From Billiard Balls to Lead Balls balanced on Matchsticks in a Vacuum
There is an excellent refutation of the official collapse theory over at ST911.org by Dr. Judy Wood, professor of Mechanical Engineering.
I came across this after listening to Professor Fetzer interview Professor Judy Wood on a live talkback radio show Non Random Thoughts.
The point Judy was making was if billiard balls were used to represent the WTC floors. If the first ball was dropped from the 110th floor and each ball had to wait for the ball immediately above it to arrive before it could fall. Even with just 1 ball every 10th floor of the WTC, the total time for the all the balls to hit the ground would be over 30 seconds. Yet the buildings consisted of 110 floors and came down in under 10 seconds.
One of the listeners phoned in an asked what if as each ball was struck, they connected together and continued their fall onto the lower balls? Well that seemed like a interesting question. It seems to be close to the way many rationlize the discrepency between what they saw and the explaination given verbatim in the corporate media. So I decided to try and figure out how long it would take for a series of lead balls to cascade down in a vacuum.
Imagine a tower made out of lead balls balanced on very thin matchsticks. So thin that as soon the ball is touched the matchstick gives way with no resistance. Now take out the support for the top lead ball. It falls and hits the next lead ball the two then fall together and hit the next and so on. How long does it take the tower to fall? Of course it is silly to imagine that the WTC towers had absolutely zero structural strength and would collapse the moment somebody sneezed. They were designed to take mulitple jet liner impacts and hurricane winds and even afterall a rather large bomb was detonated in the basement of one tower in the 1993, no structural damage was caused. But lets pretend!
Well working it out for one ball is just a straight forward free fall calculation. There is even a JAVA script on the web that allows you to just plug in the numbers.
Working it out for two is just a case of using the end velocity of the first and conserving momentum to get the starting velocity of the ball pair for the second half of the fall. The more balls the more calculations. It starts to get really messy and tedious quite quickly!
Solution: Write a simple script to do the calculations.
Here are the results. Not only does this ignor air resistance (favours the official story) I make my use the 80th floor as the start of the collapse.
Using the numbers Professor Wood used.
WTC height as 1368 feet and gravity at 32.2 ft/sec^2.
1 ball takes 9.22 seconds to fall (freefall)
Total balls = 1
Initial balls falling = 1
Total height = 1368 ft
Partial fall height = 1368 ft
Time = + 9.21786006073963 (freefall) = 9.21786006073963 secs
2 balls: (freefall halfway, collide and combined fall) takes 10.55 secs
Total balls = 2
Initial balls falling = 1
Total height = 1368 ft
Partial fall height = 684 ft
Time = + 6.51801135697764 + 4.02835255767 (freefall) = 10.5463639146476 secs
Total balls = 3
Initial balls falling = 1
Total height = 1368 ft
Partial fall height = 456 ft
Time = + 5.32193398742033 + 3.28913609010902 + 2.67088248277207 (freefall) = 11.2819525603014 secs
Now how about if instead of the top ball starting the collapse we have the bottom ball fall first and all the above balls fall with it. If the calculations are correct then we'd expect this to give the same result as a single ball falling from the top.
Total balls = 3
Initial balls falling = 3
Total height = 1368 ft
Partial fall height = 456 ft
Time = + 5.32193398742033 (freefall) + 2.20441723564382 (freefall) + 1.69150883767548 (freefall) = 9.21786006073963 secs
Wow! How about that!
Now lets get really complicated and have a ball for every floor of the WTC.
Total balls = 110
Initial balls falling = 1
Total height = 1368 ft
Partial fall height = 12.4363636363636 ft
Time = + 0.878888472081634 + 0.543182948066913 + 0.441081725166416 + 0.381342718297224 + 0.340828188014806 + 0.311008385823917 + 0.287869567234543 + 0.269236199690226 + 0.253811873681622 + 0.240769199003812 + 0.229551837444769 + 0.219770003494173 + 0.211141359129493 + 0.203455687948702 + 0.196552806165603 + 0.190308219556759 + 0.184623507169615 + 0.179419694197376 + 0.174632574266541 + 0.170209337631762 + 0.166106095101648 + 0.162286029360622 + 0.15871799404033 + 0.155375437756057 + 0.152235567609683 + 0.149278691611235 + 0.14648769647729 + 0.143847629051774 + 0.141345357890983 + 0.138969297476796 + 0.13670918180468 + 0.134555877227667 + 0.132501226757351 + 0.130537919757961 + 0.128659382279585 + 0.126859684274923 + 0.125133460711072 + 0.123475844182077 + 0.121882407091757 + 0.120349111840847 + 0.118872267740892 + 0.117448493607009 + 0.116074685165569 + 0.114747986561072 + 0.113465765366488 + 0.112225590599066 + 0.111025213323545 + 0.109862549490403 + 0.108735664710999 + 0.107642760716461 + 0.10658216328457 + 0.105552311450194 + 0.104551747841044 + 0.103579110002623 + 0.102633122594899 + 0.101712590359013 + 0.100816391765819 + 0.0999434732694771 + 0.0990928440991369 + 0.0982635715301698 + 0.0974547765836139 + 0.0966656301087511 + 0.0958953492091193 + 0.0951431939769322 + 0.0944084645049409 + 0.093690498148303 + 0.0929886670121083 + 0.0923023756429075 + 0.0916310589049507 + 0.0909741800239214 + 0.0903312287827722 + 0.0897017198558826 + 0.0890851912691761 + 0.0884812029750946 + 0.0878893355324391 + 0.0873091888820789 + 0.0867403812104062 + 0.0861825478932017 + 0.0856353405132717 + 0.0850984259458427 + 0.0845714855062605 + 0.0840542141550362 + 0.0835463197557371 + 0.0830475223816178 + 0.0825575536672547 + 0.0820761562017709 + 0.0816030829605354 + 0.0811380967724867 + 0.0806809698204699 + 0.0802314831721976 + 0.0797894263396405 + 0.0793545968648326 + 0.0789267999302407 + 0.0785058479919941 + 0.0780915604344065 + 0.0776837632443444 + 0.0772822887041084 + 0.0768869751015968 + 0.0764976664566128 + 0.0761142122622639 + 0.0757364672404799 + 0.0753642911107473 + 0.0749975483712231 + 0.0746361080914541 + 0.0742798437159796 + 0.0739286328781503 + 0.0735823572235394 + 0.0732409022423691 + 0.0729041571104117 + 0.0725720145378654 (freefall) = 15.01731760107 secs
And what if the collapse starts from the bottom ball?
