A Better Polarization Index

[PistolPete23]

The polarization index as discussed on this forum is mathematically as follows:

PI = RW/M

Where PI is the polarization index, RW is the recoil weight, and M is the static weight of the racquet. It occurred to me recently that this formula for PI is not dimensionless, as indices typically should be. RW has units of kg cm^2, while M has units of kg. So it doesn't quite make sense to normalize RW by the static weight to derive an index that tells you how polarized a racquet is. My new proposal for PI is as follows - normalize (i.e., divide) the RW by the RW of a hypothetical racquet with the same weight but completely uniform mass distribution. Values greater than 1 means that the mass in the racquet is polarized; the larger the value, the greater the degree of polarization. Values less than one means that the racquet is more depolarized than a hypothetical racquet with uniform mass distribution, which should be very rare.

The RW of a uniform racquet is easily derived with some simple calculus. The formula comes out to (ML^2)/12, where L is the length of the racquet. So the new polarization index would be:

PI = (12 * RW)/(ML^2)

Units:
RW: kg cm^2
M: kg
L: cm

The numbers on http://racquetsavant.streamlit.app have been updated to reflect this new polarization index

 

[sureshs]

@travlerajm

 

[PistolPete23]

For easier interpretation of this new PI, I further suggest subtracting 1 from the formula in the OP:

PI = (12 * RW)/(ML^2) - 1

Negative numbers indicate truly depolarized racquets, and positive numbers indicate polarized mass distributions, with the degree of polarity increasing with higher values.

Spoiler: Most racquets are polarized to a degree even in stock form. Very few racquets are truly depolarized, relative to a hypothetical racquet with uniform mass distribution.

 

[PistolPete23]

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