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The Impossible Fast Collapse of The Towers


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#106    jimv

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Posted 09 June 2011 - 11:29 AM

View PostLittle Fish, on 09 June 2011 - 10:54 AM, said:

I assume here since you don't describe, that you have calculated velocities after floor impacts using simple momentum equations. the numbers in column 6 (last but one column) look ball park figure correct using simple momentum equations for suspended in air storeys. also the height of a floor is 3.79 meters, not 3.0 meters.
you provide 6 columns of data but refer to 7 columns in your text.

what you have not accounted for is the loss in velocity due to kinetic energy drain during collision which has been calculated as 8.9 times more than the loss of velocity due to conservation of momentum.

factor that into your column 6 (last but one column) and what is your collapse time? I suspect you will have refuted your own argument.

Utter nonsense.  Kinetic energy lost was lost in the form of heat, you'll find that this amount almost exacly equals the difference in velocities squared time half the impacting mass.  And the velocity used to calculate kinetic energy lost in inelastic collisions...is derived from the velocity found from the conservation of momentum equations.  To have a different velocity due to kinetic energy drain as opposed to conservation of momentum (which you were big on not long ago) would violate the law of conservation of momentum.

Here's an idea.  You wanted numbers.  You got numbers.  Now why don't you show me where the kinetic energy goes.  Give me some numbers of your own devising.  Or....admit you're in to a depth so far over your head your ears are popping.

And anytime you make some absurd reference assume you're being held to a real engineer's standards.  We have to cite credible sources when we make an assertion, and the do the math to justify our use of said citation.  You've been asked over and over and have failed.

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#107    Little Fish

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Posted 09 June 2011 - 11:41 AM

View PostBr Cornelius, on 09 June 2011 - 11:26 AM, said:

It would seem that that figure has been plucked from thin air to justify a belief that a spontanious collapse could not have taken place.
that is very unkind.

it has been calculated.
"CALCULATION OF VELOCITY CHANGES DUE TO ENERGY DRAINS DURING THE COLLISION OF THE UPPER AND LOWER BLOCKS"
http://www.journalof...issingJolt7.pdf


Quote

A detailed analysis places the initial loss of energy from kinetic to heat as low as 6.7%, and this figure decreases at each successive impact;
I never mentioned "heat", neither does the above link.

"We do not consider energy losses due to vibration of the building, heat, and sound, during the initiating impulse, all of which would have required energy from the impulse to produce and thus have an additional effect on velocity loss"

so if we include a further velocity reduction due to generation of heat, then the velocity loss due to collision is actually greater than 8.9 times the velocity loss due to conservation of momentum.

Quote

Utter nonsense. Kinetic energy lost was lost in the form of heat, you'll find that this amount almost exacly equals the difference in velocities squared time half the impacting mass
you are saying it takes zero energy to buckle, deform, compress and break all those steel columns?

if the only energy loss is in the form of "heat", then where did the energy come from to break all the columns? I think again you might be in agreement with the "conspiracy theorists".

Edited by Little Fish, 09 June 2011 - 12:40 PM.


#108    Br Cornelius

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Posted 09 June 2011 - 01:39 PM

View PostLittle Fish, on 09 June 2011 - 11:41 AM, said:

that is very unkind.

it has been calculated.
"CALCULATION OF VELOCITY CHANGES DUE TO ENERGY DRAINS DURING THE COLLISION OF THE UPPER AND LOWER BLOCKS"
http://www.journalof...issingJolt7.pdf



I never mentioned "heat", neither does the above link.

"We do not consider energy losses due to vibration of the building, heat, and sound, during the initiating impulse, all of which would have required energy from the impulse to produce and thus have an additional effect on velocity loss"

so if we include a further velocity reduction due to generation of heat, then the velocity loss due to collision is actually greater than 8.9 times the velocity loss due to conservation of momentum.


you are saying it takes zero energy to buckle, deform, compress and break all those steel columns?

if the only energy loss is in the form of "heat", then where did the energy come from to break all the columns? I think again you might be in agreement with the "conspiracy theorists".

No the paper I linked to and Jimv both explained that this kinetic energy loss ends up as heat - it cannot do otherwise since it is lost and must be conserved as another form of energy - the lowest form of energy is always heat (thermodynamics).

