
in the 24 March 2006 issue of The Citizen Scientist
(Expressions
Containing pi and e That Have Numerical Values Very Close
to Rational Numbers).
I discovered one expression that was in my opinion not quite
good enough (didn't have enough consecutive zeros in its value)
to be included in my paper. It is the following expression:
Sin(e rad.) + Cos(e rad.) = - 0.500952624284056402417707825787432…
With a little bit of doctoring up (by adding – ½),
the value of the expression has an extra consecutive 0, and
is, thus, on the border line of acceptability for inclusion
in my paper. The fact that the value of this expression comes
so close to – 1, in addition to the number of consecutive
zeros, makes it interesting.
Sin(e rad.) + Cos(e rad.) - 1/2 = -1.000952624284056402417707825787…
I think that I will put this in a revised version of my paper,
to be published sometime in the future.
Expression number 6 in my paper was originally discovered
in the following form:
e pi/4 + sin (pi/4) + cos (pi/4)
= 3.6074936131111105053614583834877…
Multiplying the expression by 9 made it acceptable for inclusion
in my paper.
9[e pi/4 + sin (pi/4) + cos (pi/4)] = 32.467442517999994548253125451383…
If I had added 8/9 to the expression, instead of multiplying
by 9, I would have produced the following expression, which
has an extra consecutive 9 in the decimal part of its value:
e pi/4 + sin (pi/4) + cos (pi/4) + 8/9 = 4.49638250199999939425034727237589...
This expression will also be put in a revised version of my
paper.
Bob Warren
Contrails and Weather
Editor,
Have you had a chance to see the recent NOVA special "Dimming
the Sun"?
There is a climatologist from the University of Wisconsin
named David Travis who took the opportunity to study the effect
of contrails on weather. On and after 9/11 all air traffic
was grounded (except for a few military jets), and David Travis
made some sunlight measurement and determined that contrails
had a significant effect.
Did you make any measurements on 9/11 or on the following
days when air traffic was grounded? I would be interested
if you found higher than normal amounts of sunlight reaching
the ground.
I thought that the combination of contrails and sunlight study
would doubly interest you!
The NOVA episode also started me thinking about charge in
clouds. As pollen and other small particles become aerosolized,
they gain a charge, this charge could very well be transferred
to raindrops in clouds. There was a great project done by
the Army several years ago, where they used honey bees as
biological weapons detectors. As the bees fly through the
air, they gain a charge and attract airborne material. The
hive was set up to "dust off" the bees when they
returned sp the aerosolized material could be analyzed.
Sincerely,
Mike Dziekan
Vice President, Engineering
Connecticut Analytical Corporation
www.ctanalytical.com
NOVA's global dimming program was well done and certainly
attracted considerable attention within the atmospheric science
community. David Travis's post-911 contrail study is very
important. He and I co-authored a short paper about sunlight
reduced by contrails based on sun and sky measurements I made
in Lausanne, Switzerland, while teaching a course on hands-on
science at the University of the Nations (F. M. Mims III,
and D. J. Travis, Aircraft Contrails Reduce Solar Irradiance,
EOS 78, 448-449, 1997).
Here is the optical depth I measured at 630 nm (red light)
at local noon on the days before and after 9/11. The measurements
were made from the field I call Geronimo
Creek Observatory in South Texas (low values indicate
cleaner skies):
05-Sep-01--0.13
06-Sep-01--0.10
07-Sep-01--0.07
08-Sep-01--0.12
09-Sep-01--(no data)
10-Sep-01--(no data)
11-Sep-01--0.08
12-Sep-01--0.12
13-Sep-01--0.21
14-Sep-01--0.22
15-Sep-01--0.28
16-Sep-01--(mo data)
17-Sep-01--0.43
18-Sep-01--0.06
19-Sep-01--0.09
20-Sep-01--0.08
21-Sep-01--0.03
While the optical depth on 11 September suggests a possible
9/11 effect, it probably is not, for on-site fisheye photographs
made of the entire sky on 11-13 September show only cumulus
clouds and no cirrus, which are usually present at this site
when contrails occur. There is a large switch of cirrus at
the zenith on 14 September. This demonstrates the value of
coupling optical depth measurements with sky photographs.
