#### stoneage

##### Rookie

The TWU way of measuring the swingweight by measuring the swing time of the racquet is a convenient and accurate method, provided that you get the data right. However, there is a small modification you can make to improve the TWU setup.

There are two lengths and the swing time that has to be measured. All three enter the equation squared, so care is needed. To measure the swing time accurately an app like swingTool comes in handy. The lenghts has to be measured with a ruler. In the TWU procedure it is recommended that you hang the the racquet from the top strings. But as I will show a lower point is probably better. You can hang it at any point you like, this is both theoretically sound and works in practice, as was shown in this thread. (It is actually the reason why hanging it from the strings works to begin with).

If you take the equation that calculate the swing weight from the swing time, keep the time constant and plot it for different hanging points you get a curve like this (the distance is measured from the balance point):

What is interesting is that the curve has a peak around 23 cm above the balance point and that the peak is rather flat. This means that around this peak the swing weight value changes very little when you change the distance. This in its turn means that an error when measuring the distance to the hang point will influence the resulting swing weight very little!

The curve will vary a little for different racquets, but you can generalize it by differentiating the expression that calculates the swing weight. That leads to the following expression:

Where h is the distance in m from the balance point, and T is the swing time. So if you have a racquet with a swing time of 1.3 s and a balance of 33 cm, you get h = 0.124*1.3^2 + 0.33 = 0.54 i.e the best place to hang the racquet is 54 cm from the end but. It doesn't mean you have to hit this point exactly, but if you hang it somewhere around there you will minimize the error from measuring the hang point.

Then it only remains to find the balance with enough accuracy

/Sten

___________________________________________________________

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

There are two lengths and the swing time that has to be measured. All three enter the equation squared, so care is needed. To measure the swing time accurately an app like swingTool comes in handy. The lenghts has to be measured with a ruler. In the TWU procedure it is recommended that you hang the the racquet from the top strings. But as I will show a lower point is probably better. You can hang it at any point you like, this is both theoretically sound and works in practice, as was shown in this thread. (It is actually the reason why hanging it from the strings works to begin with).

If you take the equation that calculate the swing weight from the swing time, keep the time constant and plot it for different hanging points you get a curve like this (the distance is measured from the balance point):

What is interesting is that the curve has a peak around 23 cm above the balance point and that the peak is rather flat. This means that around this peak the swing weight value changes very little when you change the distance. This in its turn means that an error when measuring the distance to the hang point will influence the resulting swing weight very little!

The curve will vary a little for different racquets, but you can generalize it by differentiating the expression that calculates the swing weight. That leads to the following expression:

Where h is the distance in m from the balance point, and T is the swing time. So if you have a racquet with a swing time of 1.3 s and a balance of 33 cm, you get h = 0.124*1.3^2 + 0.33 = 0.54 i.e the best place to hang the racquet is 54 cm from the end but. It doesn't mean you have to hit this point exactly, but if you hang it somewhere around there you will minimize the error from measuring the hang point.

Then it only remains to find the balance with enough accuracy

/Sten

___________________________________________________________

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

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