Xaihe wrote:The strength of the supports did not actually play a role in the collapse, since the supports were essentially bypassed (stresed in ways they were not designed to handle). Given the design, those supports would have to have been many orders of magnitude stronger to slow down or even halt an ongoing collapse. So, the question still remains: how is the mass distribution relevant?
Bending supports or breaking joints would require energy. Since the only source would be the kinetic energy of the falling mass it would have to slow down to supply that energy. Let's see you build a physical model that can support itself but collapse with those being bypassed.
A data file with a 10 ton difference between levels is like this:
1,0,3895.0,0.0,12.0
1,0,3885.0,0.0,24.0
1,0,3875.0,0.0,36.0
1,0,3865.0,0.0,48.0
1,0,3855.0,0.0,60.0
1,0,3845.0,0.0,72.0
.
.
.
1,1,2865.0,0.0,1248.0
1,1,2855.0,0.0,1260.0
1,1,2845.0,0.0,1272.0
1,1,2835.0,0.0,1284.0
1,1,2825.0,0.0,1296.0
1,1,2815.0,0.0,1308.0
The first two fields are flags controlling the program, The third field is the weight in tons. The next field is velocity and the last is height. The file is upside down in that the lightest and highest for the simulated structure is at the bottom of the file.
The data file with an 11% difference between levels is like this:
1,0,36230.4028832,0.0,12.0
1,0,32640.0042368,0.0,24.0
1,0,29405.4093248,0.0,36.0
1,0,26491.3567808,0.0,48.0
1,0,23866.0880608,0.0,60.0
1,0,21500.9778272,0.0,72.0
1,0,19370.2496288,0.0,84.0
.
.
.
1,1,1.063356,0.0,1236.0
1,1,0.9610016,0.0,1248.0
1,1,0.86433,0.0,1260.0
1,1,0.779036,0.0,1272.0
1,1,0.6994,0.0,1284.0
1,1,0.63119,0.0,1296.0
1,1,0.5686,0.0,1308.0
The masses are all independent until they impact when they combine into a single mass with a new velocity based on the conservation of momentum.
This is the result for 10 ton steps:
Tower Array is Loaded with 109 Levels.
=================================================
Collision 1 at 1139.99817216 feet!!!
Mass @: 1140.02411448 ft. hit Mass @: 1140.0 ft. at: 0.864 sec.
2945.0 tons traveling: 27.75408 ft/sec hit 2955.0 tons moving at: 0.0 ft/sec
New mass is: 5900.0 tons moving: 13.8535195932 ft/sec
=================================================
Collision 2 at 1127.99202059 feet!!!
Mass @: 1128.01508422 ft. hit Mass @: 1128.0 ft. at: 1.399 sec.
5900.0 tons traveling: 31.0269595932 ft/sec hit 2965.0 tons moving at: 0.0 ft/sec
New mass is: 8865.0 tons moving: 20.6496403384 ft/sec
=================================================
Collision 3 at 1123.56033432 feet!!!
Mass @: 1123.603422 ft. hit Mass @: 1123.56823633 ft. at: 1.586 sec.
2935.0 tons traveling: 50.9736 ft/sec hit 8865.0 tons moving at: 26.6635603384 ft/sec
New mass is: 11800.0 tons moving: 32.710167661 ft/sec
=================================================
Collision 4 at 1115.99103556 feet!!!
Mass @: 1116.0215188 ft. hit Mass @: 1116.0 ft. at: 1.796 sec.
11800.0 tons traveling: 39.431607661 ft/sec hit 2975.0 tons moving at: 0.0 ft/sec
New mass is: 14775.0 tons moving: 31.4919100102 ft/sec
- - - - - - - - - - - - - - - - - - - - - - - -
Collision 107 at 23.9560787309 feet!!!
Mass @: 24.072225256 ft. hit Mass @: 24.0 ft. at: 11.972 sec.
