For a very long time, for benchrest, barrel stiffness has been viewed as a virtue. I have come to question this. My current working premise is that as long as a barrel is heavy enough to deal with the thermal load without accuracy being affected during normal use, it is probably heavy enough. The potentially expensive part would be to try to determine how light a barrel can be without loosing accuracy just because of its profile. I can say one thing that is clear. If we view a free floated barrel as a cantilevered beam, and take a look at the formula for calculating deflection under load, when a barrel is shortened, it becomes a lot stiffer.
Maximum reaction forces, deflections and moments - single and uniform loads.
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My point is that if a barrel was stiff enough before shortening we can re-contour it to remove more weight and bring its shortened stiffness (deflection under a given load) down to what it was when longer. If tuning a load involves timing the exit of the bullet at the muzzle to a certain point in the motion of the muzzle's vibration, it seems to me that raising the frequency of the barrels vibration would make timing to muzzle more critical, which would seem to make close control of velocity more critical. Years ago, I asked Harold Vaugn whether his work had shown him that barrel stiffness and weight were desirable characteristics for accuracy. He told me that weight is, but stiffness may not be as clear an advantage, or words to that effect. For those that are not familiar, he wrote a very interesting book about some very interesting experiments that he had done relating to factors that affect accuracy of a rifle. It is titled,
Rifle Accuracy Facts.