25. Preconstraining with mhead, dsnap, tlurch, and vfrags

   These four variables in this group are related to each other, to the snap and lurch, but not directly to the group of variables most important to the lurch (Θcl, mcloud, vcloud, and PE). That allows us to consider the two groups separately. Because the first group relates to the snap, it may be thought of as preceding the lurch. We therefore use it to set the stage for the next group.
    We do this by determining which combinations of mhead and dsnap produce allowable values of tlurch and vfrags. (Recall that the allowable values for tlurch are 025 ms and for dsnap are >2.2 in.) Scenario SL6L was used for these calculations in order to fix the PE and to avoid dealing with Rbullet and Rhead, whose values are not well constrained. SL6A gave very similar results for default values of Rbullet and Rhead, and virtually the same constraints overall. 
    The results, as shown in the table below, are interesting and clear. Allowed values are shown in bold green, disallowed values in red. If any of dsnap, tlurch, or vfrags is disallowed, the entire combination is disallowed. The overall status of the combination is shown in the last column.
    The biggest feature of the table is that the allowed combinations of mhead and dsnap cluster near the middle. Except for the borderline combination of mhead = 4 and dsnap = 3.0, which we will not consider further, they comprise dsnap = 2.42.8 for mhead  = 57 lb, plus dsnap = 3.0 for mhead = 6 and 7 lb. There is also a single acceptable value of dsnap = 2.4 for mhead = 8. These combinations mean in essence that mhead is limited to 57 lb, which can greatly simplify the future calculations.
    All things considered, it is remarkable that physics can eliminate heads of 4, 8, 9, and 10 lb, but these results have been confirmed by other calculations, some of which are shown below. Based on these results, we should probably shift the default mhead from 7 to 6 lb.

mhead, lb dsnap, in tlurch, ms vfrags, ft s-1 Allowed?
4 2.2 31.8 188 No
  2.4 30.0 200 No
  2.6 28.1 213 No
  2.8 26.3 228 No
  3.0 24.4 246 Yes
5 2.2 26.7 224 No
  2.4 24.4 246 Yes
  2.6 22.1 272 Yes
  2.8 19.8 304 Yes
  3.0 17.4 344 Yes
6 2.2 21.6 277 No
  2.4 18.8 319 Yes
  2.6 16.0 374 Yes
  2.8 13.3 452 Yes
  3.0 10.5 573 Yes
7 2.2 16.5 363 No
  2.4 13.3 452 Yes
  2.6 10.0 599 Yes
  2.8 6.8 887 Yes
  3.0 3.5 1708 No
8 2.2 11.4 526 No
  2.4 7.7 780 Yes
  2.6 4.0 1508 No
  2.8 0.3 22,760 No
  3.0 -3.5 -1739 No
9 2.2 6.3 952 No
  2.4 2.1 2829 No
  2.6 -2.1 -2915 No
  2.8 -6.2 -962 No
  3.0 -10.4 -576 No
10 2.2 1.2 5033 No
  2.4 -3.5 -1739 No
  2.6 -8.1 -741 No
  2.8 -12.7 -471 No
  3.0 -17.3 -345 No

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