From: David Rudiak <DRudiak@earthlink.net>
Date: Wed, 30 Jul 2003 00:09:09 -0700
Fwd Date: Wed, 30 Jul 2003 09:28:45 -0400
Subject: Math vs. Moore & Debunking Hypocrisy 01 - Rudiak


>From: Dave Thomas <nmsrdave@swcp.com>
>Date: Thu, 17 Jul 2003 18:44:23 -0600
>Fwd Date: Fri, 18 Jul 2003 14:17:08 -0400
>Subject: Re: Investigator's Right & Debunking Hypocrisy -

>>[Non-Subscriber Post]

>>From: David Rudiak <DRudiak@earthlink.net
>>To: <ufoupdates@virtuallystrange.net
>>Date: Fri, 11 Jul 2003 09:19:25 -0700
>>Subject: Investigator's Right & Debunking Hypocrisy

List,

I have changed the name of the thread to "Math vs. Moore &
Debunking Hypocrisy," which is a more apt description of the
topics.  This whole debate about Charles Moore's Mogul balloon
trajectory hoax dates back to a series of debates I originally
had here on UpDates with debunker Tim Printy from October to
November 2002 in the threads "Math vs. Moore" and "Mogul Mangled
Math."  For a list of posts see:

http://www.google.com/custom?hl=en&lr=&ie=ISO-8859-1&cof=AWFID%3A0c3ec42176cbf84b%3BL%3Ahttp%3A%2F%2Fwww.virtuallystrange.net%2Fimages%2Fvsnsrch1.gif%3BLH%3A150%3BLW%3A137%3BGL%3A2%3BBGC%3A%23000000%3BT%3A%23ffffff%3BLC%3A%23ffffff%3BVLC%3A%23ffffff%3BALC%3A%23ffffff%3BGALT%3A%23ffffff%3BGFNT%3A%23ffffff%3BGIMP%3A%23ffffff%3BAH%3Acenter%3B&domains=virtuallystrange.net&q=%22Math+vs.+Moore%22&btnG=Google+Search&sitesearch=virtuallystrange.net

and

http://www.google.com/custom?hl=en&lr=&ie=ISO-8859-1&cof=AWFID%3A0c3ec42176cbf84b%3BL%3Ahttp%3A%2F%2Fwww.virtuallystrange.net%2Fimages%2Fvsnsrch1.gif%3BLH%3A150%3BLW%3A137%3BGL%3A2%3BBGC%3A%23000000%3BT%3A%23ffffff%3BLC%3A%23ffffff%3BVLC%3A%23ffffff%3BALC%3A%23ffffff%3BGALT%3A%23ffffff%3BGFNT%3A%23ffffff%3BGIMP%3A%23ffffff%3BAH%3Acenter%3B&domains=virtuallystrange.net&q=%22Mogul+Mangled++Math%22&btnG=Google+Search&sitesearch=virtuallystrange.net

I apologize for the great length of this reply, which I have
divided into two parts.  There are many critical points to be
covered that Dave Thomas refuses to acknowledge even exist,
except to disparage them as "quibbles," "shrill accusations,"
and "character assassination."  To help you wade through it, I
have inserted capitalized section headers.

PART I

>>I recently became aware of the article and am drafting a letter
>>of response to the Inquirer right now. Thomas did exactly the
>>same thing as Printy, claiming that since he could reproduce
>>Moore's (bogus) calculation, Moore was right and I was
>>mathematically "incompetent." The problem was, Moore's
>>calculation was full of "mistakes" and the mathematical
>>equivalent of 2 + 2 = 3. All the fatal math mistakes were
>>pointed out on my website, but Thomas, naturally, doesn't
>>mention a single one of them, calling them only "quibbles" and
>>"shrill accusations."

Thomas came out of the shadows to respond to my statement above,
but do notice that he continues to avoid discussing Moore's many
math mistakes.  Again, all he does is reproduce Moore's _faulty_
table calculation and claim that both Moore and he are right.

