The relation between weight (mass) and force is something most people have a natural feel for: You have to apply more force to accelerate a heavy ball than a light one when throwing it. The formula is also straight forward:
When you move in a curve, as when swinging a tennis racquet, you have something called swingweight that is supposed to tell you how it feels. The problem, however, is that most people don't know what swingweight really is. And even worse, the values you get from manufacturers and resellers are only valid when you rotate the racquet around a point 10 cm up the handle, a type of swing that rarely occurs in tennis.
I will try to shed some light on this and propose a curve where you can compare different racquets for different types of swings. Say that we have a racquet where we apply a force F
at the handle and swing it around a point p
. The the swing radius r
says if the swing is short or long. When swinging we are interested in accelerating the racquet head:
If we look at the relation between F
and the acceleration of the head acc
we can define an equivalent mass me
that tells us how much force you have to apply to get a certain acceleration, i.e. how heavy the racquets feels for different kinds of swings:
We can then plot me
and compare different racquets. But instead of plotting me
I will plot it against 15/r
. I that way we will get a convenient scale where 0 means moving it without rotation (a block) and 1 means whipping it around the wrist (5 cm outside the handle).
In the figure below I have plotted two very different racquets:
Wilson BLX Pro Staff 90, 357g, 8 pts HL, sw 327
Wilson BLX Cierzo Two, 278g, 8 pts HH, sw 350
As you can see the Pro Staff is heavier for long swings (as expected), but it is also heavier for shorter swings despite that Cierzo has a higher swingweight. The reason is that the swingweight doesn't the the full story, even for a short swing. The diagram therefore gives you a way to compare these two racquets for different swings.
For those who want hear some more details we need to define some lengths:
You can then calculate me in terms of the swing radius r:
Where m is the weight and sw is the swingweight of the racquet. I have used d=40 cm (i.e. 50 cm from the but) in the diagram above.
For those who want to play around with the figures I have an Excel-sheet that you can download here
Edit: There is an alternative and better version with a new excel sheet
presented in post 40
The "proof" of the equation can be downloaded here
racquet apps for the iPhone/iPad.