Total balls = 110
Initial balls falling = 110
Total height = 1368 ft
Partial fall height = 12.4363636363636 ft
Time = + 0.878888472081634 (freefall) + 0.36404752494958 (freefall) + 0.279343490800757 (freefall) + 0.235497456331297 (freefall) + 0.207477424052192 (freefall) + 0.187573929198882 (freefall) + 0.172492029875196 (freefall) + 0.16055166677289 (freefall) + 0.150793422182474 (freefall) + 0.14262396479837 (freefall) + 0.135653913420256 (freefall) + 0.129615681200415 (freefall) + 0.124318475840591 (freefall) + 0.119622092210177 (freefall) + 0.115420871831142 (freefall) + 0.111633472780685 (freefall) + 0.108196115203759 (freefall) + 0.105057987563347 (freefall) + 0.102178041353069 (freefall) + 0.0995227039842083 (freefall) + 0.0970642143072509 (freefall) + 0.0947793898406601 (freefall) + 0.092648699306421 (freefall) + 0.0906555549434328 (freefall) + 0.0887857655794859 (freefall) + 0.0870271090078293 (freefall) + 0.0853689940799133 (freefall) + 0.0838021910831635 (freefall) + 0.0823186146711556 (freefall) + 0.0809111476533722 (freefall) + 0.0795734968546469 (freefall) + 0.0783000743666061 (freefall) + 0.0770858990681794 (freefall) + 0.0759265144490591 (freefall) + 0.0748179196393716 (freefall) + 0.0737565112083378 (freefall) + 0.0727390337994123 (freefall) + 0.0717625380588168 (freefall) + 0.0708243446171979 (freefall) + 0.0699220131213123 (freefall) + 0.0690533154996912 (freefall) + 0.0682162127947117 (freefall) + 0.0674088350120843 (freefall) + 0.066629463534024 (freefall) + 0.0658765157193251 (freefall) + 0.0651485313760423 (freefall) + 0.0644441608434774 (freefall) + 0.0637621544619846 (freefall) + 0.0631013532435547 (freefall) + 0.0624606805846326 (freefall) + 0.0618391348862995 (freefall) + 0.0612357829666945 (freefall) + 0.060649754167084 (freefall) + 0.0600802350668779 (freefall) + 0.0595264647346067 (freefall) + 0.0589877304517848 (freefall) + 0.0584633638549977 (freefall) + 0.0579527374487154 (freefall) + 0.0574552614474504 (freefall) + 0.0569703809111206 (freefall) + 0.0564975731419752 (freefall) + 0.0560363453153193 (freefall) + 0.0555862323196182 (freefall) + 0.0551467947844581 (freefall) + 0.0547176172773553 (freefall) + 0.0542983066525875 (freefall) + 0.0538884905371306 (freefall) + 0.0534878159404455 (freefall) + 0.0530959479763166 (freefall) + 0.0527125686862231 (freefall) + 0.0523373759548466 (freefall) + 0.051970082509308 (freefall) + 0.0516104149945987 (freefall) + 0.0512581131184452 (freefall) + 0.0509129288595258 (freefall) + 0.0505746257335683 (freefall) + 0.0502429781123913 (freefall) + 0.0499177705914359 (freefall) + 0.0495987974017576 (freefall) + 0.0492858618628318 (freefall) + 0.0489787758728672 (freefall) + 0.0486773594336244 (freefall) + 0.0483814402070148 (freefall) + 0.0480908531009956 (freefall) + 0.0478054398825027 (freefall) + 0.0475250488153573 (freefall) + 0.0472495343212663 (freefall) + 0.046978756662194 (freefall) + 0.0467125816425316 (freefall) + 0.0464508803296223 (freefall) + 0.0461935287913201 (freefall) + 0.0459404078493681 (freefall) + 0.0456914028474825 (freefall) + 0.0454464034331164 (freefall) + 0.0452053033519597 (freefall) + 0.0449680002543071 (freefall) + 0.0447343955124907 (freefall) + 0.0445043940486398 (freefall) + 0.0442779041720824 (freefall) + 0.0440548374257588 (freefall) + 0.0438351084410617 (freefall) + 0.0436186348005621 (freefall) + 0.04340533690812 (freefall) + 0.0431951378659146 (freefall) + 0.0429879633579621 (freefall) + 0.0427837415397221 (freefall) + 0.0425824029334177 (freefall) + 0.0423838803287246 (freefall) + 0.0421881086885068 (freefall) + 0.0419950250592977 (freefall) = 9.21786006073964 secs
Now lets see the time if the collapse starts at the 81st ball.