>I have reviewed Rudiak's website again,

For reader reference:

http://www.roswellproof.com/Flight4_trajectory.html

If he's read and reviewed it "again," why does he continue to
avoid the key issues that were raised there?  He can't pretend
he isn't aware of them.

Maybe Thomas should have read it _carefully_ the first time
around before he wrote his highly dishonest attack piece in the
March/April 2003 Skeptical Inquirer. Thomas claims he is a
working physicist and mathematician, but you would never know it
from his S.I. article.  What sort of "scientific" argumentation
is it to misrepresent or completely ignore your opponent's key
arguments?

Had he actually bothered to study my arguments, graphs, and
tables he might have learned something.  Instead he has yet to
address my many points proving Moore wrong and he tried to make
light of my website by talking only of its "mindnumbing" length.
 This New Mexico debunker "scientist" apparently doesn't like to
be bothered with such annoying things like facts and detailed
arguments.  Has he ever read an actual science paper?

Avoiding the real issues -- Moore's big math mistakes

> and my own copy of the
>math calculations for Charles Moore's trajectory calculation,
>and have come to this conclusion:

Thomas will bury you with the details of his spreadsheet
calculation below.  But all it amounts to is repeating Moore's
_wrong_ calculation, while asserting it is right.

What Thomas never addresses, either here or in his Skeptical
Inquirer article, is the many arguments _proving_ the
calculation to be incorrect mathematically.   He avoids these
like the plague.  Thomas would rather deceive the reader into
believing that Moore made zero mistakes.

>David Rudiak has disagreements with C. B. Moore over how to
>model the Flight #4 trajectory.

Dave Thomas immediately starts out with spin rather than facts.
 The "disagreement" is NOT over how to model the trajectory.  It
is about bad math and science.  Specifically Moore did the
following:

Moore violated his own assumptions

1.  Moore violated his own assumptions in setting up his table.  Moore stated he was assuming "Flight #4 used our best equipment" and was configured like and "performed as well as or better than" the successful Flight #5 the next day.  But in his table he treated the balloon like it had faulty altitude control equipment and had it rising and falling much too fast.

Moore's balloon falls much too fast, shortening the descent

A.  On descent it fell almost twice as fast as Flight #5 and
even faster than Flight #6, which did have damaged altitude
control equipment.  This drastically shortened his model #4's
descent trajectory.  Otherwise the balloons would have overshot
the Foster ranch when coming down by nearly 40 miles, even
assuming Moore had done everything else properly before this.
 Does Thomas dispute this?

Moore's balloon rises too fast, shortening the ascent

B.  On ascent, Moore eliminated lifter balloon cutoff present on
Flight #5, making #4 rise much too rapidly through the upper
atmosphere where his winds were blowing at gale and hurricane
force.  This foreshortened the ascent trajectory by over 20
miles.  Does Thomas dispute this?

Improper calculation of his own table

2.  Moore (and Thomas and Tim Printy) used a mathematically
incorrect "push-back" method of calculating the final
trajectory.  Wind values from one data point were carried back
through to the previous data point.  There were five reasons
listed on my website why this was mathematically wrong, three of
them being absolutely fatal.  It destroyed the symmetry in winds
Moore had built into his table and the various correspondences
between Flight #4 and Flight #5.  Winds on balloon rise now no
longer matched those on balloon fall.  The balloon train now
turned at drastically different altitudes on rise and fall
instead of the same altitude.  Likewise #4 now turned at a
different altitude than Flight #5.  Moore's stratospheric winds
on rise, modeled directly after Flight #5, were used in the
_opposite_ direction from how Moore originally calculated them
in another table for #5.  And Moore threw out his first data
point.  Does Thomas dispute this?

