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 = 30
For Θcl = 70

For Θcl = 105

Summary of the constraints

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