Regarding your comments, Warren...Free wrote:Please stop pretending that there was ever a discussion seeking a specualtive hypothesis.

That is entirely your fabrication.

bobk wrote:I said I was trained as an engineer and that's how we go about finding the truth. We ask a question, collect observations, propose hypotheses, and explore those hypotheses to see which ones are more or less likely to account for those observations.

For me, that's the gold standard for finding the truth in any matter. If you don't want to do that, then all we've got are our opinions.

Free wrote:You are equating the amount of effort you have put into the physics of 9/11 as the gold standard?

Please read what I said again, and you'll see that I was saying that the Scientific Method (question, observe, hypothesize, test) is the gold standard. That's the method ... and it

is the gold standard. I never said that I equated my efforts in the physics of 9/11 (which have been minimal) with that gold standard. But I was proposing that we try to apply that method to see where it leads us. But as with Tad, I'm not going to waste much of my time if you're not open to the possibility that you're wrong.

Regarding the Video ...Free wrote:The observed and measured speed at which WTC7 collapses.

...

You can find more at

http://ae911truth.org/ Save yourself the work of a thousand experts in the field.

Warren, out of respect for you (and the scientific method) I watched that video several times. I paid particular attention to the graph which appears to be the main supporting evidence provided:

- Building7_slope_0.png (105 KiB) Viewed 2282 times

I looked into the slope (green line) that they drew on top the data points. I started by calibrating the pixel values on the screen with the engineering units shown on the graph. I used the far corners of the plot (0,0) and (5,-35) to get the most accurate measurement. I've included the detailed notes of the calibration below. Here's a picture of the calibration points:

- Building7_slope_1.png (114.67 KiB) Viewed 2282 times

From that calibration, I was able to calculate the slope of the line that they drew and found that it indeed reflected an acceleration greater than the speed of gravity. In my calculation from that line, I got an acceleration of 9.927 (greater than the standard of 9.81 that we used in college). But then I asked myself what would an acceleration of

less than 9.81 look like on that same graph. So I plugged a lower value (9.80) back into the equations and re-drew the line for that acceleration (see Java program attached below). I plotted the two alternately (one with "Gravity" greater than 9.81 and one with it less than 9.81) and combined them in an animated GIF. The result is shown directly below.

Please watch this animation carefully for at least 10 seconds and watch as the two red lines alternate between the two different accelerations ("Gravity > 9.81" and "Gravity < 9.81"). You'll see that they're both about the same line, and it's hard to claim that one of them represents the data so much better than the other - especially given the spread of the data points. Here's the animation:
- Building7_slope_4ab.gif (88.5 KiB) Viewed 2281 times

The red lines (that switch about once every second) show the results of the velocity with the acceleration ("Gravity") both greater than and less than 9.81. You'll see that the difference between falling at an acceleration greater than or less than gravity is not all that different (in fact, you have to look carefully to see the lines change). Remember that the fat green line they drew to give them the "smoking gun" acceleration, was simply drawn through a bunch of points which were taken from a video camera. Look at those points. How accurate do you think they are? And given the dispersion of those points, do you think that one of those red lines is so much better than the other line that it justifies an entire conspiracy theory? I'm sorry, but that graph is not the "smoking gun" that they claim it is.

Here's a quote from the video:

Buildings cannot fall at freefall through themselves because even a weakened building requires energy to break up the pieces, crush the concrete and push things around. When the falling building pushes things, the fall is not free. The things push back and the reaction forces will measurably slow the descent of the building. This is why one would reasonably expect crumbling structures to come down in a tumbling, halting, irregular manner. In short, the evidence is clear. We are witnessing not the collapse of a building, but it's demolition. And we have received not a report from an independent scientific investigation, but a cover up by a government agency.

That's pretty strong language for a line that could be drawn with 4 pixels of difference and give a totally different conclusion. Additionally, if you look at the actual data points (which are difficult to see because they're partially covered up with their green line), you'll see that those data points are all over the place. Between some of the points, the building seems to be accelerating slower than the acceleration of gravity. But between other points, the building seems to be accelerating

faster than the acceleration of gravity. How can that be? Are they hypothesizing that something is "pushing" or "pulling" the building down? Where would that force come from? I suggest that these "super gravitational" accelerations are simply showing the large margins of error in their data.

This is a classic case of "Garbage In / Garbage Out". The data they took was not accurate enough to support the conclusions that they drew. You can see that by the variations of the individual data points and how sensitive the result is to simply drawing a slightly different line through the data points (only 4 pixels of difference made a significant difference in the outcome). This kind of sloppy work does not set a good example for Mr. Chandler's students. Consequently, I suggest that Mr. Chandler be reassigned to teaching in the school's Video Arts and Drama program (where he's amply qualified) and stay away from teaching Physics and Mathematics.

Supporting Notes, Software, Numbers ...Detailed Notes on Calibration

From the figure, we can calculate engineering units (velocity and time) from the pixel values on the graph. But first we have to calibrate the pixel values with the engineering units. We start by taking two points from the graph and relate the engineering units (shown with decimal points) with pixel coordinates (shown as integers without decimal points):

From the upper left corner we get:

EQ1: (0.0,0.0) = (100,32)

From the lower right corner we get:

EQ2: (5.0,-35.0) = (585,471)

Therefore, converting pixels (capital letters X and Y) to engineering units (lower case x and y) we get:

In x we use the standard point-slope forumla:

EQ3: x = mX + b

We substitute our known relationships for our corners to create two simultaneous equations:

EQ4: 0.0 = 100m + b

EQ5: 5.0 = 585m + b

We solve the first equation for the intercept (b):

EQ6: b = -100m

We substitute that into the second equation and solve for the slope (m):