Total balls = 110
Initial balls falling = 30
Total height = 1368 ft
Partial fall height = 12.4363636363636 ft
Time = + 0.878888472081634 + 0.372515722735165 + 0.29038713482395 + 0.248418466941806 + 0.221902492148921 + 0.203255151903454 + 0.189247660862859 + 0.17824061805459 + 0.169302003810394 + 0.161858128145399 + 0.155534331209412 + 0.150074435797131 + 0.145296726152184 + 0.141068369613814 + 0.137289798558051 + 0.133884774407415 + 0.130793844137016 + 0.127969901796355 + 0.125375100013283 + 0.122978652411087 + 0.120755238911283 + 0.11868382815334 + 0.116746794252494 + 0.114929244960041 + 0.113218504096986 + 0.111603708206849 + 0.110075488890951 + 0.108625720195748 + 0.107247315936554 + 0.105934065745522 + 0.104680501432303 + 0.103481787280268 + 0.102333629396246 + 0.101232200342257 + 0.100174076110927 + 0.0991561831371949 + 0.0981757535209493 + 0.097230287006428 + 0.0963175185523702 + 0.0954353905521385 + 0.094582028940341 + 0.093755722562941 + 0.092954905299805 + 0.0921781405183957 + 0.0914241075096756 + 0.0906915896159151 + 0.0899794638078513 + 0.0892866915077088 + 0.08861231048671 + 0.0879554276922049 + 0.0873152128815263 + 0.0866908929579588 + 0.0860817469194818 + 0.0854871013437518 + 0.0849063263435602 + 0.084338831936093 + 0.0837840647770196 + 0.0832415052169753 + 0.0827106646435736 + 0.0821910830768435 + 0.0816823269900662 + 0.0811839873314864 + 0.0806956777253912 + 0.0802170328336546 + 0.079747706861099 + 0.0792873721899808 + 0.0788357181306082 + 0.0783924497765785 + 0.0779572869544189 + 0.0775299632585437 + 0.0771102251634348 + 0.0766978312058234 + 0.0762925512304178 + 0.0758941656934001 + 0.0755024650185081 + 0.0751172490010523 + 0.0747383262556824 + 0.0743655137041355 + 0.0739986360995664 + 0.0736375255843922 + 0.0732820212788733 (freefall) + 0.0722837921842979 (freefall) + 0.0713252775851049 (freefall) + 0.0704039119102279 (freefall) + 0.0695173557934057 (freefall) + 0.0686634710586758 (freefall) + 0.0678402990059145 (freefall) + 0.067046041493925 (freefall) + 0.066279044404848 (freefall) + 0.0655377831435279 (freefall) + 0.0648208498823291 (freefall) + 0.0641269423084057 (freefall) + 0.0634548536686444 (freefall) + 0.0628034639390472 (freefall) + 0.0621717319714655 (freefall) + 0.0615586884923651 (freefall) + 0.0609634298464816 (freefall) + 0.0603851123934785 (freefall) + 0.0598229474785561 (freefall) + 0.0592761969087989 (freefall) + 0.0587441688762375 (freefall) + 0.0582262142764074 (freefall) + 0.0577217233778483 (freefall) + 0.057230122803677 (freefall) + 0.0567508727912558 (freefall) + 0.0562834647001718 (freefall) + 0.0558274187423676 (freefall) + 0.0553822819113908 (freefall) + 0.0549476260904426 (freefall) + 0.0545230463212624 (freefall) = 11.5945710059708 secs
Oops! Thats longer than the official time for the WTC South tower collapse. According to the 911 Commission the South tower came down in 10 seconds. Seismic data recorded at Palisades New York also suggest it was 10 seconds. Well maybe we should group the floors together. How about groups of ten. Thats a total of 11 balls with 3 balls starting the collapse.
Total balls = 11
Initial balls falling = 3
Total height = 1368 ft
Partial fall height = 124.363636363636 ft
Time = + 2.77928938104327 + 1.38964469052164 + 1.15121935538765 + 1.02025428770385 + 0.931193578976778 + 0.864284631031415 + 0.811078337369369 + 0.767191749768957 + 0.730053778687875 (freefall) + 0.646032814875451 (freefall) + 0.58569696224756 (freefall) = 11.6759395676138 secs
Wow that is even worse!
Well maybe the North Tower came down at a more leisurely pace. After all the damage was on the 95th floor. However the seismic data recorded at Palisades New York suggest the North Tower came down in 8 seconds. Lets see how long our lead ball tower will take to collapse. Lets be generous and start the collapse at the 94th ball.
