# What is the physics behind Roger Federer's & Rafael Nadal's iconic shots

Two Iconic players of Tennis, Roger Federer & Rafael Nadal, with two iconic shots. One with a top spin forehand & other with a slice backhand.

I want to understand the physics of these two shots.

The top spin forehand of Nadal, although looks like it(ball) might go over the baseline when played, lands well inside it & then jumps by an enormously amplified bounce.
The backhand slice of Federer, although looks like it might land mid court, lands just inside the baseline & skids through with an enormously attenuated bounce.

In my knowledge, the two shots behave the way they do because of the relation between velocity of the ball, friction with the air & pressure difference from the top & bottom side.
From basic physics, I know that, as velocity increases, pressure decrease. An example I learned in Physics class: If you stand too close to a fast moving train, you will be sucked in. Because of high velocity of the train, pressure in front decreases while pressure on your back is constant & hence you are moving towards the train.

Applying the same concept, Nadal's top spin forehand makes the ball rotate clockwise. So, Upper half is opposing air, while bottom half is assisting it. More pressure from up, less pressure from down, thus it dives to the ground quickly.
Exactly opposite with Federer's backhand slice. Ball is rotating anticlockwise, Upper half assisting air & lower half opposing it. Less pressure from up, more pressure from down. So its stays afloat longer.

If i am wrong about my Physics up till here, correct me.

My real doubt is, why does the ball, after pitching, bounce more (for Nadal) & less (for Federer) Can anyone explain this physics. Assume they are playing on Clay court

Here is a link to Roger Federer's best backhand slices In the video, first there are a series of flat slices which are retrieved below the knees, much lower than the net. In the next couple of shots, there are some loopy slice which die out after landing.
Here is Nadal's topspin forehand See the 2nd point at 0.20. Look where Federer takes that shot from, near his head.

PS: BTW, Andy Roddick has the best backhand slice in Men's game, but Federer inclusion was for dramatic effect. GOAT nonetheless.

• Newtonian Mechanics. – MattS Aug 31 '13 at 8:29
• Nice Question! It would be even better if you could include a gif image of the shots you have in mind. – Ali Aug 31 '13 at 8:50
• I would think that Nadal's ball comes in at a larger (less flat) angle than Federer's (video please) and that this causes "more" bounce. I think the effect of the spin on bouncing might be opposite to the angle affect (depending on the grippiness), but certainly smaller. – Řídící Aug 31 '13 at 8:56
• Then again, the bottom of Federer's ball has a higher velocity than Nadal's, because of the back-spin. So, Federer's ball will lose lots of energy to (horizontal) friction (include tag?) with the ground. Energy that cannot go into the bounce anymore. So, the spin-on-bounce effect seems to contribute as well (and isn't opposite to the angle effect). Note that I am not answering, just guessing. :) – Řídící Aug 31 '13 at 9:09
• I would try to link a youtube video/gif after i go back home from work. Soon – KharoBangdo Aug 31 '13 at 9:33

You are absolutely correct that the change in direction of the tennis ball is due to the difference in pressure on the top and bottom of the ball. Below is an example of a top-spin shot with the ball traveling from left to right.

The speed of the air passing the ball on the top is slower than on the bottom of the ball. You can see this by summing the blue and yellow arrows on the top and bottom of the ball. Since faster flow creates lower pressure, there will be a pressure difference between the top and bottom of the ball, with high pressure on top and low on bottom. This will force the ball to the right of its motion (down in this example).

Here you can see the streamlines around the ball:

The closer the streamlines, the faster the flow. The flow is moving faster on the bottom of the ball since the streamlines are closer.

Now onto you specific question of why it bounces differently. Let's look at the forces on the ball in back-spin:

When the ball hits the ground on the other side of the court, the upward vertical velocity (speed moving up) that it leaves the ground with is proportional to the downward vertical velocity (speed moving down) that it hits the ground with. There are two forces in the up and down direction on the ball: the gravitational force and the lift force as seen in the picture above. In a back spin shot, the lift force is up. If we only look at the velocity of the ball in the vertical direction, you can see that the ball will fall slower to the ground since there is an additional force on the ball up. Thus, the ball will hit the opposite side of the court with less vertical velocity and thus not bounce as high as "usual". The reverse is true for a top-spin shot. The top-spin increases the downward force and increases the velocity in which it hits the ground since the aerodynamic and gravitational forces both force the ball down. This increases the bounce height. (Note that I have neglected the fact that the lift force direction is perpendicular to motion and not gravity. But since the ball moves perpendicular to gravity most of the time, this is a good assumption and way of showing the physics.)

There is also the friction effect when the ball hits the ground. This changes the trajectory of the ball and would have the opposite perceived effect on bounce height as above:

The change in ball direction does not affect the bounce height as much as the difference in vertical velocity when the ball hits the ground. Note that this balance of effects is greatly dependent on the velocity of the ball. Since the tennis pros hit the ball at a very fast speed, the pressure forces have a greater affect than the frictional forces when the ball hits the ground. When amateurs play tennis, they may spin the ball with the same rotational velocity but without the horizontal speed to cause much curving of the ball. This would cause a higher bounce with back-spin and lower with top-spin. As with everything, it is a balancing of forces.

• Good answer. This is known as the "Magnus effect". Once you know that name, you can google your heart out... in fact, on of your pictures is the first one that shows up when you use that search term. – Floris Apr 17 '14 at 14:39