EQ7: 5.0 = 585m -100m

EQ8: 5.0 = m (585-100)

EQ9: m = 5.0 / 485

We substitute the slope back into EQ6 to find the intercept:

EQ10: b = -100m = -500 / 485

Therefore:

EQ11: x = (5.0/485) X - (500/485)

In y we repeat the process again starting with the standard point-slope forumla:

EQ14: y = mY + b

We substitute our known relationships for our corners to create two simultaneous equations:

EQ15: 0.0 = 32m + b

EQ16: -35.0 = 471m + b

We solve the first equation for the intercept (b):

EQ17: b = -32m

We substitute that into the second equation and solve for the slope (m):

EQ18: -35.0 = 471m - 32m

EQ19: -35.0 = m (471-32)

EQ20: m = -35.0 / 439

We substitute the slope back into EQ17 to find the intercept:

EQ21: b = -32m = -32 ( -35 / 439 ) = 1120 / 439

Therefore:

EQ22: y = (-35/439) Y - (32/439)

Taken together:

EQ23: x = (5/485) X - (500/485)

EQ24: y = (-35/439) Y + (1120/439)

This gives us a way to use pixel values (X,Y) from the graph to calculate engineering values (x,y) to use for further calculations. As a check, here are some of the corresponding pixel values converted to engineering units on the graph:

Pixel values: (100,32) gives engineering units of (0.0,0.0)

Pixel values: (585,471) gives engineering units of (5.0,-35.0)

Java Program to Perform Calculationsimport java.io.*;

import java.util.*;

public class free_fall_graph {

public static double X_to_x ( int X ) {

// EQ23: x = (5/485) X - (500/485)

double x = ( (((double)5.0)/((double)485.0)) * X ) - (((double)500.0)/((double)485.0));

return x;

}

public static double Y_to_y ( int Y ) {

// EQ24: y = (-35/439) Y + (1120/439)

double y = ( (((double)-35.0)/((double)439.0)) * Y ) + (((double)1120.0)/((double)439.0));

return y;

}

public static double x_to_X ( double x ) {

// EQ23: x = (5/485) X - (500/485)

// So x + (500/485) = (5/485) X

// And X = ( x + (500/485) ) / (5/485)

double X = ( x + ((double)500.0/(double)485.0) ) / ((double)5.0/(double)485.0);

return X;

}

public static double rnd ( double d, int n ) {

double v = d;

for (int i=0; i<n; i++) v = v * 10.0;

v = java.lang.Math.round(v);

for (int i=0; i<n; i++) v = v / 10.0;

return ( v );

}

public static void main ( String args[] ) {

int X, Y;

double x, y;

// Test the upper left corner of the plot (should be 0,0)

X = 100; Y = 32;

x = X_to_x ( X );

y = Y_to_y ( Y );

System.out.println ( "Pixel values: (" + X + "," + Y + ") gives engineering units of (" + rnd(x,3) + "," + rnd(y,3) + ")" );

// Test the lower right corner of the plot (should be 5,-35)

X = 585; Y = 471;

x = X_to_x ( X );

y = Y_to_y ( Y );

System.out.println ( "Pixel values: (" + X + "," + Y + ") gives engineering units of (" + rnd(x,3) + "," + rnd(y,3) + ")" );

// Test the point at (2,-10)

X = 296; Y = 158;

x = X_to_x ( X );

y = Y_to_y ( Y );

System.out.println ( "Pixel values: (" + X + "," + Y + ") gives engineering units of (" + rnd(x,3) + "," + rnd(y,3) + ")" );

// Now produce the slope of the graph

int X0, Y0, X1, Y1;

double x0, y0, x1, y1;

X0 = 162; Y0 = 32;

X1 = 504; Y1 = 471;

x0 = X_to_x ( X0 );

y0 = Y_to_y ( Y0 );

x1 = X_to_x ( X1 );

y1 = Y_to_y ( Y1 );

System.out.println ( "x0,y0 = " + rnd(x0,3) + "," + rnd(y0,3) );

System.out.println ( "x1,y1 = " + rnd(x1,3) + "," + rnd(y1,3) );

double slope;

slope = (y1 - y0) / (x1 - x0);

System.out.println ( "The slope is " + rnd(slope,3) );

// Now solve for the X1 value that gives a slope of 9.81 (approximately gravity)

double x1g;

x1g = ( (y1 - y0) / -9.81 ) + x0;

System.out.println ( "The required x1 for g=-9.81 is " + rnd(x1g,3) + " instead of " + rnd(x1,3) );

System.out.println ( "Therefore the bottom pixel should be " + rnd(x_to_X(x1g),3) + " instead of " + rnd(X1,3) );

// Now solve for the X1 value that gives a slope of 9.80 (less than gravity)

double x1gm;

x1gm = ( (y1 - y0) / -9.80 ) + x0;

System.out.println ( "The required x1 for g=-9.80 is " + rnd(x1gm,3) + " instead of " + rnd(x1,3) );

System.out.println ( "Therefore the bottom pixel should be " + rnd(x_to_X(x1gm),3) + " instead of " + rnd(X1,3) );

}

}

Output from Running the Previous Java ProgramPixel values: (100,32) gives engineering units of (0.0,0.0)

Pixel values: (585,471) gives engineering units of (5.0,-35.0)

Pixel values: (296,158) gives engineering units of (2.021,-10.046)

x0,y0 = 0.639,0.0

x1,y1 = 4.165,-35.0

The slope is -9.927

The required x1 for g=-9.81 is 4.207 instead of 4.165

Therefore the bottom pixel should be 508.075 instead of 504.0

The required x1 for g=-9.80 is 4.211 instead of 4.165

Therefore the bottom pixel should be 508.429 instead of 504.0