The paper I linked to says the overall loss of kinetic energy - as heat is 6.7% of the system energy and falling thereafter. This could be the 8.9 times the loss due to momentum of redistribution, but what that proves is that that momentum loss (loss of velocity at each impact) is only 0.7% of the overall system energy, and heat loss are both tiny and insignificant in comparison to the increase in linear momentum imparted by gravity.

As for your last statement it shows your utter lack of knowledge of energy - buckling causes heating that is where the energy ends up. Try bending a pieces of metal repeatedly and feeling it after - its hot :tu:


Br Cornelius

Edited by Br Cornelius, 09 June 2011 - 01:59 PM.

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#109    flyingswan

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Posted 09 June 2011 - 02:35 PM

View PostLittle Fish, on 09 June 2011 - 11:41 AM, said:

it has been calculated.
"CALCULATION OF VELOCITY CHANGES DUE TO ENERGY DRAINS DURING THE COLLISION OF THE UPPER AND LOWER BLOCKS"
http://www.journalof...issingJolt7.pdf
There are glaring errors in that paper, an obvious problem if you do not have a peer-review process prior to publication.

They use the actual velocity (at less than 1g) after a drop of one floor as the measure of input energy.  However, the actual potential energy available corresponds to a 1g acceleration, so a lower velocity means that some of the energy has already gone into deforming the structure.

Secondly, they calculate the energy required to crush the floors above and below the drop and say that this must be instantaneously subtracted from the energy of the upper block to give their reduction in velocity at first impact.  However, in reality this energy is only absorbed as the drop continues for those two floors, by which time gravity has continued to act to increase the drop velocity.

They thus have incorrect values for both the amount of energy available and for the change in velocity, hence loss of kinetic energy, at first impact.

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#110    Br Cornelius

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Posted 09 June 2011 - 03:33 PM

It is my contention that there are compelling reasons to suspect that all is not as it seems regarding the twin towers attack, but the actual impact and collapse are not one of them and pursuing this line of inquiry is barking up the wrong tree :devil:

Br Cornelius

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#111    jimv

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Posted 09 June 2011 - 05:00 PM

Spreadsheet adjusted for average floor height of 3.79 meters or approximately 12 feet.  Time to ground impact:  13.573 seconds now.  Again, we're totally neglecting the minimal mass lost to pulverization that escapes vertical descent due to air compression (the dust you see) and aerodynamic drag, and of course the nugatory time associated with   Did you think that adding .79 meters per floor would increase the collapse time by roughly 27%???  Nope.  The increased space between floors gives the falling mass more time to accelerate unimpeded without having to transfer momentum.  Hence the difference amounted to about 1.6 seconds total.  About a 13% difference from my rough dimensions in the original model.

Oh, in the original, I did have a 7th column but didn't copy it.  It was a dummy column for outputs of an iterative logic loop to ensure the distance traveled was 3.79 meters (within .02 meters).  I used this instead of a quadratic to plug in time intervals that would satisfy the distance equation of motion.

The sheet below shows in 1: mass  2: velocity the instant before impact  3: (duh) 4: velocity after impact  5: Delta V  6: Time between successive impacts  7:  Total time elapsed.  If you want the iterative column and the code to satisfy some morbid curiosity, I can of course provide them as well.

As for the energy loss due to buckling, shearing, etc...since energy is conserved, as Cornelius mentioned, it becomes heat and acoustic energy (primarily heat of course.)

Edit, just perused the amateur paper linked.  The assumption of flow is erroneous first off.  Even if flow happened very briefly, and a portion of a lower floor failed, the failure would propagate in short order to catastrophic total failure in extremely short order due to the nature of the supports.  The redundancies in velocity calculations are also completely amateurish.  As stated earlier...reputable sources.  Some kids who clearly haven't made it out of undergrad vs say...scholars from Northwestern, one of the most reputable schools in the nation (who's findings WERE reviewed)...would not be considered credible...ever.  Just because it looks good to you, does not mean that it is.  That paper looks like my sophomore year lab reports (only I would have obtained the right results.)  Yah, I'd bet on the team from Northwestern.

