by einsteen on Thu Sep 25, 2008 9:44 pm
I think it is good you posted it, I get this using a near identical method as the last set of data.
Based on height=174 meter
t,y(t)
------------------------------
0.02,0.737149312747129
0.04,0.737149312747129
0.06,0.737149312747129
0.08,0.737149312747129
0.1,0.737149312747129
0.12,0.737149312747129
0.14,0.737149312747129
0.16,0.737149312747129
0.18,0.737149312747129
0.2,0.737149312747129
0.22,0.737149312747129
0.24,0.737149312747129
0.26,0.737149312747129
0.28,0.737149312747129
0.3,0.737149312747129
0.32,0.737149312747129
0.34,0.737149312747129
0.36,0.737149312747129
0.38,0.737149312747129
0.4,0.737149312747129
0.42,0.737149312747129
0.44,0.737149312747129
0.46,0.737149312747129
0.48,0.737149312747129
0.5,0.737149312747129
0.52,0.737149312747129
0.54,0.737149312747129
0.56,0.737149312747129
0.58,0.982865750329505
0.6,0.737149312747129
0.62,0.982865750329505
0.64,0.982865750329505
0.66,0.982865750329505
0.68,0.982865750329505
0.7,0.982865750329505
0.72,0.982865750329505
0.74,0.982865750329505
0.76,0.982865750329505
0.78,0.982865750329505
0.8,0.982865750329505
0.82,0.982865750329505
0.84,0.982865750329505
0.86,0.982865750329505
0.88,0.982865750329505
0.9,1.22858218791188
0.92,0.982865750329505
0.94,1.22858218791188
0.96,1.22858218791188
0.98,1.22858218791188
1,1.22858218791188
1.02,1.47429862549426
1.04,1.22858218791188
1.06,1.47429862549426
1.08,1.47429862549426
1.1,1.72001506307663
1.12,1.72001506307663
1.14,1.72001506307663
1.16,1.72001506307663
1.18,1.96573150065901
1.2,1.96573150065901
1.22,1.96573150065901
1.24,2.21144793824139
1.26,2.21144793824139
1.28,2.45716437582376
1.3,2.45716437582376
1.32,2.70288081340614
1.34,2.70288081340614
1.36,2.94859725098851
1.38,2.94859725098851
1.4,2.94859725098851
1.42,3.19431368857089
1.44,3.19431368857089
1.46,3.44003012615327
1.48,3.68574656373564
1.5,3.93146300131802
1.52,3.93146300131802
1.54,4.1771794389004
1.56,4.1771794389004
1.58,4.42289587648277
1.6,4.66861231406515
1.62,4.66861231406515
1.64,4.91432875164752
1.66,5.1600451892299
1.68,5.40576162681228
1.7,5.65147806439465
1.72,5.65147806439465
1.74,5.89719450197703
1.76,6.14291093955941
1.78,6.38862737714178
1.8,6.38862737714178
1.82,6.63434381472416
1.84,6.88006025230653
1.86,7.37149312747129
1.88,7.37149312747129
1.9,7.61720956505366
1.92,7.61720956505366
1.94,8.10864244021841
1.96,8.35435887780079
1.98,8.60007531538317
2,9.09150819054792
2.02,9.09150819054792
2.04,9.3372246281303
2.06,9.58294106571267
2.08,9.82865750329505
2.1,10.3200903784598
2.12,10.5658068160422
2.14,10.8115232536246
2.16,11.0572396912069
2.18,11.3029561287893
2.2,11.5486725663717
2.22,11.7943890039541
2.24,12.0401054415364
2.26,12.5315383167012
2.28,12.7772547542836
2.3,13.0229711918659
2.32,13.2686876294483
2.34,13.7601205046131
2.36,14.0058369421954
2.38,14.2515533797778
2.4,14.7429862549426
2.42,14.9887026925249
2.44,15.4801355676897
2.46,15.7258520052721
2.48,15.9715684428545
2.5,16.4630013180192
2.52,16.7087177556016
2.54,17.2001506307663
2.56,17.4458670683487
2.58,17.9372999435135
2.6,18.4287328186782
2.62,18.6744492562606
2.64,19.1658821314253
2.66,19.4115985690077
2.68,19.9030314441725
2.7,20.1487478817548
2.72,20.3944643193372
2.74,20.885897194502
2.76,21.1316136320844
2.78,21.8687629448315
2.8,22.1144793824139
2.82,22.6059122575786
2.84,23.0973451327434
2.86,23.3430615703257
2.88,23.8344944454905
2.9,24.3259273206552
2.92,24.5716437582376
2.94,25.0630766334024
2.96,25.8002259461495
2.98,26.0459423837319
3,26.2916588213143
3.02,26.783091696479
3.04,27.2745245716438
3.06,27.7659574468085
3.08,28.2573903219733
3.1,28.5031067595556
3.12,28.9945396347204
3.14,29.4859725098851
3.16,30.2231218226323
3.18,30.4688382602147
3.2,30.9602711353794
3.22,31.4517040105442
3.24,31.9431368857089
3.26,32.4345697608737
3.28,32.9260026360384
3.3,33.6631519487855
3.32,33.9088683863679
3.34,34.4003012615327
3.36,34.8917341366974
3.38,35.3831670118622
3.4,35.8745998870269
3.42,36.3660327621917
3.44,36.8574656373564
3.46,37.3488985125212
3.48,38.0860478252683
3.5,38.5774807004331
3.52,38.8231971380154
3.54,39.3146300131802
3.56,40.0517793259273
3.58,40.5432122010921
3.6,41.0346450762568
3.62,41.5260779514216
3.64,42.0175108265863
3.66,42.5089437017511
3.68,43.2460930144982
3.7,43.737525889663
3.72,44.2289587648277
3.74,44.7203916399925
3.76,45.2118245151572
3.78,45.703257390322
3.8,46.4404067030691
3.82,46.6861231406515
3.84,47.4232724533986
3.86,48.1604217661457
3.88,48.4061382037281
3.9,49.3890039540576
3.92,49.63472039164
3.94,50.1261532668047
3.96,50.8633025795519
3.98,51.3547354547166
4,52.0918847674638
4.02,52.5833176426285
4.04,53.0747505177933
4.06,53.566183392958
4.08,54.3033327057051
4.1,55.0404820184523
4.12,55.531914893617
4.14,56.0233477687818
4.16,56.7604970815289
4.18,57.2519299566937
4.2,57.7433628318584
maple:
1.885752215 - 5.29509154079076082 y + 4.46825429942136942 y^2
1.916029506 - 5.38017916952337494*y + 4.51854212045183168*y^2- .794436351192172493e-2*y^3
The 2nd or 3rd order curves fit well with the complete collapse(time) function, but that also increases its value around t=t_init, at t=t_init the acceleration is slower than the values maple's least squares gave. Perhaps 186/174 will compensate that...
Where's DBB ?
ps. I want to create a demo video to show how this primitive method gave the data.