Moore's used rise/fall rates don't match his listed rates

3.  Moore's listed rise and fall rates disagree with calculated
ones (based simply on dividing change in altitude by elapsed
time) in 40 out of 41 cases!  If you throw out minor
differences, about half disagree by 5% or more.  About a quarter
disagree by 40% or more! In the most serious example when Moore
"slammed on the brakes" in his balloon's ascent (at 52,000'),
his table lists the rise rate at 350 ft/min.  But Moore has the
balloon rising only 100 feet over the next 12 minutes.  That's a
rise rate of only about 8 ft/min, a factor of 40 error!  Does
Thomas dispute this?

Many more very serious errors occur on the fall side.  E.g.,
Moore's table lists his balloon falling at 900 ft/sec all the
way from 29,500 feet to the ground.  But his two last fall rates
when calculated are actually 1490 and 1550 feet/min, or
differences of 66% and 84% from his claimed rate.

This is real simple math folks, yet Moore couldn't even do this
right.  These are not "disagreements" over proper modeling.
 This is just flat-out, crappy, wrong math!  It also has serious
consequences for the trajectory.

Thomas can try to deceive the Skeptical Inquirer audience that
these are nothing but "quibbles" and "shrill accusations," but
the math doesn't lie.

2 + 2 does not equal 3, and 100/12 does not equal 350, no matter
how much Thomas wants to spin it.  That is why Thomas refuses to
discuss the real math points, as does Moore, because the math
simply cannot be defended.  All that's left for Thomas is
propaganda and his own "shrill accusations" that this is nothing
more than "character assassination."

Some more Thomas propaganda:  2 + 2 = 3 is not a mistake; it's a
"disagreement"

>Some of these disagreements
>might even have some merit - say, using the same wind speed for
>a given altitude interval on the way up as on the way down.

Again the spin word "disagreements."  No it's not
"disagreements" -- it's Moore's provably wrong math.  Saying
that what I say "might even have some merit" is also Thomas'
evasive way of saying that I'm dead right.  He just doesn't have
he integrity to admit it.  I'll have more to say on this later
when I discuss how Moore's calculation destroyed the agreement
in his table wind values on the way up vs. on the way down.

>However, all of these disagreements amount to simply "Well, if
>I was modeling this trajectory, I would have used THIS
>approach, and THESE assumptions."

More spin.  What it _really_ amounts to is that Moore should
have stuck to his stated assumptions of best equipment, perfect
flight, etc., instead of changing his table numbers to make it
into a faulty balloon on the way up and down so that he could
drastically shorten these trajectories and prevent overshoot.

Just pretend that no evidence of fraud exists

>However, I can find NO justification whatsoever for Rudiak's
>persistent accusations of fraud and hoaxing against Dr. Moore

"No justification whatsoever?"  What is it about the words
"fraud" and "hoax" that Thomas doesn't understand?  When you say
you are doing one thing and then do something else entirely how
is this not fraudulent?  When your table says you are using one
set of rise and fall rates, but you use a completely different
set, how is this not fraudulent?  When you calculate your own
table improperly and corrupt your own data in the process, how
is this not fraudulent?

Now here's the important point.  Unless Moore does every last
one of these things he can't get his balloon "exactly" to the
Foster Ranch (as he boasted in a 1997 Sci Fi special on
Roswell).  Yet they are all wrong!

Either Moore is guilty of gross incompetence, or he is guilty of
a hoax.  There are no two ways about it.  Thomas can continue to
lie about this being nothing more than a difference of opinion
about approaches and assumptions, but that's not what it is at
all.  Nobody of Moore's stature can make this many "mistakes" by
accident, every last one of them designed to get his balloon
"exactly" to where he wants it.  His "incompetence" is very
selective.

The usual, pointless appeal to authority

>(Moore received an honorary doctorate from New Mexico Tech
>earlier this year).

Gee, do they know that Moore calculated a 100 foot rise in 12
minutes and got 350 ft/min?