Total balls = 110
Initial balls falling = 17
Total height = 1368 ft
Partial fall height = 12.4363636363636 ft
Time = + 0.878888472081634 + 0.378841790322338 + 0.298365810755618 + 0.257449852205161 + 0.231662898635931 + 0.21353280845043 + 0.199891903484093 + 0.189139193504839 + 0.180368856870843 + 0.173026038894543 + 0.166750123682388 + 0.161295685284289 + 0.156489402842559 + 0.152205099173438 + 0.148348546484856 + 0.144847831356131 + 0.141647030878793 + 0.138701938088554 + 0.135977098100962 + 0.133443706799565 + 0.131078091506842 + 0.128860593090793 + 0.12677473046388 + 0.124806567262057 + 0.122944225593401 + 0.121177508320543 + 0.11949760249742 + 0.117896844222069 + 0.116368530484868 + 0.114906767346687 + 0.113506346468836 + 0.112162643964067 + 0.110871536965339 + 0.109629334366504 + 0.108432718980437 + 0.10727869895772 + 0.106164566764331 + 0.105087864366525 + 0.104046353541804 + 0.103037990445939 + 0.102060903731719 + 0.101113375646024 + 0.100193825635907 + 0.0993007960776264 + 0.0984329398094799 + 0.0975890092034222 + 0.0967678465544064 + 0.0959683756022748 + 0.0951895940304682 + 0.0944305668100694 + 0.093690420277758 + 0.092968336852917 + 0.0922635503130265 + 0.0915753415581084 + 0.0909030348047573 + 0.090245994158523 + 0.0896036205203782 + 0.0889753487889108 + 0.0883606453249096 + 0.0877590056493039 + 0.0871699523490953 + 0.08659303316907 + 0.086027819269801 + 0.0854739036347906 + 0.0849308996116318 + 0.0843984395738287 + 0.0838761736914438 + 0.0833637688000739 + 0.0828609073588215 + 0.0823672864889461 + 0.081882617085777 + 0.0814066229972513 + 0.0809390402631373 + 0.0804796164096112 + 0.0800281097943957 + 0.0795842889981504 + 0.0791479322582241 + 0.0787188269412597 + 0.0782967690514779 + 0.0778815627717646 + 0.0774730200349546 + 0.0770709601229465 + 0.0766752092914944 + 0.0762856004187173 + 0.0759019726755393 + 0.0755241712164309 + 0.0751520468889587 + 0.0747854559607821 + 0.0744242598628467 + 0.0740683249476293 + 0.0737175222613826 + 0.0733717273294136 + 0.0730308199535065 + 0.0726946840206707 (freefall) + 0.0717199496155702 (freefall) + 0.0707834039287392 (freefall) + 0.0698826166033962 (freefall) + 0.0690153684610716 (freefall) + 0.0681796284789926 (freefall) + 0.067373533762796 (freefall) + 0.0665953720646243 (freefall) + 0.0658435664728888 (freefall) + 0.0651166619619019 (freefall) + 0.0644133135401175 (freefall) + 0.0637322757771763 (freefall) + 0.0630723935240981 (freefall) + 0.0624325936692298 (freefall) + 0.0618118777960346 (freefall) + 0.061209315628399 (freefall) + 0.0606240391655364 (freefall) = 12.4202053908114 secs
Gee wizz! How can this be? The North Tower came down in two thirds the time our lead ball and matchstick tower took. It seems gravity alone can't explain this!
Remember I'm bending over backwards to try and make the official story even remotely plausible by using this simple model (and it looks like there are many people who are just bending over). I've ignored air resistance, no account is made for lost mass and momentum as steel beams shatter and fly out sideways or for the concrete and office contents that turned to dust. I also ignor the fact that the upper floors were lighter and the lower floors stronger and heavier. If we were to just factor the loss of mass and momentum alone then the numbers would get rediculous. And if we were to factor in the energy needed to shatter steel beams and pulverise concrete the collapse would be impossible! Just goes to show how ridiculous the official story is.
So when was the pancake collapse theory first put forward? Answer: Within 3 mins of the first tower coming down. The late Peter Jennings remarked when seeing the South Tower come down "Anyone who's ever watched a building being demolished on purpose knows that if you're going to do this, you have to get at the under infrastructure of a building and bring it down." No sooner had he said this and the reporter on the scene said he was just 4 blocks away and saw it clearly, it was a pancake collapse. (I'll dig out my copy of this news footage shortly and put in the exact quote as well as the name of the reporter)
For those interested. Here is the Perl script I wrote to do the math. The blog HMTL editor makes a mess of the formating but anyone who knows Perl should be able to repair it easy enough.
sub lead_ball_tower {
my $start_velocity = 0;
my $total_balls = 110;
my $initial_balls_falling = 17;
my $balls_stationary = $total_balls - $initial_balls_falling;
my $height = 1368; # (1368 feet)
my $partial_fall_height = $height/$total_balls;
print "Total balls = $total_balls Initial balls falling = $initial_balls_falling ";
print "Total height = $height ft Partial fall height = $partial_fall_height ft ";
print "Time = ";
$time = &fall_time($partial_fall_height, $start_velocity, $initial_balls_falling, $balls_stationary, $initial_balls_falling);
print " = $time secs";
}
sub fall_time { # calculate the time to fall to the next ball given the start velocity
my ($fall_height, $start_velocity, $balls_falling, $balls_stationary, $initial_balls_falling) = @_;
my $gravity = 32.2; # (32.2 ft/sec2)
my $end_velocity = sqrt($start_velocity**2 + 2*$gravity*$fall_height);
my $time = 2*$fall_height / ($start_velocity + $end_velocity);
print "+ $time ";
if ($balls_stationary == 0) { print "(free fall) "};
if ($balls_stationary > 0) {
$end_velocity = $end_velocity * $balls_falling / ($balls_falling+1); # conservation of momentum
$balls_stationary--;
$balls_falling++;
$time = $time + &fall_time($fall_height, $end_velocity, $balls_falling, $balls_stationary, $initial_balls_falling);
} elsif ($initial_balls_falling > 1) {
$initial_balls_falling--;
$time = $time + &fall_time($fall_height, $end_velocity, $balls_falling, $balls_stationary, $initial_balls_falling);
}
return $time;
}
I came across this after listening to Professor Fetzer interview Professor Judy Wood on a live talkback radio show Non Random Thoughts.
