travlerajm

01-08-2007, 09:16 PM

One of the common sense rules of tennis is that looser strings give more power than tighter strings.

A recent study (Goodwill and Haake, 2004) has confused many people because the data were presented only with respect to the racquet frame of reference (as opposed the court frame of reference that we actual use on the tennis court). To some people, the data seemed to defy conventional wisdom.

The study showed that decreasing string tension from 70 lbs to 40 lbs gives approximately 2% increase in rebound ball velocity (in the racquet frame of reference).

This has led some posters on this forum to mistakenly believe that this translates to 2% increase in the court frame of reference also, with the difference in perceived power level due mainly instead to the significant difference in rebound angle associated with different string tensions. The purpose of this thread is to put an end to this misconception.

The study showed that with stationary racquet, incoming ball velocity of 31 m/s, and incoming ball angle of 39deg from normal, and incoming ball spin of 300 rad/s, and string tension of 70 lbs, the rebound velocity is 21.5 m/s and the rebound angle is 14deg from normal. When the tension is decreased to 40 lbs, the rebound velocity is 22 m/s and the rebound angle is 10 deg. For both string tensions, the rebound spin was about 220 rad/s.

To translate the power ratio of the two string tensions to the court frame of reference we must use the following equation:

V1’/V2’ = [V1*cos(A1+B1)]/[V2*cos(A2+B2)]

V1’ = rebound ball velocity for low tension in court frame of reference.

V2’ = rebound ball velocity for high tension in court frame of reference.

V1 = rebound ball velocity for low tension in racquet frame of reference.

V2 = rebound ball velocity for high tension in racquet frame of reference.

A1 = incoming angle for low tension

A2 = incoming angle for high tension

B1 = rebound angle for low tension

B2 = rebound angle for high tension

V1’/V2’ = [22*cos(39+10)]/[21.5*cos(39+14)] = 1.115

This suggests that the 40 lb tension produces over 11% more ball rebound velocity than 70 lb tension. But this calculation assumes that none of the extra energy imparted by the lower tension goes into increasing the rebound spin. It has been shown that adjustment in racquet face angle to compensate for the change in rebound angle does in fact increase spin generation (Cross, 2005). However, it can easily be shown that even at high rpm, spin contributes only a very small percentage (typically about 5%) of the total kinetic energy of a tennis ball.

So a string tension of 40 lbs does in fact produce roughly 10% more ball velocity than 70 lb tension if the ball is struck at the oblique angles typically used during the execution of a topspin groundstroke.

It should be noted that only one incoming angle was tested. The magnitude of the effect varies with racquet approach angle, incoming spin, and relative incoming velocity.

A recent study (Goodwill and Haake, 2004) has confused many people because the data were presented only with respect to the racquet frame of reference (as opposed the court frame of reference that we actual use on the tennis court). To some people, the data seemed to defy conventional wisdom.

The study showed that decreasing string tension from 70 lbs to 40 lbs gives approximately 2% increase in rebound ball velocity (in the racquet frame of reference).

This has led some posters on this forum to mistakenly believe that this translates to 2% increase in the court frame of reference also, with the difference in perceived power level due mainly instead to the significant difference in rebound angle associated with different string tensions. The purpose of this thread is to put an end to this misconception.

The study showed that with stationary racquet, incoming ball velocity of 31 m/s, and incoming ball angle of 39deg from normal, and incoming ball spin of 300 rad/s, and string tension of 70 lbs, the rebound velocity is 21.5 m/s and the rebound angle is 14deg from normal. When the tension is decreased to 40 lbs, the rebound velocity is 22 m/s and the rebound angle is 10 deg. For both string tensions, the rebound spin was about 220 rad/s.

To translate the power ratio of the two string tensions to the court frame of reference we must use the following equation:

V1’/V2’ = [V1*cos(A1+B1)]/[V2*cos(A2+B2)]

V1’ = rebound ball velocity for low tension in court frame of reference.

V2’ = rebound ball velocity for high tension in court frame of reference.

V1 = rebound ball velocity for low tension in racquet frame of reference.

V2 = rebound ball velocity for high tension in racquet frame of reference.

A1 = incoming angle for low tension

A2 = incoming angle for high tension

B1 = rebound angle for low tension

B2 = rebound angle for high tension

V1’/V2’ = [22*cos(39+10)]/[21.5*cos(39+14)] = 1.115

This suggests that the 40 lb tension produces over 11% more ball rebound velocity than 70 lb tension. But this calculation assumes that none of the extra energy imparted by the lower tension goes into increasing the rebound spin. It has been shown that adjustment in racquet face angle to compensate for the change in rebound angle does in fact increase spin generation (Cross, 2005). However, it can easily be shown that even at high rpm, spin contributes only a very small percentage (typically about 5%) of the total kinetic energy of a tennis ball.

So a string tension of 40 lbs does in fact produce roughly 10% more ball velocity than 70 lb tension if the ball is struck at the oblique angles typically used during the execution of a topspin groundstroke.

It should be noted that only one incoming angle was tested. The magnitude of the effect varies with racquet approach angle, incoming spin, and relative incoming velocity.