>Instead, the "Fuzzy Math" Rudiak complains
>about stems from Rudiak's approach to how HE (Rudiak) would have
>done the calculations, and NOT what Moore published or said he
>did.

My "Fuzzy Math" "approach" would be to divide 100 feet by 12 to
get 8.3 ft/min, which is indeed quite different than "what Moore
published."  Am I going too fast for you?  Maybe you can explain
to us what Moore "said he did" to get 350 ft/min when he
divides, because most of the "UFO believers" are a bit confused
here.  Is it some sort of honorary PhD math Moore is using?

Thomas reproduces Moore's 2 + 2 = 3, so what's the problem?

>Using Moore's own data, and following the directions in his
>table, I was able to easily reproduce Moore's chart.

Giggle.  This is Thomas reproducing Moore's 2 + 2 = 3
calculation of his trajectory.  The question is not whether it
is possible to "easily reproduce" how Moore got 2 + 2 = 3.  It's
whether this is correct or not.   Notice again he never once
addresses my mathematical objections to it being wrong.  That
would be too scientific, not to mention honest, of him.

>I did not
>have to "push back 5 points" as Rudiak claims. I did not have
>to "push back all data points" as Rudiak claims.

That is _exactly_ what Thomas has done, just like Moore did.
 Tim Printy also did this, but unlike Thomas at least he
acknowledged he was carrying back the data to reproduce Moore's
calculation.  Either Thomas is too math incompetent to realize
that he has done this or he is trying to conceal the fact for
some obscure reason.  I detail below why this is completely
wrong.

> I simply typed in the givens,

He typed in the given wind data, and then carried the values
from one elapsed time _back_ to the previous elapsed time clear
through the entire table.  Then he denies pushing back the data.
 I'll point out below exactly where this happens when he details
his spreadsheet calculation.

>applied Moore's stated formulas, and plotted the
>trajectory, which agreed extremely well with Moore's own
>calculations.

Moore calculated it wrong.  Thomas calculates it wrong in the
same way.  Of course they "agree extremely well."  Duhhh!

>I've included a chart of same on my web page about Rudiak and
>the Sci Fi Channel's "Roswell- Smoking Gun" show; this is at:

Actually Tim Printy did the same thing first on his web page,
and like Thomas accused me of incompetence.  Also like Thomas,
Printy was clueless that this was mathematically incorrect for
multiple reasons, all of which I already detailed on my website,
had Thomas bothered to read it carefully.

Thomas' Skeptical Inquirer article:
>http://www.nmsr.org/sf-gun.htm

IF I USE A LOT OF NUMBERS, MAYBE THEY WON'T NOTICE I'M DUCKING THE BIG ISSUES

>Here's an example from my calculation:
>The 15th line of Moore's table (reproduced on Rudiak's site >here:

> http://roswellproof.homestead.com/Flight4_Table5.html

Here's where Thomas starts to bury you in trivia, instead of
dealing with the key mathematical arguments outlined above.
 Again, all you need to remember in slogging through his
spreadsheet reproduction is that he simply reproducing Moore's
_wrong_ push-back method of calculation without dealing with a
single one of my arguments proving it to be wrong.

Even many of Moore's "givens" are wrong

>The first 5 entries are givens - assumed values developed by
>Moore in his analysis.

Thomas has already made a serious mistake by taking Moore's
"assumed values" at face value.  There are numerous mistakes in
the way Moore set up his values before even calculating his
trajectory.  The dozens of false rise/fall rates in his table
were already mentioned.

>The first entry is altitude in feet: 42651.
>The 2nd entry is rate of rise in feet per minute: 600.

Let's stop right here and examine this "assumed" rise rate,
because it too is wrong when compared to that of Flight #5.

How Moore secretly altered his assumptions to shorten the ascent
trajectory

Moore stated that he was assuming Flight #4 used their best
equipment, was configured similarly, and worked as well or
better than the successful Flight #5 the next day.  Flight #5
had extra lifter balloons, as did Flights #2 and #6, so
presumably would Flight #4.  These gave the balloon trains a
high rate of lift in the early going.