The point Judy was making was if billiard balls were used to represent the WTC floors. If the first ball was dropped from the 110th floor and each ball had to wait for the ball immediately above it to arrive before it could fall. Even with just 1 ball every 10th floor of the WTC, the total time for the all the balls to hit the ground would be over 30 seconds. Yet the buildings consisted of 110 floors and came down in under 10 seconds.
One of the listeners phoned in an asked what if as each ball was struck, they connected together and continued their fall onto the lower balls? Well that seemed like a interesting question. It seems to be close to the way many rationlize the discrepency between what they saw and the explaination given verbatim in the corporate media. So I decided to try and figure out how long it would take for a series of lead balls to cascade down in a vacuum.
Imagine a tower made out of lead balls balanced on very thin matchsticks. So thin that as soon the ball is touched the matchstick gives way with no resistance. Now take out the support for the top lead ball. It falls and hits the next lead ball the two then fall together and hit the next and so on. How long does it take the tower to fall? Of course it is silly to imagine that the WTC towers had absolutely zero structural strength and would collapse the moment somebody sneezed. They were designed to take mulitple jet liner impacts and hurricane winds and even afterall a rather large bomb was detonated in the basement of one tower in the 1993, no structural damage was caused. But lets pretend!
Well working it out for one ball is just a straight forward free fall calculation. There is even a JAVA script on the web that allows you to just plug in the numbers.
Working it out for two is just a case of using the end velocity of the first and conserving momentum to get the starting velocity of the ball pair for the second half of the fall. The more balls the more calculations. It starts to get really messy and tedious quite quickly!
Solution: Write a simple script to do the calculations.
Here are the results. Not only does this ignor air resistance (favours the official story) I make my use the 80th floor as the start of the collapse.
Using the numbers Professor Wood used.
WTC height as 1368 feet and gravity at 32.2 ft/sec^2.
1 ball takes 9.22 seconds to fall (freefall)
Total balls = 1
Initial balls falling = 1
Total height = 1368 ft
Partial fall height = 1368 ft
Time = + 9.21786006073963 (freefall) = 9.21786006073963 secs
2 balls: (freefall halfway, collide and combined fall) takes 10.55 secs
Total balls = 2
Initial balls falling = 1
Total height = 1368 ft
Partial fall height = 684 ft
Time = + 6.51801135697764 + 4.02835255767 (freefall) = 10.5463639146476 secs
Total balls = 3
Initial balls falling = 1
Total height = 1368 ft
Partial fall height = 456 ft
Time = + 5.32193398742033 + 3.28913609010902 + 2.67088248277207 (freefall) = 11.2819525603014 secs
Now how about if instead of the top ball starting the collapse we have the bottom ball fall first and all the above balls fall with it. If the calculations are correct then we'd expect this to give the same result as a single ball falling from the top.
Total balls = 3
Initial balls falling = 3
Total height = 1368 ft
Partial fall height = 456 ft
Time = + 5.32193398742033 (freefall) + 2.20441723564382 (freefall) + 1.69150883767548 (freefall) = 9.21786006073963 secs
Wow! How about that!
Now lets get really complicated and have a ball for every floor of the WTC.
Total balls = 110
Initial balls falling = 1
Total height = 1368 ft
Partial fall height = 12.4363636363636 ft
Time = + 0.878888472081634 + 0.543182948066913 + 0.441081725166416 + 0.381342718297224 + 0.340828188014806 + 0.311008385823917 + 0.287869567234543 + 0.269236199690226 + 0.253811873681622 + 0.240769199003812 + 0.229551837444769 + 0.219770003494173 + 0.211141359129493 + 0.203455687948702 + 0.196552806165603 + 0.190308219556759 + 0.184623507169615 + 0.179419694197376 + 0.174632574266541 + 0.170209337631762 + 0.166106095101648 + 0.162286029360622 + 0.15871799404033 + 0.155375437756057 + 0.152235567609683 + 0.149278691611235 + 0.14648769647729 + 0.143847629051774 + 0.141345357890983 + 0.138969297476796 + 0.13670918180468 + 0.134555877227667 + 0.132501226757351 + 0.130537919757961 + 0.128659382279585 + 0.126859684274923 + 0.125133460711072 + 0.123475844182077 + 0.121882407091757 + 0.120349111840847 + 0.118872267740892 + 0.117448493607009 + 0.116074685165569 + 0.114747986561072 + 0.113465765366488 + 0.112225590599066 + 0.111025213323545 + 0.109862549490403 + 0.108735664710999 + 0.107642760716461 + 0.10658216328457 + 0.105552311450194 + 0.104551747841044 + 0.103579110002623 + 0.102633122594899 + 0.101712590359013 + 0.100816391765819 + 0.0999434732694771 + 0.0990928440991369 + 0.0982635715301698 + 0.0974547765836139 + 0.0966656301087511 + 0.0958953492091193 + 0.0951431939769322 + 0.0944084645049409 + 0.093690498148303 + 0.0929886670121083 + 0.0923023756429075 + 0.0916310589049507 + 0.0909741800239214 + 0.0903312287827722 + 0.0897017198558826 + 0.0890851912691761 + 0.0884812029750946 + 0.0878893355324391 + 0.0873091888820789 + 0.0867403812104062 + 0.0861825478932017 + 0.0856353405132717 + 0.0850984259458427 + 0.0845714855062605 + 0.0840542141550362 + 0.0835463197557371 + 0.0830475223816178 + 0.0825575536672547 + 0.0820761562017709 + 0.0816030829605354 + 0.0811380967724867 + 0.0806809698204699 + 0.0802314831721976 + 0.0797894263396405 + 0.0793545968648326 + 0.0789267999302407 + 0.0785058479919941 + 0.0780915604344065 + 0.0776837632443444 + 0.0772822887041084 + 0.0768869751015968 + 0.0764976664566128 + 0.0761142122622639 + 0.0757364672404799 + 0.0753642911107473 + 0.0749975483712231 + 0.0746361080914541 + 0.0742798437159796 + 0.0739286328781503 + 0.0735823572235394 + 0.0732409022423691 + 0.0729041571104117 + 0.0725720145378654 (freefall) = 15.01731760107 secs
And what if the collapse starts from the bottom ball?
