I have developed a fairly (to say the least) advanced string bed calculator that I thought that I would share some results from. I also made it into an iPhone/iPad app called stringBed. It uses a non-linear finite element model with about 700 elements to model the strings in a racquet. This means that you apply fairly large loads to the racquet and see how the strings deform and calculate the stiffness. There are some calculators and measurement tools around, e.g. Stringway. But they only work in the low deformation/linear range where the stiffness is independent of the string type. To some results: A 95 sq in racquet, 16x20 string pattern, 25 kg string tension. Two different strings: Babolat natural Gut 1.25 mm and Big Banger 1.25 mm, the string data taken from the USRSA string selector. If you apply increasing load levels in the middle of the racquet and plot it versus the deformation you get a curve like this: The load is in N(ewton) i.e. 1000 N is roughly 100 kg or 220 lb. If you look at stiffness (probably more interesting) when you increase the load you get a curve like like the one below. The stiffness is in N/mm which is equal to the kg/cm used by Stringway and others. As you can see from both curves the stiffness increases quite dramatically when the load goes up (this is total stiffness, not incremental which is even higher). This is not surprising since it is typical for cable structures. Another thing to note is that the string bed stiffness for small loads is independent of the string type and dimension, but vary quite a lot when the load increases. Neither this is strange, but important since it emphasizes that it could be "dangerous" to only look at small deformations. The load levels here are realistic for a tennis game, even though you have to be really good to achieve the highest loads in the curve. If you instead look at how the tension influences the stiffness for two different load levels. You get curves like this: The relation between tension and stiffness seems to be linear, but the slope is less than 1, i.e. doubling the tension doesn't double the stiffness. This is especially true for the high load. Interesting to note is also that the two string types are almost identical at 250 N, whereas at 1 500 N the 16 kg poly is as stiff as the 28 kg gut. There are lot more to be said about this, but I leave it open for discussion here and will come back later with more results. /Sten _________________________________________________ racquetTune, stringBed and swingTool tennis apps for the iPhone.

Sten, Can you please show the physical setup for the measurement? I use racquetTune & I am interested in this app, but would like to see what is involved in making the measurements. Is there possibly a video tutorial? Can this app be adapted to measure racquet frame stiffness? Thanks, kev

This is a simulation tool based on a FEM (Finite Element Method) model of the string bed. So there are no measurements involved. It gives you the chance to simulate different combinations of strings and impact points and see how it affects the stiffness and other parameters. You can compare it to when you design an airplane. You do a lot of computer simulations of structural integrity and aerodynamics (using FEM in both cases) to find the best solution. In the end you of course have to test fly the plane/play the racquet, but you will hopefully have eliminated some bad designs. I might do a video tutorial, but it is very easy to use: Enter the string data and place the "ball" at the impact point, read of the result. No, you can't use it for frame stiffness. It is possible to use FEM to model a racquet (and I suppose that the manufacturers do that). But it is fairly complex and you would for example have to know the material thickness and material stiffness. And I don't think it would be very interesting for a player or stringer since you can't affect the result, the racquet is already manufactured. The string bed on the other hand is partly "designed" by you every time you string. /Sten

Proportional stringing As the next example I will be looking at proportional stringing. The idea is that if you vary the tension in the strings (usually according to some rather fuzzy theory) toward the edges you might achieve a different feeling. I therefore let the tension in the stringBed racquet vary quite radically with the tension in the mains being (in kg): 12, 14, 16, 18, 20, 22, 24, 26, 26, 24, 22, 20, 18, 16, 14, 12 And in the crosses: 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8 The stiffness of this configuration was 35.2 kg/cm for a low impact load (25 kg) and 62.6 kg/cm for a high load (150 kg). The first step was to get a "standard" configuration to compare it to. By testing I found that a racquet with all the strings at 22 kg gave the same stiffness when loaded in the middle, both with the low and the high load. So what is the difference? If you look at a hit off the center there should be some difference. If I place the load/hit quite off I get stiffnesses of 37.6 (low load) and 73.9 (high load) for the proportional case and 44.1 and 82.2 for the standard case. This means that the stiffness is around 15% higher for the standard racquet. The conclusion is that you could achieve a more evenly distributed stiffness and a larger sweetspot through proportional stringing, But you have a rather large tension variation to get an effect. In the figures below you can see the deformation of the string bed with the of center hit for the proportional case (left) and the standard (right). You can also see where I placed the hit. _________________________________________________ racquetTune, stringBed and swingTool racquet apps for the iPhone/iPad.

Not very likely, especially considering the limited interest it has generated so far. I will give you some results like the one above instead. If it is anything special you are interested in, please let me know. /sten

Hi... just purchased the app. Very interesting and I'd like to maximize it's potential for my own use. I've been stringing my own racquets for about 10 yrs and have really liked my poly/gut hybrid...but I have a reel of POSG and figured I'd do a full job of it to try it out. Although I can't mimick the exact feel, I'd like to understand what should I be looking at to figure out what tension to string the POSG at. I'm no where near a pro, but play 4.5 level tennis and wanting to one day get to a 5.0...and I hit the ball w/ hard ground strokes... so I was using the Hard load. Is it best to look at stiffness, linear stiffness or something else to give me a best guess at what tension to string it at? Thanks.