Racquet stiffness - RDC/RA and frame frequency

[stoneage]

I have been thinking a little about measuring the frame stiffness and would be interested in hearing you input.

You can bend the frame and measure the deflection, as you do in the Babolat RDC, or you can look at the frequency of the vibrating frame. The latter is easier to measure without any special equipment: Record the sound and use a program like the free Audacity (PC and Mac) to calculate the frequency. I have also added frame frequency measurement to the latest version of racquetTune.

To get the relation between the stiffness and the vibration we can look at simple beam theory. If we have a beam with a load in the middle we can define the stiffness as the load over deflection F/d:

The Babolat RDC has this setup. The deflection is measured at one end, but the difference is only a question of a constant.
The free vibrating beam has a basic frequency f:

If we combine these two models using basic beam theory we can get a relation between the stiffness and the frequency:

Where M is the mass of the beam. The constant 4 is a round off (it is actually 3.78

This formula is simple, but contains several approximations. The worst being that it assumes that the cross section of the beam is constant which definitely not is true for a racquet. However, since all racquets have a similar form it might serve to classify racquets.

To test this assumption you can look at the frequency data compiled at:
http://twu.tennis-warehouse.com/cgi-bin/vibfrequency.cgi

If you take this data and plot the 4Mf^2 vs RA values you get:

You can make two observations from this:
1. There is definitely a relation between the two stiffness expressions
2. The scatter is too large to make a direct calculation of RA from the frequency with acceptable accuracy.

Which expression is "best"? Well here I leave it open for discussion.

/Sten

PS If anyone want to play around with the TWU frequency data I have put them in a spreadsheet that you can download here

_________________________________________________
racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.

 

[mawashi]

That's a lot of work you did... very nice!

 

[pennc94]

To test this assumption you can look at the frequency data compiled at:
http://twu.tennis-warehouse.com/cgi-bin/vibfrequency.cgi

Wow! A PT57A comes in at 123 Hz.

 

[flume]

Just to clarify on this measurement by stoneage for racket matching purposes...
We seem to conclude that the 4Mf^2 measurement is not ideal for predicting RA because of the scatter in the data, presumably due to all the different flex behaviors for all the different frames.
But given tests of 2 of the same frame model, is a comparison of measured 4Mf^2 good for predicting that one identical racquet must have lower RA than another?
Is it then reasonable to use the best fit slope to predict how much less this RA likely is?

 

[Shroud]

Does it work the other way around? Meaning if you do things that alters the frequency does it also alter the stiffness??

I am not sure that is the case, and wouldnt lead and grips mess up the rating?

 

[Cengusiento]

Awesome post stoneage

 

[stoneage]

Just to clarify on this measurement by stoneage for racket matching purposes...
We seem to conclude that the 4Mf^2 measurement is not ideal for predicting RA because of the scatter in the data, presumably due to all the different flex behaviors for all the different frames.
But given tests of 2 of the same frame model, is a comparison of measured 4Mf^2 good for predicting that one identical racquet must have lower RA than another?
Is it then reasonable to use the best fit slope to predict how much less this RA likely is?

If you check if two racquets of the same model and find that the frequencies are different, it could depend on the stiffness being different, or that the weight distribution is different (or both). You can then check the weight, the balance and preferably also the swingweight (which indicates the weight distribution). If all three are the same for both racquets you can probably assume that the stiffness is different.

Sten

___________________________________________________________
racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.

 

[stoneage]

Does it work the other way around? Meaning if you do things that alters the frequency does it also alter the stiffness??

I am not sure that is the case, and wouldnt lead and grips mess up the rating?

Not necessary. And yes, adding point weights like lead tape messes up things. The simple formula above is based on a beam with constant cross section and even weight distribution.

Adding a point weight might affect the frequency, little if it is close to a node, substantially if it is in the middle.

A weight will never change the stiffness of the racquet. It might alter the forces on the racquet at impact, which means that the deformation might be different. But the relation between force and deformation will be the same.

This emphasises what I said in the original post: The frequency can be used as a quick, but crude, estimate of the stiffness, but you should not to much focus on the last decimal.

Sten

___________________________________________________________
racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.

 

[Gyswandir]

Hi Stone,

When I was investigating what racket to get after suffering from the APDGT causing me elbow pain, I remember reading somewhere, think it was TWU, that vibration frequency is the better measure for knowing if a racket is more comfortable than RDC, which explains why some stiff rackets are considered relatively comfortable.

I chose the EZone XI98 based on the frequency table in TWU and think it was the correct choice. However, the RDC for that is also low. So, which is the better metric then?