Total balls = 110
Initial balls falling = 110
Total height = 1368 ft
Partial fall height = 12.4363636363636 ft
Time = + 0.878888472081634 (freefall) + 0.36404752494958 (freefall) + 0.279343490800757 (freefall) + 0.235497456331297 (freefall) + 0.207477424052192 (freefall) + 0.187573929198882 (freefall) + 0.172492029875196 (freefall) + 0.16055166677289 (freefall) + 0.150793422182474 (freefall) + 0.14262396479837 (freefall) + 0.135653913420256 (freefall) + 0.129615681200415 (freefall) + 0.124318475840591 (freefall) + 0.119622092210177 (freefall) + 0.115420871831142 (freefall) + 0.111633472780685 (freefall) + 0.108196115203759 (freefall) + 0.105057987563347 (freefall) + 0.102178041353069 (freefall) + 0.0995227039842083 (freefall) + 0.0970642143072509 (freefall) + 0.0947793898406601 (freefall) + 0.092648699306421 (freefall) + 0.0906555549434328 (freefall) + 0.0887857655794859 (freefall) + 0.0870271090078293 (freefall) + 0.0853689940799133 (freefall) + 0.0838021910831635 (freefall) + 0.0823186146711556 (freefall) + 0.0809111476533722 (freefall) + 0.0795734968546469 (freefall) + 0.0783000743666061 (freefall) + 0.0770858990681794 (freefall) + 0.0759265144490591 (freefall) + 0.0748179196393716 (freefall) + 0.0737565112083378 (freefall) + 0.0727390337994123 (freefall) + 0.0717625380588168 (freefall) + 0.0708243446171979 (freefall) + 0.0699220131213123 (freefall) + 0.0690533154996912 (freefall) + 0.0682162127947117 (freefall) + 0.0674088350120843 (freefall) + 0.066629463534024 (freefall) + 0.0658765157193251 (freefall) + 0.0651485313760423 (freefall) + 0.0644441608434774 (freefall) + 0.0637621544619846 (freefall) + 0.0631013532435547 (freefall) + 0.0624606805846326 (freefall) + 0.0618391348862995 (freefall) + 0.0612357829666945 (freefall) + 0.060649754167084 (freefall) + 0.0600802350668779 (freefall) + 0.0595264647346067 (freefall) + 0.0589877304517848 (freefall) + 0.0584633638549977 (freefall) + 0.0579527374487154 (freefall) + 0.0574552614474504 (freefall) + 0.0569703809111206 (freefall) + 0.0564975731419752 (freefall) + 0.0560363453153193 (freefall) + 0.0555862323196182 (freefall) + 0.0551467947844581 (freefall) + 0.0547176172773553 (freefall) + 0.0542983066525875 (freefall) + 0.0538884905371306 (freefall) + 0.0534878159404455 (freefall) + 0.0530959479763166 (freefall) + 0.0527125686862231 (freefall) + 0.0523373759548466 (freefall) + 0.051970082509308 (freefall) + 0.0516104149945987 (freefall) + 0.0512581131184452 (freefall) + 0.0509129288595258 (freefall) + 0.0505746257335683 (freefall) + 0.0502429781123913 (freefall) + 0.0499177705914359 (freefall) + 0.0495987974017576 (freefall) + 0.0492858618628318 (freefall) + 0.0489787758728672 (freefall) + 0.0486773594336244 (freefall) + 0.0483814402070148 (freefall) + 0.0480908531009956 (freefall) + 0.0478054398825027 (freefall) + 0.0475250488153573 (freefall) + 0.0472495343212663 (freefall) + 0.046978756662194 (freefall) + 0.0467125816425316 (freefall) + 0.0464508803296223 (freefall) + 0.0461935287913201 (freefall) + 0.0459404078493681 (freefall) + 0.0456914028474825 (freefall) + 0.0454464034331164 (freefall) + 0.0452053033519597 (freefall) + 0.0449680002543071 (freefall) + 0.0447343955124907 (freefall) + 0.0445043940486398 (freefall) + 0.0442779041720824 (freefall) + 0.0440548374257588 (freefall) + 0.0438351084410617 (freefall) + 0.0436186348005621 (freefall) + 0.04340533690812 (freefall) + 0.0431951378659146 (freefall) + 0.0429879633579621 (freefall) + 0.0427837415397221 (freefall) + 0.0425824029334177 (freefall) + 0.0423838803287246 (freefall) + 0.0421881086885068 (freefall) + 0.0419950250592977 (freefall) = 9.21786006073964 secs
Now lets see the time if the collapse starts at the 81st ball.
