29. Constraints on mcloud and vcloud from mcloud and vcloud
The previous section has shown the constraints arising for
vlurch and vcloud that arise by varying Θcl
and PE. But those calculations leave mcloud fixed. Here
we take a more general look at mcloud and vcloud
by varying them both and examining the constraints imposed by PE. This
requires us to use SL7A, which solves for PE instead of vcloud.
It will be seen that mcloud and vcloud can
roam quite freely but are related roughly inversely when they do. This means
that their product, the momentum of the cloud, tends toward constancy, and is
therefore a more fundamental quantity than mcloud or vcloud.
It also means that we don't have to worry about their individual ranges, for the
product is the thing that really counts.
This section presents the constraints separately for Θcl = 30°, 70°, and 105°. For each angle, separate sets of results are presented for masses of the head ranging from 5 to 10 lb. (As before, however, all solutions for 9 and 10 lb are disallowed by constraints on PE and vfrags.) The last part summarizes the constraints for these different conditions. There it is seen that the constraints, particularly for the lurch, are essentially independent of the mass of the head. Most importantly, the allowed speeds of the lurch are all negative and bracket the observed value of -0.8 ft s-1.
For Θcl = 70°
For Θcl = 105°
Summary of the constraints
Ahead to Grand Summary of Constraints
Back to Constraints on mcloud and vcloud from Θcl and PE
Back to Intro to Constraints
Back to Physics of the Head Shot