29. Constraints on m_cloud and v_cloud from m_cloud and v_cloud 

    The previous section has shown the constraints arising for v_lurch and v_cloud that arise by varying Θ_cl and PE. But those calculations leave m_cloud fixed. Here we take a more general look at m_cloud and v_cloud by varying them both and examining the constraints imposed by PE. This requires us to use SL7A, which solves for PE instead of v_cloud. It will be seen that m_cloud and v_cloud 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 m_cloud or v_cloud. 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 Θ_cl = 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 v_frags.) 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 Θ_cl = 30°
For Θ_cl = 70°
For Θ_cl = 105°
Summary of the constraints

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