Total balls = 110
Initial balls falling = 30
Total height = 1368 ft
Partial fall height = 12.4363636363636 ft
Time = + 0.878888472081634 + 0.372515722735165 + 0.29038713482395 + 0.248418466941806 + 0.221902492148921 + 0.203255151903454 + 0.189247660862859 + 0.17824061805459 + 0.169302003810394 + 0.161858128145399 + 0.155534331209412 + 0.150074435797131 + 0.145296726152184 + 0.141068369613814 + 0.137289798558051 + 0.133884774407415 + 0.130793844137016 + 0.127969901796355 + 0.125375100013283 + 0.122978652411087 + 0.120755238911283 + 0.11868382815334 + 0.116746794252494 + 0.114929244960041 + 0.113218504096986 + 0.111603708206849 + 0.110075488890951 + 0.108625720195748 + 0.107247315936554 + 0.105934065745522 + 0.104680501432303 + 0.103481787280268 + 0.102333629396246 + 0.101232200342257 + 0.100174076110927 + 0.0991561831371949 + 0.0981757535209493 + 0.097230287006428 + 0.0963175185523702 + 0.0954353905521385 + 0.094582028940341 + 0.093755722562941 + 0.092954905299805 + 0.0921781405183957 + 0.0914241075096756 + 0.0906915896159151 + 0.0899794638078513 + 0.0892866915077088 + 0.08861231048671 + 0.0879554276922049 + 0.0873152128815263 + 0.0866908929579588 + 0.0860817469194818 + 0.0854871013437518 + 0.0849063263435602 + 0.084338831936093 + 0.0837840647770196 + 0.0832415052169753 + 0.0827106646435736 + 0.0821910830768435 + 0.0816823269900662 + 0.0811839873314864 + 0.0806956777253912 + 0.0802170328336546 + 0.079747706861099 + 0.0792873721899808 + 0.0788357181306082 + 0.0783924497765785 + 0.0779572869544189 + 0.0775299632585437 + 0.0771102251634348 + 0.0766978312058234 + 0.0762925512304178 + 0.0758941656934001 + 0.0755024650185081 + 0.0751172490010523 + 0.0747383262556824 + 0.0743655137041355 + 0.0739986360995664 + 0.0736375255843922 + 0.0732820212788733 (freefall) + 0.0722837921842979 (freefall) + 0.0713252775851049 (freefall) + 0.0704039119102279 (freefall) + 0.0695173557934057 (freefall) + 0.0686634710586758 (freefall) + 0.0678402990059145 (freefall) + 0.067046041493925 (freefall) + 0.066279044404848 (freefall) + 0.0655377831435279 (freefall) + 0.0648208498823291 (freefall) + 0.0641269423084057 (freefall) + 0.0634548536686444 (freefall) + 0.0628034639390472 (freefall) + 0.0621717319714655 (freefall) + 0.0615586884923651 (freefall) + 0.0609634298464816 (freefall) + 0.0603851123934785 (freefall) + 0.0598229474785561 (freefall) + 0.0592761969087989 (freefall) + 0.0587441688762375 (freefall) + 0.0582262142764074 (freefall) + 0.0577217233778483 (freefall) + 0.057230122803677 (freefall) + 0.0567508727912558 (freefall) + 0.0562834647001718 (freefall) + 0.0558274187423676 (freefall) + 0.0553822819113908 (freefall) + 0.0549476260904426 (freefall) + 0.0545230463212624 (freefall) = 11.5945710059708 secs
Oops! Thats longer than the official time for the WTC South tower collapse. According to the 911 Commission the South tower came down in 10 seconds. Seismic data recorded at Palisades New York also suggest it was 10 seconds. Well maybe we should group the floors together. How about groups of ten. Thats a total of 11 balls with 3 balls starting the collapse.
Total balls = 11
Initial balls falling = 3
Total height = 1368 ft
Partial fall height = 124.363636363636 ft
Time = + 2.77928938104327 + 1.38964469052164 + 1.15121935538765 + 1.02025428770385 + 0.931193578976778 + 0.864284631031415 + 0.811078337369369 + 0.767191749768957 + 0.730053778687875 (freefall) + 0.646032814875451 (freefall) + 0.58569696224756 (freefall) = 11.6759395676138 secs
Wow that is even worse!
Well maybe the North Tower came down at a more leisurely pace. After all the damage was on the 95th floor. However the seismic data recorded at Palisades New York suggest the North Tower came down in 8 seconds. Lets see how long our lead ball tower will take to collapse. Lets be generous and start the collapse at the 94th ball.
