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 0–25 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 = 2.4–2.8 for mhead = 5–7 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 5–7 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?|
Ahead to Constraints on Θcl
Back to Intro to Constraints
Back to Physics of the Head Shot