All the flights with lifter balloons had cutoff devices to
release the extra lifter balloons at higher elevations and slow
ascent in the upper troposphere.  E.g. Flight #5 cut loose its
lifter balloons at around 35,000 feet.  This is evident in both
Moore's table for Flight #5:

http://www.roswellproof.com/Flight5_Table2.html

and in his time-altitude plot:

http://www.roswellproof.com/Flight5_Fig1_Moore.html

If you examine Moore's plot, you can even see that he has it
labeled "2 lifting balloons released," and you'll see a sharp
"kink" in the ascent plot as the balloons' rise rate drops in
half.  Before lifter balloon cutoff, Flight #5 had an average
rise rate of 623 ft/min.  After cutoff it's average rate up to
about 52,000 feet was 314 ft/sec.

THE MISSING KINK IN MOORE'S FLIGHT #4 ASCENT

Now the POINT:  Notice that Moore's rise rate at 42651' is 600
ft/min!  In fact, Moore's table lists a constant 600 ft/min from
ground level up to about 46,000 feet.

But if Moore had actually used his stated assumptions of best
equipment, similar configuration, working as well or better than
Flight #5, then he should have modeled a similar lifter balloon
cutoff as #5, i.e., the rise rate should have similarly dropped
in half at around 35,000 ft., just like for #5.  I call this the
"missing kink" in Moore's time/altitude trajectory.

Thus Moore says he's doing one thing but he is actually doing
something completely different when he sets up the numbers in
his table (and he does it on the sly, without telling you about
it).  He is eliminating the lifter balloon cutoff.  Instead of
treating #4 like the successful #5, he treats it like the faulty
Flight #6, where the lifter balloon cutoff device failed.  The
balloons shot straight up, rapidly popped, and then came
straight down again.

And now a SECOND POINT:  This has fairly drastic effect on the
ascent trajectory.  The reason is, if you look at Moore's table
for Flight #4 winds:

http://www.roswellproof.com/Flight5_Table2.html

...you'll see that the winds above 35,000 feet are blowing in
the 50-80 mph range until the balloon stops its rapid rise.  By
sneakily removing lifter balloon cutoff, Moore has the balloons
racing right through this high wind speed region.  In fact, if
you look at my second graph on my main Flight #4 web page where
I plot the time/altitude trajectories for the various balloons
(or compare #4 and #5 tables), you will see that Moore has
shaved about 20 minutes off the ascent time compared to Flight
#5, until they both level off at about the 52,000 ft. level.
 This ruse shortens the ascent trajectory by over 20 miles.

Even Moore's times are questionable

>The 3rd entry is time into the flight, in minutes (67.0)

Even the elapsed times are not a "given."  If one wants to
"correct" the calculated rise rates so that they agree 100% with
Moore's listed table rates, it is necessary to completely
recalculate these times for the entire table! E.g., the time-of-
flight in this instance becomes 72.0 minutes instead of 67.0
minutes.  (This, in turn, plays absolute havoc with the
trajectory and times of flight, as Tim Printy found out to his
everlasting dismay as he desperately tried to salvage what was
left of Moore's model.) See:

http://www.virtuallystrange.net/ufo/updates/2002/nov/m07-001.shtml

>The 4th entry is wind speed in miles per hour (83 mph).
>The 5th entry is the angle the wind is coming from (242 degrees)

One of the high wind speeds that Moore wants to shorten exposure
to by eliminating lifter balloon cutoff.  This is his primary
means of shortening the ascent trajectory, and he doesn't tell
you he's doing it.

