Originally Posted by stoneage
Maybe many great racquets have the same MgR/I (e.g. 21), but the reverse is not true.
Very few racquets with MgR/I = 21 are great. So as a design criterion for customizing racquets it is a very dangerous concept and would avoid it if I were you!
If you still want to find the minimum added weight m you can use:
m = (M*R-c*J)/r(cr-1)
Where M, R and J are the values for the original racquet. m and r are for the added weight and c = 21/g (or what ever value you are striving for).
You can find the r that gives you the minimum m by taking the derivative dm/dr = 0.
But that leads to a fourth order equation, so it is not so fun. It is probably easier to plot the equation in Excel and see where min lies.
You can also see from the equation that you should avoid r=1/c (46.7 cm) since that will require an infinite weight to achieve the right value.
racquet apps for the iPhone/iPad.
The MgR/I formula can be used as a mass distribution design criterion as long as other design criteria are used along with it.
For example, when I design my own racquets, I use 3 critical mass distribution design criteria:
1. MgR/I = 21.0 (this assures a tuned forehand for an eastern to semiwestern grip).
2. MgR'/I' = 22.5 to 22.6, where R' = R - 10cm, and I' = the sw about the axis 10cm from butt. (this assures that my 2hb is tuned).
3. I' (SW) = 360 to 370. This assures that my serve will have maximum velocity without wearing my shoulder out. I start to lose speed on the serve if I go lower than that range (as measured by how high it hits on the back fence after a bounce in the service box). And if I go higher than that range, my serve is still fast, but my arm runs out of gas and I start to labor and lose accuracy after serving several sets.
Those 3 design criteria are in my opinion the most important.
Other design criteria, such as length, stiffness, string pattern, string type, head size, matter less and can be varied as long as I work within the first three constraints. If I want a bigger serve, I might go longer (and use SW at the upper edge of the range). If I want more control on groundies and volleys, I might go shorter.