24. Introduction to ranges and constraints
The major task of the previous sections has been to
identify the most important variables out of the 30 or so that are used in the
most complex simulations. The results were listed in two tables in section 23,
"Summary of the solutions and the most important variables." Those
variables and the range of solutions derived with their default values show
clearly that the more realistic the simulation, the more the answers approach
the observed rearward lurch. This answers the second question, Can the rearward
lurch be explained by a shot from Oswald's rifle?, in the positive.
The next step is to see whether the lurch must be rearward, in other words to address the third question, Must a rearward shot from Oswald's rifle have created a lurch similar to that observed? We do this by examining all reasonable combinations of the important variables and seeing what the results imply for the velocity of the lurch, the factors that control it, and the uncertainties in these answers. The answer turns out to be positive, that all reasonable combinations of the important variables produce rearward lurches compatible with the actual one. In fact, the majority of the reasonable combinations produce initial lurches that are stronger than the actual one, making the practical problem how to weaken the lurch rather than how to strengthen it. In other words, there must be a rearward mechanical lurch, and it must be large enough to be easily observable. This solves the mystery of the lurchit begins with a quick mechanical recoil from the cloud and large fragments thrown forward, and continues with a more modest acceleration that cannot have been from a bullet (from any direction) because it is too prolonged. This leaves no room for a frontal hit.
The key to narrowing down the range of the lurch and other variables is to take advantage of several built-in constraints on the important variables. Any answer that violates one or more of these constraints can be rejected. It must be recognized, however, that only some of the variables are constrained. Here is a list of the major constraints:
Some of these constraints are stronger than others. The strongest constraints are the absolute ones, such as that the potential energy cannot be zero or negative (1). The less-strong constraints usually involve a value that seems obvious but is not absolute. An example would be that the mass of the head cannot be less than 4 lb (8). Most of these nonabsolute constraints are actually stronger than they first appear. It is for this reason that we do not differentiate among them in practice.
Dealing with the important variables
One effective way to search for constraints is to vary one or two of the important variables and list their effects on other variables in a series of tables. A solution disallowed for one variable must then be disallowed for all, which means that the same pattern of constraints must be applied to every variable. In other words, an allowable solution may not violate the constraints on any of the variables.
Given the number of variables and constraints listed above, the process of searching out all allowable combinations is daunting. It can be simplified, however, by breaking the procedure into two steps, a prescreening (preconstraining) followed by a more-detailed constraining. This is made possible by the fact that two of the important constraining variables, tlurch and vfrags, combine with mhead and dsnap to form a group of four that is related to the snap and is nearly independent of the variables more directly related to the lurch, such as Θcl, mcloud, vcloud, and PE. This first group can be used to find the allowable combinations of mhead and dsnap, the lurches for which can then be examined in more detail.
Preconstraining with mhead, dsnap, tlurch,
26. Constraints on Θcl and PE
27. Constraints on mcloud and vcloud from Θcl and mcloud
28. Constraints on mcloud and vcloud from Θcl and PE
29. Constraints on mcloud and vcloud from mcloud and vcloud
30. Grand summary of constraints
Back to Summary of Solutions and Variables
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