Thomas' spreadsheet calculation begins -- yawn

>The remaining entries are all calculated from the givens. The
>6th entry is for u, east-west wind speed in mph: this is
>calculated as =D16*SIN((E16-180)*PI()/180) in my spreadsheet,
>where cell D16 is 83 mph, and cell E16 is 242 degrees. This
>formula results in a value of u for this row that is 73.3 mph
>(towards the East). Moore's table shows his calculation to have
>the same result: 73.3 mph.

MOORE'S "SELECTIVE INCOMPETENCE"

>The 7th entry is for v, north-south wind speed in mph: this is
>calculated as =D16*COS((E16-180)*PI()/180) in my spreadsheet,
>where cell D16 is still 83 mph, and cell E16 is still 242
>degrees. This formula results in a value of v for this row that
>is 39.0 mph (towards the North), again agreeing exactly with
>Moore's calculation in his table.

Yes, Moore is very exact down to the decimal point in
calculations such as these, yet horribly wrong in others like
the rise/fall rates.  The "incompetence" seems to be very
selective, and oddly always seems to guide the balloons
"exactly" to the Foster Ranch.

Thomas says he didn't calculate backwards, but looky here

>The 8th and 9th entries are the actual trajectory values (x and
>y), the subject of this discussion.

The "actual" x,y values depend on how the calculation is done.
 Thomas recreates Moore's improper back-calculation which gives
an incorrect trajectory.  All the math reasons why this is wrong
and what the correct trajectory should be are the true subjects
of discussion, which is why Thomas deliberately avoids
discussing them.

>In my spreadsheet, I calculated east-west distance x as the
>value of the preceding line's x-position (which was 33.9 miles
>in my spreadsheet), PLUS the product of the east-west wind
>speed for the interval (73.3 mph) and the time interval. The
>latter I obtained by subtracting the previous time value
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
>minutes from the current time value (67.0 minutes), obtaining
>67.0 -61.6 = 5.4 minutes.

OK, here is where Thomas did the push-back while claiming above
that he didn't.  He is taking the current wind value and
applying it to the _previous_ time interval.  Notice where he
states that he is "subtracting the _previous_ time value" to get
the time interval.

DETAILING WHY THE PUSH-BACK CALCULATION IS WRONG -- MY YAWN

As I pointed out on my website, and also here on Updates in my
debates with Tim Printy, this is mathematically wrong for a
number of reasons.

1. THROWING OUT THE FIRST DATA POINT

Consider the first data point in the table at time t = 0: wind 9
mph, azimuth 197.  How do you subtract the time before t = 0 to
get a time interval to multiply times the wind velocity?  The
answer is you can't.  The Moore/Thomas/Printy way means that
first wind data point never gets used.  It's thrown out, a
curious way to treat one's data. (Except Moore didn't even do
that. More on what he really did below, which is even more
mathematically bizarre!)

What they are really doing to get the first x,y value is taking
the _second_ wind velocity value and multiplying it times the
_first_ time interval from t = 0 to the next elapsed time (t =
2.8 min.)

This carry-back of velocity to the previous time interval
extends throughout their entire calculation clear to the last
data point, even though Thomas claims it doesn't.

2. DESTRUCTION OF WIND SYMMETRY ON RISE AND FALL

What this means is that on the ascent side of the trajectory,
the velocity is applied from the current altitude _down_ through
the next _lower_ altitude.  But on the descent side, the exact
same velocity for the given altitude is applied _upward_ through
the next _higher_ altitude.

(If you want a homely analogy, this is like a rope over a
pulley.  If you pull down on one side, as Moore/Thomas/Printy
are doing, you end up pulling up everything on the other side.)

Because Moore made his wind values in his Flight #4 table
exactly the same on the rise and fall sides, this means the
M/T/P push-back method causes the same wind values to be applied
to _different_ altitude intervals instead of the same altitude
intervals.

In my debate with Tim Printy, I produced the table below
illustrating how the wind values match up in Moore's table, but
then go completely out of whack the M/T/P way of calculating.
 (Hopefully the table will format properly this time when
posted.  Otherwise copy it into a word processor and line up the
columns.)

