At first glance, the spectacular conclusion of the men’s singles competition at the Australian Open may seem to suggest that Rafael Nadal is still clueless when it comes to playing the tireless Novak Djokovic. However, there is a difference to Nadal’s game this year compared to last. Nadal, former world number one, surrendered 6 defeats in 6 meetings against the Serb in the 2011 season as Djokovic rose to power, completing one of the most successful seasons ever.

Rafa fighting hard in Doha, Jan 2012

The problems arose for Nadal with the start of a shoulder injury which has reduced his ability to serve at top speed. He had been struggling to out-muscle top players in baseline rallies like he had previously, relying more on wearing them down. Not content with a season producing a French Open title and two major semi-finals, Nadal and his team decided to make changes for 2012 and the change they opted for was to add weight to the racket, as Nadal explained after being knocked out of the Doha ATP Tour event earlier in January:

“We thought about [changing the weighting] after Wimbledon, but I, you know, I was injured,” Nadal said. “I played all Wimbledon, injury. You are remember in my fourth against Del Potro? I had problems, so I finished the tournament playing with infiltrations every day. So after Wimbledon I had to stop for three weeks. I only was able to practice five days before Montreal, Cincinnati. So I did not have the chance to do it. We wanted to do it after US Open, and we put it a little bit too much weight on the racquet.”

*Nadal, after losing to Gael Monfils in Doha this January**.*

Eventually in the close season over winter Nadal’s team settled on adding a small 3 gram mass to the end of his Babolat Aeropro Drive GT racket. This might seem like a miniscule change to make, especially on a racket that already has a mass of 300g. However, as we can see below it has the potential to allow Nadal to play with more comfort and produce more powerful shots if needed.

While the mass of a racket can be important to a player, it is more important to get the right swing weight, or Moment of Inertia (*I*). The swing weight of a racket describes it’s resistance to rotational acceleration (when swung). Nadal’s old racket has a moment of inertia of 0.0963kgm^{2} about the end of the handle, which is quite high compared to a lot of rackets anyway. The change due to the additional mass can be calculated using the following moment of inertia equation, which sums the mass of additional particles multiplied by the distance from the axis of rotation squared,

*I = Io + mr^2* (1)

where *Io* is the moment of inertia, m is the mass of a particle and r is the distance of the particle from the axis of rotation, in this case being treated as the handle end. Using equation 1 it can be calculated that the addition of a 3g mass to the racket tip (685mm from the butt end) increases the swing weight by 1.46%.

If we consider the change this makes for a serve we can see the maximum effect of the added mass, in a serve the ball will hit the racket close to the top, where the added mass will be most influential. It has to be assumed for these calculations that Rafa’s technique isn’t affected by the added mass and he is able to swing in the same manner. We also assume that the racket behaves rigidly and the coefficient of restitution (COR – measure of collision elasticity) of the ball on the string bed is 0.85, which is the known value taken from literature.

If we assume that the impact occurs at the racket’s dead spot (the sweet spot most likely to be struck in a serve), we can then use equation 2 to see what effect any change in racket speed has upon the ball speed (which is the important part). Equation two describes the relationship between the ball speed (v‘) and the racket speed (V), which are proportional but the ball speed is also dependant upon racket mass (M), ball mass (m) and COR (e).

** v’ = (MV(1+e))/(M+m) **(2)

We can see from the equation that if the masses and COR are constants then an increase in racket head speed will produce an increase in ball speed and a faster serve.

In these conditions, if Nadal wanted to serve with the same ball velocity he is used to doing with his old racket, he can drop his racket velocity to 96% of what it previously was with the old racket and his serve speed will be matched thanks to the increased swing weight. This difference may be a small change but it has a large impact on the energy involved as kinetic energy and velocity are squarely proportional. A reduction in the energy needed to serve could prove very important for Rafa as it might help to reduce the strain on his shoulder and prevent further injury. However, if we want to look at it from the other side and also assume that Rafa is able to swing his newly weighted racket with the same rotational velocity as his old one, which isn’t too far fetched as he is a strong player, then the ball speed for his serves could be increased by up to 2%, which in the world of elite sport could be a big gain.

Nadal warming up with his new racket in Melbourne

The data shows that the changes Nadal has made have the potential to let him play more comfortably for the majority of the time but also to be able to pull out big, more powerful shots when needed. This is assuming he is strong enough to wield his new racket in the same way his did his previous one, but given he only had a few short weeks preparing with it before the first big championship of the season he hasn’t done too badly. Nadal is now taking February off from competing on the tour in order to train and learn how to use his new racket most effectively, so it will be interesting to see how he fares against his Serbian nemesis at Rolland Garros come June.

Dave Schorah

*Editor’s note: This article originally had different figures with regards to velocity reduction (83%, now 96%) and increases in serve speed (10%, now 2%). The errors were noticed after posting but have now been corrected.*