Mass Velocity (initial) m/s g new velocity Velocity Dif time/floor total time
3 8.62 9.8 6.47 2.16 0.880 0.880
4 10.78 9.8 8.62 2.16 0.440 1.320
5 12.19 9.8 10.16 2.03 0.364 1.684
6 13.32 9.8 11.42 1.9 0.323 2.007
7 14.3 9.8 12.51 1.79 0.294 2.301
8 15.2 9.8 13.51 1.69 0.274 2.575
9 16.03 9.8 14.43 1.6 0.257 2.832
10 16.8 9.8 15.27 1.53 0.242 3.074
11 17.53 9.8 16.07 1.46 0.231 3.305
12 18.24 9.8 16.84 1.4 0.221 3.526
13 18.91 9.8 17.56 1.35 0.212 3.738
14 19.56 9.8 18.26 1.3 0.204 3.942
15 20.19 9.8 18.93 1.26 0.197 4.139
16 20.8 9.8 19.58 1.22 0.191 4.330
17 21.39 9.8 20.2 1.19 0.185 4.515
18 21.96 9.8 20.81 1.16 0.180 4.695
19 22.52 9.8 21.4 1.13 0.175 4.870
20 23.07 9.8 21.97 1.1 0.171 5.041
21 23.6 9.8 22.53 1.07 0.166 5.207
22 24.13 9.8 23.08 1.05 0.163 5.370
23 24.63 9.8 23.61 1.03 0.159 5.529
24 25.13 9.8 24.12 1.01 0.155 5.684
25 25.61 9.8 24.63 0.99 0.152 5.836
26 26.1 9.8 25.13 0.97 0.150 5.986
27 26.57 9.8 25.62 0.95 0.147 6.133
28 27.03 9.8 26.1 0.93 0.144 6.277
29 27.48 9.8 26.57 0.92 0.141 6.418
30 27.93 9.8 27.03 0.9 0.139 6.557
31 28.37 9.8 27.48 0.89 0.137 6.694
32 28.81 9.8 27.93 0.87 0.135 6.829
33 29.24 9.8 28.38 0.86 0.133 6.962
34 29.66 9.8 28.81 0.85 0.131 7.093
35 30.08 9.8 29.24 0.84 0.129 7.222
36 30.49 9.8 29.66 0.82 0.127 7.349
37 30.89 9.8 30.08 0.81 0.125 7.474
38 31.29 9.8 30.49 0.8 0.124 7.598
39 31.68 9.8 30.89 0.79 0.122 7.720
40 32.07 9.8 31.29 0.78 0.120 7.840
41 32.45 9.8 31.68 0.77 0.119 7.959
42 32.84 9.8 32.07 0.76 0.118 8.077
43 33.21 9.8 32.45 0.75 0.116 8.193
44 33.58 9.8 32.83 0.75 0.115 8.308
45 33.94 9.8 33.2 0.74 0.113 8.421
46 34.31 9.8 33.58 0.73 0.113 8.534
47 34.67 9.8 33.95 0.72 0.111 8.645
48 35.02 9.8 34.31 0.71 0.110 8.755
49 35.38 9.8 34.67 0.71 0.109 8.864
50 35.73 9.8 35.03 0.7 0.108 8.972
51 36.08 9.8 35.38 0.69 0.107 9.079
52 36.42 9.8 35.74 0.69 0.106 9.185
53 36.75 9.8 36.07 0.68 0.104 9.289
54 37.09 9.8 36.42 0.67 0.104 9.393
55 37.43 9.8 36.76 0.67 0.103 9.496
56 37.76 9.8 37.1 0.66 0.102 9.598
57 38.09 9.8 37.43 0.66 0.101 9.699
58 38.41 9.8 37.76 0.65 0.100 9.799
59 38.73 9.8 38.08 0.65 0.099 9.898
60 39.04 9.8 38.4 0.64 0.098 9.996
61 39.36 9.8 38.73 0.63 0.098 10.094
62 39.68 9.8 39.05 0.63 0.097 10.191
63 39.99 9.8 39.37 0.62 0.096 10.287
64 40.3 9.8 39.68 0.62 0.095 10.382
65 40.61 9.8 39.99 0.62 0.095 10.477
66 40.91 9.8 40.3 0.61 0.094 10.571
67 41.21 9.8 40.61 0.61 0.093 10.664
68 41.51 9.8 40.91 0.6 0.092 10.756
69 41.81 9.8 41.21 0.6 0.092 10.848
70 42.1 9.8 41.51 0.59 0.091 10.939
71 42.39 9.8 41.8 0.59 0.090 11.029
72 42.69 9.8 42.1 0.58 0.090 11.119
73 42.97 9.8 42.39 0.58 0.089 11.208
74 43.27 9.8 42.69 0.58 0.089 11.297
75 43.55 9.8 42.98 0.57 0.088 11.385
76 43.83 9.8 43.26 0.57 0.087 11.472
77 44.11 9.8 43.55 0.57 0.087 11.559
78 44.39 9.8 43.83 0.56 0.086 11.645
79 44.67 9.8 44.11 0.56 0.086 11.731
80 44.95 9.8 44.39 0.55 0.085 11.816
81 45.23 9.8 44.67 0.55 0.085 11.901
82 45.5 9.8 44.95 0.55 0.084 11.985
83 45.77 9.8 45.23 0.54 0.084 12.069
84 46.04 9.8 45.5 0.54 0.083 12.152
85 46.31 9.8 45.77 0.54 0.083 12.235
86 46.58 9.8 46.04 0.54 0.082 12.317
87 46.85 9.8 46.31 0.53 0.082 12.399
88 47.11 9.8 46.58 0.53 0.081 12.480
89 47.37 9.8 46.84 0.53 0.081 12.561
90 47.63 9.8 47.11 0.52 0.080 12.641
91 47.89 9.8 47.37 0.52 0.080 12.721
92 48.14 9.8 47.63 0.52 0.079 12.800
93 48.4 9.8 47.88 0.51 0.079 12.879
94 48.66 9.8 48.15 0.51 0.079 12.958
95 48.91 9.8 48.4 0.51 0.078 13.036
96 49.17 9.8 48.66 0.51 0.078 13.114
97 49.41 9.8 48.91 0.5 0.077 13.191
98 49.66 9.8 49.16 0.5 0.077 13.268
99 49.92 9.8 49.42 0.5 0.077 13.345
100 50.16 9.8 49.67 0.5 0.076 13.421
101 50.41 9.8 49.92 0.49 0.076 13.497
102 50.66 9.8 50.17 0.49 0.076 13.573