(see: http://www.virtuallystrange.net/ufo/updates/2002/oct/m09-
008.shtml)

      Table 5 as written              Carry Wind Data Back
  Altitude    Wind Dir  Wind Spd      Wind dir.  Wind Spd
 Rise  Fall  Rise Fall  Rise Fall     Rise Fall  Rise Fall
 4069         197         9           236         12
 4921  5900   236  236   12  12       242         15
 6562  6562   242  242   15  15       247  236    23  12
 8202              247       23       242         17
 9843  9843   242  242   17  17       219  242    32  15
13123 13123   219  219   32  32       225  242    38  17
16404 16404   225  225   38  38       225  219    54  32
19685 19685   225  225   54  54       242  225    46  38
22966 22966   242  242   46  46       225  225    52  54
26247         225        52           225         54
29528 29528   225  225   54  54       242  242    44  46
32808 32808   242  242   44  44       242  225    53  54
36089         242        53           242         58
39370 39370   242  242   58  58       242  242    83  44
42651 42651   242  242   83  83       242  242    79  58
45932         242        79           242         66
49213 49000   242  242   66  66       242  242    38  83
52000 52000   242  242   38  38       242  242    20  66
52100         242        20           144*        17    <=Turn
53700 54000   144* 144*  17  17<=Turn 115  242    14  38
54500         115        14           100         10
57000 57000   100  100   10  10        80  144*   10  17<=Turn
58000          80        10            80         12
60600          80        12            80         12
60700 60750    80  80    12  12        80  100    12  10

Notice in the leftmost columns for rise/fall wind direction and
speed, the winds are exactly the same for a given altitude.  But
in the rightmost columns, the perfect symmetry is destroyed.
 Notice that none of the wind speeds match up any more, and
neither do many of the wind azimuths.

Take, e.g., Thomas' sample data point 42651 ft.  The wind speed
and direction match up Moore's table (left-hand columns) on both
the rise and fall sides (83 mph, azimuth 242).  But the way
Thomas is calculating things, (see right hand columns) the same
wind of 83 mph on the rise side is applied to the interval
between 39370 and 42651 ft.  But on the fall side, the 83 mph
wind is applied to the interval between 42651 and 49000 ft!

This is complete mathematical and scientific nonsense!  The
CORRECT way to do the calculation, given the way Moore set up
his table, is to use the SAME wind values for the SAME altitude
interval, not for intervals in opposite directions.

Now lets go back to Thomas' little bit of spin above when he
vaguely references this point:

>Some of these disagreements
>might even have some merit - say, using the same wind speed for
>a given altitude interval on the way up as on the way down.

What is _really_ being said here by Thomas is that he _knows_
that he and Moore are wrong to do it this way, but he isn't
Mensch enough to simply come out and admit it.  He's already
painted himself into a corner in his Skeptical Inquirer article
by saying my math points are nothing but "quibbles" and "shrill
accusations" and by calling me "mathematically incompetent."

So instead of apologizing, he uses propaganda techniques.  He
buries you in a lot of details of how he calculated his
spreadsheet (never mind that it's completely wrong).  He
pretends that he isn't using a carry-back technique, when that's
exactly what he is doing.

He refers to my point as a mere "disagreement," as if it were
nothing more than a difference of opinion, instead of an
irrefutable math mistake made by himself and Moore.   It "might
even have some merit," he writes.  With ThomasSpeak, if they say
2 + 2 = 3 and I say, "Hey guys, 2 + 2 = 4," it is a
"disagreement," though my "opinion" "might even have some
merit."

