Method of tuning a bat and a tuned bat

A method of tuning a bat, comprising the steps of:

• estimating a ball-bat interaction time, Ti, of an impact between a ball and the bat;
• tuning a hoop mode of vibration of the bat produced by the impact, by selecting a factor and selecting properties of the bat such that the first hoop mode of vibration has a period approximately equal to Ti multiplied by the factor;
• and
• tuning an axial bending mode of vibration produced by the impact, by selecting properties of the bat such that the axial bending mode of vibration has a period approximately equal to 4/3 T.

A method of tuning a tubular bat, comprising the steps of:

• estimating a ball-bat interaction time, Ti, of an impact between a ball and the bat;
• tuning a first hoop mode of vibration of the bat produced by the impact, by selecting properties of the bat such that the first hoop mode of vibration has a period approximately equal to 4/3 Ti;
• and
• tuning an axial bending mode of vibration of the bat produced by the impact, by selecting properties of the bat such that the axial bending mode of vibration has a period approximately equal to 4/3 Ti.

A method of tuning a bat, comprising the steps of:

• providing a bat including a tubular barrel having a wall thickness and a density, the barrel including fibers supported within a matrix;
• estimating a ball-bat interaction time, Ti, of an impact between a ball and the barrel;
• selecting a bat performance factor for the bat;
• tuning a first hoop mode of vibration of the bat produced by the impact, by selecting the wall thickness of the barrel, the density of the barrel, and a direction of at least a portion of the fibers relative to a longitudinal axis of the bat, such that the first hoop mode of vibration has a period approximately equal to 4/3 Ti;
• and
• tuning a third or fourth axial bending mode of vibration of the bat produced by the impact, by selecting a direction of at least a portion of the fibers relative to a longitudinal axis of the bat, such that the axial bending mode of vibration has a period approximately equal to 4/3 Ti, and such that the bat has the selected bat performance factor.