Edited by jimv, 09 June 2011 - 05:16 PM.

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#112    Little Fish

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Posted 09 June 2011 - 06:03 PM

View PostBr Cornelius, on 09 June 2011 - 01:39 PM, said:

The paper I linked to says the overall loss of kinetic energy - as heat is 6.7% of the system energy and falling thereafter. This could be the 8.9 times the loss due to momentum of redistribution, but what that proves is that that momentum loss (loss of velocity at each impact) is only 0.7% of the overall system energy, and heat loss are both tiny and insignificant in comparison to the increase in linear momentum imparted by gravity.
What you are referring to here is not the "overall loss of kinetic energy" but the loss of kinetic energy due to conservation of momentum. check greenings equations, they are just simple momentum equations rearranged in unconventional format, these equations are the same as jimv has used (we have to assume that since he has not revealed his equations). if that is all that is being considered then you are modelling a series of Ali Baba floating slabs/carpets whose magical lift properties disappear at impact.
The loss of kinetic energy due to buckling of columns and beams, deformation etc (App D) is 8.9 times higher than the loss of kinetic energy due to conservation of momentum (App E), as calculated in Appendix D and Appendix E:
http://www.journalof...issingJolt7.pdf

To underline the point of your misunderstanding and state in non mathematics terms which you find so confusing, you said this:
"A detailed analysis places the initial loss of energy from kinetic to heat as low as 6.7%, and this figure decreases at each successive impact;"

By claiming that this statement represents the entire kinetic energy loss from the system, you are thus claiming here it requires less energy to destroy the more massive bottom floor than it does the less massive floor near the top.

Quote

As for your last statement it shows your utter lack of knowledge of energy - buckling causes heating that is where the energy ends up. Try bending a pieces of metal repeatedly and feeling it after - its hot :tu:
I don't know what you think you have demonstrated here, other than your usual caustic brand of ad hominem and preference for adjectives over facts. It matters not where the "energy ends up", what matters is that energy is subtracted from the kinetic energy, which results in a further decrease in velocity (in addition to the velocity loss from conservation of momentum).

Edited by Little Fish, 09 June 2011 - 06:13 PM.