Total balls = 110
Initial balls falling = 17
Total height = 1368 ft
Partial fall height = 12.4363636363636 ft
Time = + 0.878888472081634 + 0.378841790322338 + 0.298365810755618 + 0.257449852205161 + 0.231662898635931 + 0.21353280845043 + 0.199891903484093 + 0.189139193504839 + 0.180368856870843 + 0.173026038894543 + 0.166750123682388 + 0.161295685284289 + 0.156489402842559 + 0.152205099173438 + 0.148348546484856 + 0.144847831356131 + 0.141647030878793 + 0.138701938088554 + 0.135977098100962 + 0.133443706799565 + 0.131078091506842 + 0.128860593090793 + 0.12677473046388 + 0.124806567262057 + 0.122944225593401 + 0.121177508320543 + 0.11949760249742 + 0.117896844222069 + 0.116368530484868 + 0.114906767346687 + 0.113506346468836 + 0.112162643964067 + 0.110871536965339 + 0.109629334366504 + 0.108432718980437 + 0.10727869895772 + 0.106164566764331 + 0.105087864366525 + 0.104046353541804 + 0.103037990445939 + 0.102060903731719 + 0.101113375646024 + 0.100193825635907 + 0.0993007960776264 + 0.0984329398094799 + 0.0975890092034222 + 0.0967678465544064 + 0.0959683756022748 + 0.0951895940304682 + 0.0944305668100694 + 0.093690420277758 + 0.092968336852917 + 0.0922635503130265 + 0.0915753415581084 + 0.0909030348047573 + 0.090245994158523 + 0.0896036205203782 + 0.0889753487889108 + 0.0883606453249096 + 0.0877590056493039 + 0.0871699523490953 + 0.08659303316907 + 0.086027819269801 + 0.0854739036347906 + 0.0849308996116318 + 0.0843984395738287 + 0.0838761736914438 + 0.0833637688000739 + 0.0828609073588215 + 0.0823672864889461 + 0.081882617085777 + 0.0814066229972513 + 0.0809390402631373 + 0.0804796164096112 + 0.0800281097943957 + 0.0795842889981504 + 0.0791479322582241 + 0.0787188269412597 + 0.0782967690514779 + 0.0778815627717646 + 0.0774730200349546 + 0.0770709601229465 + 0.0766752092914944 + 0.0762856004187173 + 0.0759019726755393 + 0.0755241712164309 + 0.0751520468889587 + 0.0747854559607821 + 0.0744242598628467 + 0.0740683249476293 + 0.0737175222613826 + 0.0733717273294136 + 0.0730308199535065 + 0.0726946840206707 (freefall) + 0.0717199496155702 (freefall) + 0.0707834039287392 (freefall) + 0.0698826166033962 (freefall) + 0.0690153684610716 (freefall) + 0.0681796284789926 (freefall) + 0.067373533762796 (freefall) + 0.0665953720646243 (freefall) + 0.0658435664728888 (freefall) + 0.0651166619619019 (freefall) + 0.0644133135401175 (freefall) + 0.0637322757771763 (freefall) + 0.0630723935240981 (freefall) + 0.0624325936692298 (freefall) + 0.0618118777960346 (freefall) + 0.061209315628399 (freefall) + 0.0606240391655364 (freefall) = 12.4202053908114 secs
Gee wizz! How can this be? The North Tower came down in two thirds the time our lead ball and matchstick tower took. It seems gravity alone can't explain this!
Remember I'm bending over backwards to try and make the official story even remotely plausible by using this simple model (and it looks like there are many people who are just bending over). I've ignored air resistance, no account is made for lost mass and momentum as steel beams shatter and fly out sideways or for the concrete and office contents that turned to dust. I also ignor the fact that the upper floors were lighter and the lower floors stronger and heavier. If we were to just factor the loss of mass and momentum alone then the numbers would get rediculous. And if we were to factor in the energy needed to shatter steel beams and pulverise concrete the collapse would be impossible! Just goes to show how ridiculous the official story is.
So when was the pancake collapse theory first put forward? Answer: Within 3 mins of the first tower coming down. The late Peter Jennings remarked when seeing the South Tower come down "Anyone who's ever watched a building being demolished on purpose knows that if you're going to do this, you have to get at the under infrastructure of a building and bring it down." No sooner had he said this and the reporter on the scene said he was just 4 blocks away and saw it clearly, it was a pancake collapse. (I'll dig out my copy of this news footage shortly and put in the exact quote as well as the name of the reporter)
For those interested. Here is the Perl script I wrote to do the math. The blog HMTL editor makes a mess of the formating but anyone who knows Perl should be able to repair it easy enough.
sub lead_ball_tower {
my $start_velocity = 0;
my $total_balls = 110;
my $initial_balls_falling = 17;
my $balls_stationary = $total_balls - $initial_balls_falling;
my $height = 1368; # (1368 feet)
my $partial_fall_height = $height/$total_balls;
print "Total balls = $total_balls Initial balls falling = $initial_balls_falling ";
print "Total height = $height ft Partial fall height = $partial_fall_height ft ";
print "Time = ";
$time = &fall_time($partial_fall_height, $start_velocity, $initial_balls_falling, $balls_stationary, $initial_balls_falling);
print " = $time secs";
}
sub fall_time { # calculate the time to fall to the next ball given the start velocity
my ($fall_height, $start_velocity, $balls_falling, $balls_stationary, $initial_balls_falling) = @_;
my $gravity = 32.2; # (32.2 ft/sec2)
my $end_velocity = sqrt($start_velocity**2 + 2*$gravity*$fall_height);
my $time = 2*$fall_height / ($start_velocity + $end_velocity);
print "+ $time ";
if ($balls_stationary == 0) { print "(free fall) "};
if ($balls_stationary > 0) {
$end_velocity = $end_velocity * $balls_falling / ($balls_falling+1); # conservation of momentum
$balls_stationary--;
$balls_falling++;
$time = $time + &fall_time($fall_height, $end_velocity, $balls_falling, $balls_stationary, $initial_balls_falling);
} elsif ($initial_balls_falling > 1) {
$initial_balls_falling--;
$time = $time + &fall_time($fall_height, $end_velocity, $balls_falling, $balls_stationary, $initial_balls_falling);
}
return $time;
}
posted by War On Suckers at 1:04 PM
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