3. DIFFERENT TURN POINTS ON RISE AND FALL

Now look at the 52,000 and 53,700 foot levels in the table in
the leftmost columns.  You'll see that the wind azimuth abruptly
changes from azimuth 242 deg. to 144 deg.  These are the balloon
turn points in the stratosphere, where the wind abruptly shifts
direction.  In Moore's table, as written, the turn points on
rise and fall are the same (except Moore uses a slightly
different value of 54,000' on the fall side).  Note I have
labeled this "<=Turn."

But what happens with the M/T/P push-back calculation?  That's
in the right hand columns.  Remember on the rise side, the wind
values get carried down through to the next lower altitude,
whereas on the fall side, they get carried through to the next
higher altitude.  Now we have two completely different turn
altitudes on the rise and fall sides, again labeled "<=Turn".
 On the rise side, the wind direction change gets carried down
to the next lowest altitude data point at 52,100'.  But on the
fall side it gets carried up to the next altitude at 57,000'.
 Now the turns on rise and fall are separated by nearly a mile!

This is another big red flag that something is seriously wrong
with calculating things this way, but Thomas pretends everything
is just hunky dory.  Even Tim Printy noticed something was very
odd here, but instead of realizing the obvious, he said Moore
must have had a "good reason" for doing this.  There's a "good
reason" all right -- the method of calculation is all wrong.

4. DIFFERENT TURN POINTS FOR FLIGHTS #4 and #5

The rise side turn also destroys the correspondence Moore had
built into his tables for Flight #4 and Flight #5.  If you
compare the two tables again:

http://roswellproof.homestead.com/Flight4_Table5.html
http://www.roswellproof.com/Flight5_Table2.html

... Moore has Flight #5 changing wind directions to 144 deg
azimuth starting at 53,700' and carrying through to the _next_
_higher_altitude at 54,500', i.e., the balloon turn starts at
53,700', just as Moore's table for Flight #4 would seemingly
have.

But because M/T/P are carrying through wind values to the
_previous_ _lower_ altitude, the turn for Flight #4 starts at
52,100' instead of 53,700'.

5. THE MISSING 30 MINUTES--CUTTING THE ASCENT TRAJECTORY AGAIN

An extremely serious consequence of point 4, if you examine the
table for Flight #4, is that Moore has also started the turn 30
minutes earlier, since the elapsed time at 52,100' is 95.5'
instead of 125.5' for 53,700'. (By comparison, if you look at
Flight #5, the turn at 53,700' doesn't begin until 135' into
flight.)

This is the second way in which Moore drastically shortens the
ascent trajectory, and amounts to slicing off about another 10
miles.  This is over and above how he cut over 20 miles from the
trajectory earlier by eliminating the lifter balloon cutoff so
that the balloons raced through the high wind region in the
upper atmosphere.

This is also the primary reason Moore calculated his own table
wrong using push-back--he needed to shorten his ascent even
further than he had already.  It has other subtle consequences
on the trajectory as well, by adding extra time and distance
onto a needed backward drift to the west and south so that he
could get his balloon "exactly" to the Foster Ranch.

6.  STRATOSPHERIC WINDS USED IN OPPOSITE DIRECTIONS

Here's a another fatal error in a similar vein to point 5.
 Again examine Moore's table for Flight #5.  Moore back-
calculated wind speed and directions from the ground x,y values
and corresponding times by averaging _forward_ from one data
point to the next.  There is no arguing the point -- this is
simply the way he did it and is perfectly correct.

Thus for Flight #5, Moore carries his wind values _forward_ to
the next _higher_ altitude on the rise side of the trajectory.
 But for Flight #4, when he incorporates the derived
stratospheric winds from Flight #5 into his model, Moore carries
the rise winds _backward_ to the next _lower altitude.  He is
using the data in opposite directions for Flights #4 and #5!
 That's why the turn point for Flight #4 gets pushed _down_ in
altitude and back in time.  To remain consistent with what he
did for Flight #5, he should have started the turn at 53,700'
and carried the wind data forward to the next higher altitude,
and then done the same for all the other stratospheric wind
values.

End PART I


David Rudiak