#113    Br Cornelius

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Posted 09 June 2011 - 06:15 PM

View PostLittle Fish, on 09 June 2011 - 06:03 PM, said:

What you are referring to here is not the "overall loss of kinetic energy" but the loss of kinetic energy due to conservation of momentum. check greenings equations, they are just simple momentum equations rearranged in unconventional format, these equations are the same as jimv has used (we have to assume that since he has not revealed his equations). if that is all that is being considered then you are modelling a series of Ali Baba floating slabs/carpets whose magical lift properties disappear at impact.
The loss of kinetic energy due to buckling of columns and beams, deformation etc (App D) is 8.9 times higher than the loss of kinetic energy due to conservation of momentum (App E), as calculated in Appendix D and Appendix E:
http://www.journalof...issingJolt7.pdf

To underline the point of your misunderstanding and state in non mathematics terms which you find so confusing, you said this:
"A detailed analysis places the initial loss of energy from kinetic to heat as low as 6.7%, and this figure decreases at each successive impact;"

By claiming that this statement represents the entire energy loss from the system, you are thus claiming here it requires less energy to destroy the more massive bottom floor than it does the less massive floor near the top.

I don't know what you think you have demonstrated here, other than your usual caustic brand of ad hominem. It matters not where the "energy ends up", what matters is that energy is subtracted from the kinetic energy, which results in a further decrease in velocity (in addition to the velocity loss from conservation of momentum).

What I demonstrated here is that you have no understanding of what energy does when it is transformed - you did not account for what the transformation of energy actually was - kinetic > heat. As such you showed a lack of basic understanding of conservation of energy and of energy transformation. With such a basic lack of understanding I refuse to believe that you actually have the slightest idea what you are talking about.

As to the rest - I will come back to it :tu:

One small observation - you are still not seeing that the debris is accumulating with the fall causing both an increase in mass and speed. Your objection that it would take more energy/momentum to crush the lower floors is indeed correct and that is exactly what is happening - both the velocity and mass are increasing and so the momentum is also increasing. If this is not true then where is the missing mass as each floor compounds into the debris load ?

I think the issue with their assumptions is that the structure is acting as a spring load to resist kinetic energy delivered by the fall. I will have to defer to an engineer as to whether this is a valid assumption and whether their estimates are reasonable.
It seems that the initial elastic resistance of the columns had been severely compromised by heat stress due to the fires and so there would have been much reduced elastic resistance to the initial floor drop. Once the initial floor collapse took place gravity driven momentum took over. It also has to be asked, under such a massive load - what was the potential for elastic rebound rather than plastic deformation to take place ?

Br Cornelius

Edited by Br Cornelius, 09 June 2011 - 07:13 PM.

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Robert Anton Wilson

#114    The Silver Thong

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Posted 09 June 2011 - 06:26 PM

View PostQ24, on 05 June 2011 - 12:14 AM, said:



You take these guys seriously?



Not really as I just don't believe the official version of events. Even after reading these threads for years I am not convinced of the official report. It does not add up as some seem to think. There is far more to 9/11 IMO.

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#115    Little Fish

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Posted 09 June 2011 - 06:31 PM

View PostBr Cornelius, on 09 June 2011 - 06:15 PM, said:

If this is not true then where is the missing mass as each floor compounds into the debris load ?
look at the videos of the collapse, do you observe all the mass accumulating underneath the top block, or do you see something else?
look at pictures of the aftermath, do you observe a square pile of debris fitting the buildings footprint, or do you see something else?


#116    Br Cornelius

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Posted 09 June 2011 - 06:54 PM

View PostLittle Fish, on 09 June 2011 - 06:31 PM, said:

look at the videos of the collapse, do you observe all the mass accumulating underneath the top block, or do you see something else?
look at pictures of the aftermath, do you observe a square pile of debris fitting the buildings footprint, or do you see something else?
The majority remained in the drop zone. The mass reduced to dust was blown out by the compressive air force blast. Dust only represents a small fraction of the overall mass.

Br Cornelius

Edited by Br Cornelius, 09 June 2011 - 06:54 PM.

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#117    Br Cornelius

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Posted 09 June 2011 - 06:56 PM

View PostThe Silver Thong, on 09 June 2011 - 06:26 PM, said:

Not really as I just don't believe the official version of events. Even after reading these threads for years I am not convinced of the official report. It does not add up as some seem to think. There is far more to 9/11 IMO.
As I said I am inclined to agree with you - but the mechanism for collapse is entirely credible from an engineering point of view and a controlled blast just doesn't account for the actual evidence of a progressive compression from the point of impact (which could not be predicted before the crash).