357915.0 tons traveling: 160.051714258 ft/sec hit 3885.0 tons moving at: 0.0 ft/sec
New mass is: 361800.0 tons moving: 158.333082667 ft/sec
=================================================
Collision 108 at 11.9953237654 feet!!!
Mass @: 12.1513765335 ft. hit Mass @: 12.0 ft. at: 12.047 sec.
361800.0 tons traveling: 160.712922667 ft/sec hit 3895.0 tons moving at: 0.0 ft/sec
New mass is: 365695.0 tons moving: 159.001176994 ft/sec
=================================================
Collision 109 at 0.170591293936 feet!!!
Mass @: 0.302547524866 ft. hit Mass @: 0.2 ft. at: 12.121 sec.
365695.0 tons traveling: 161.348856994 ft/sec hit 0.1 tons moving at: 0.0 ft/sec
New mass is: 365695.1 tons moving: 161.348812873 ft/sec
Mass: # 109 hit the ground at 12.123 sec
365695.1 tons at: 161.380972873 ft/sec
============== This is the result for 11% difference at each level: =================
Tower Array is Loaded with 109 Levels.
=================================================
Collision 1 at 1139.99817216 feet!!!
Mass @: 1140.02411448 ft. hit Mass @: 1140.0 ft. at: 0.864 sec.
2.206323 tons traveling: 27.75408 ft/sec hit 2.450838 tons moving at: 0.0 ft/sec
New mass is: 4.657161 tons moving: 13.1484535424 ft/sec
=================================================
Collision 2 at 1127.99734368 feet!!!
Mass @: 1128.02541125 ft. hit Mass @: 1128.0 ft. at: 1.411 sec.
4.657161 tons traveling: 30.7078135424 ft/sec hit 2.718099 tons moving at: 0.0 ft/sec
New mass is: 7.37526 tons moving: 19.3906698374 ft/sec
=================================================
Collision 3 at 1124.62314462 feet!!!
Mass @: 1124.66677632 ft. hit Mass @: 1124.62982724 ft. at: 1.565 sec.
1.99024 tons traveling: 50.29824 ft/sec hit 7.37526 tons moving at: 24.3433098374 ft/sec
New mass is: 9.3655 tons moving: 29.8589299545 ft/sec
=================================================
Collision 4 at 1115.98175774 feet!!!
Mass @: 1116.00155913 ft. hit Mass @: 1116.0 ft. at: 1.82 sec.
9.3655 tons traveling: 38.0275699545 ft/sec hit 3.019478 tons moving at: 0.0 ft/sec
New mass is: 12.384978 tons moving: 28.756385874 ft/sec
- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
Collision 107 at 23.9794770425 feet!!!
Mass @: 24.0228671687 ft. hit Mass @: 24.0 ft. at: 20.218 sec.
296729.174731 tons traveling: 63.8970037363 ft/sec hit 32640.0042368 tons moving at: 0.0 ft/sec
New mass is: 329369.178968 tons moving: 57.5649040565 ft/sec
=================================================
Collision 108 at 11.9756128596 feet!!!
Mass @: 12.0151422233 ft. hit Mass @: 12.0 ft. at: 20.416 sec.
329369.178968 tons traveling: 63.9004240565 ft/sec hit 36230.4028832 tons moving at: 0.0 ft/sec
New mass is: 365599.581851 tons moving: 57.5679821641 ft/sec
=================================================
Collision 109 at 0.169207168816 feet!!!
Mass @: 0.202237439797 ft. hit Mass @: 0.2 ft. at: 20.611 sec.
365599.581851 tons traveling: 63.8070221641 ft/sec hit 0.1 tons moving at: 0.0 ft/sec
New mass is: 365599.681851 tons moving: 63.8070047114 ft/sec
Mass: # 109 hit the ground at 20.614 sec
365599.681851 tons at: 63.8713247114 ft/sec
So mass distribution alone changed the time from 12 seconds to 20 seconds.
psik