These data have not yet been corrected for the effect
of ozone absorption at 630 nm, but the ozone was fairly consistent
on these days and the corrections will not cause significant
differences in the data. Editor.
Twisted Contrails
Editor,
Twisted contrails are not particularly uncommon, though
many people have not seen them. They are caused by merging
of the contrail cloud (ice crystals) and the wing tip vortex
flows. The vortex flows are always created off of wingtips
of aircraft in motion. They are much increased during high
angle of attack operations.
These occur most often during takeoff and landing, and, interestingly,
also during cruise at high altitudes. These vortexes can be
as long as several miles, and they continuously expand. So
it is not hard to see how they could entrain the ice crystals
that are in the contrail flow from the engines.
Vortex flows are sometimes very strong. Several accidents
have occurred when small aircraft were upset and crashed when
they followed too closely behind large heavy aircraft on landing
approach.
Jim Norris
Interwoof
Model Rocketry Court Decision
Editor,
It is good to see a bit of common sense has prevailed in
the court decision on model rocket motors ("Major
Court Victory for Model and Amateur Rocketry," The
Citizen Scientist, 24 March 2006). A lot of people, especially
many in Government seem to have a very limited view hen it
comes to things that "explode", but are quite at
ease with extremely dangerous everyday products. I would suggest,
the next time such a situation occurs, take a group of reporters
to a large open space. At one end, throw a few handfuls of
disposable cigarette lighters, pressure spray cans of hair
spray and anything else that comes to hand, into a 200 litre
drum, slosh a good deal of petrol (at least 10 litres) over
and around it and, from a safe distance, light it. While that
is cooking, take the reporters to the other end and set off
a few "dangerous" model rockets. It would make great
TV.
Andrew Castrique
Andrew, these very concerns often cross my mind while
waiting in line at airport security check points. But if I
were to voice them out loud, guess who would be challenged
by the authorities? Editor.
Rocket Decision Brings Back Bob Warren's Boyhood
Memories of Artist Chet Jezierski
Editor,
I was interested to see your article in the 24 March 2006
issue of The Citizen Scientist about the legal
victory for amateur rocketry. Back in the late 1950s,
I built an amateur rocket, but my parents refused to let me
load it with solid fuel. (“Too dangerous!” they
said.)
I gave the rocket to my high school friend, Chet Jezierski,
who may still have it. Chet has become a famous artist, and
he has done a lot of paintings with rocketry as the theme.
Some of them can be found here.
You will need to scroll down the page a little to see his
paintings.
Chet is an extremely prolific artist. Some of his paintings
on other themes can be found here.
Chet was the youngest and probably the brightest member of
an astronomy club that I organized in high school. He was
the most precocious young man that I have ever known. He joined
my astronomy club when he was ten and seemed so mature that
some people thought he was an adult midget. All the rest of
the members of the club were in their middle teens, yet he
was the approximate intellectual equal of the best of us.
I remember that his youthful eyes were so keen, that he
could spot double stars with his unaided eyes. The rest of
us needed binoculars to see that these stars were double.
Bob Warren
Letters to "Backscatter"
are welcome. Important: It's very important
to use a meaningful subject line! E-mails with subject lines
that read, "Hi," "Hello," "Question,"
"A comment," and so forth are routinely deleted
as spam or junk mail. Please include both your first and last
name and the author and full title of any article(s) from
THE CITIZEN SCIENTIST cited
in your letter. We'll add
the hyperlink. Letters are subject to light editing to correct
punctuation, spelling and grammar. By placing "Backscatter"
in the subject line, you give us permission to consider publishing
your letter. Send your letter to Backscatter.
|