Br Cornelius

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#118    jimv

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Posted 09 June 2011 - 11:55 PM

View PostLittle Fish, on 09 June 2011 - 06:03 PM, said:

What you are referring to here is not the "overall loss of kinetic energy" but the loss of kinetic energy due to conservation of momentum. check greenings equations, they are just simple momentum equations rearranged in unconventional format, these equations are the same as jimv has used (we have to assume that since he has not revealed his equations)

By claiming that this statement represents the entire kinetic energy loss from the system, you are thus claiming here it requires less energy to destroy the more massive bottom floor than it does the less massive floor near the top.

I don't know what you think you have demonstrated here, other than your usual caustic brand of ad hominem and preference for adjectives over facts. It matters not where the "energy ends up", what matters is that energy is subtracted from the kinetic energy, which results in a further decrease in velocity (in addition to the velocity loss from conservation of momentum).

My math is easy, I mean easy to check for anyone who knows the first thing about engineering.  You don't recognize s=s(0)+v(0)*t+1/2*a*t^2??  Or maybe conservation of momentum?  If you had the first clue, you could have backwards engineered it in 3 minutes.  Time periods, as I stated were found with an iterative loop.  The rest is high school physics material.  You've been asked to demonstrate at least a shred of real physical and mathematical competency, so that we might see you can at least decipher total bunk amateur engineering and poor modeling from the real deal.  You haven't.  This is just further testimony to your ineptitude.  This is why you're giving us Bob from youtube and two students with a paper that might get a B for effort and a D for results and citing it like it's gospel.  Because you don't know enough to know better.

You don't double model a velocity reduction lol.  That's why those people are total amateurs. They might be using many of the right equations, but they make the wrong modeling assumptions.  The velocity lost between pre and post impact instants in conservation of momentum is noteable, and that's your kinetic energy drop.  You don't then take that drop and reverse engineer to find the velocity using balance of kinetic energy and then subtract that velocity as well.  It's like saying horse is pushing the cart and the cart is pulling the horse because the horse is pushing it.  It's nonsense.

  The assumption that buckling took nearly as much energy as posited in the amateur paper.  The flanges and brackets and webs supporting lower floors (where anyone who knows structural FMEA would attest) are where failure occurs.  Before impact, these serve only to resist the floor's static weight times a small (surprisingly so frankly) FOS.  Basically, you could say they balance the floor's moment of inertia.  The velocity drop found in the momentum transfer equations is associated with overcoming inertia.  (In laymen's vernacular, the energy it takes to get something to move or move faster.)  Since the inertia of impacted floors is previously counteracted by the aforementioned supports (duh, otherwise there would be no building at all) it logically follows that the difference in velocity found in the momentum equations when applied to a kinetic energy balance is harmonious with that required to overcome inertia times a factor of safety or cause inelastic failure of support structure (they are one and the same).

The floors on the bottom are not so large at the bottom that they need to be modeled differently, and again, give the points of failure, while some more energy is required to get the job done, you'd say that this bears out using the momentum velocity and new mass changes in a balance of energy equation.

And neglecting heat transfer in support members and successively lowered elastic moduli...yah, that's just wrong too.

Look, as Cornelius suggested, there are other aspects of 9/11 that might be more debatable.  I don't buy a bit of it, but its at least more kind to speculation.  The science here doesn't lie, and placing explosives in a building so that its collapse is in agreement with sound engineering  employed as a result of plane crashes would require a time machine and a team of geniuses.  One could argue whether or not these planes were really hijacked by terrorists etc (in my opinion total, complete, disrespectful BS) but you'd have more of a leg to stand on that you do debating science that you don't understand.

"Fat, drunk and stupid is no way to go through life, son - two of the 3 is acceptable however.

#119    Fanto

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Posted 10 June 2011 - 02:17 AM

Would people be asking these questions about 911 if Obama had been president during it?


#120    aquatus1

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Posted 10 June 2011 - 02:27 AM

Are you kidding?  This is the only time engineers have ever had the chance to study the collapse of a skyscraper.  It is a goldmine of information!  Yes, engineers would have been all over it, regardless of who was the president.





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