During September,
we examined how a ball's approach angle affects its outbound angle as
spin rates vary on four different court surfaces (hard, green and
red clay, grass).
Last month we looked
at rebound height and the horizontal distance these same balls attain.
The four types of balls used were: Wilson US Open (hard court), Roland
Garros (red clay), Slazenger Wimbledon (grass), and Wilson clay court.
This month we'll
wrap things up and conclude this series by examining ball velocity
before and after the bounce on these different surfaces as spin varies.
As a reminder, these were the pre-bounce spin rates used.
There was quite a
variation within each range, however these numbers can be used as a guide.
Flat : 0 rev/min
Low Topspin: 900 rev/min
Medium Topspin: 1500 rev/min
Heavy Topspin: 3000 rev/min
Medium Underspin: 1500 rev/min
Heavy Underspin: 2500 rev/min
In the charts below we define "Rebound Distance" as the ball's
horizontal distance traveled to reach the ball's maximum rebound height.
You can click on the thumbnail charts for full sized graphics.
You might want to consider opening additional browser windows to view
the larger versions of the chart.
(NA means there was no data
available in that category.)
Ball Speed Variation With Spin
We have placed the velocity after the bounce charts for
all courts and balls next to
the horizontal distance traveled to reach maximum height.
Even without expanding the charts its easy to see that velocity out
and the distance traveled after the bounce charts look very similar.
You can see a strong correlation between the two parameters.
This makes sense since you know that
the ball travels much farther horizontally than it does vertically for
serves and most ground strokes. As
you will see, typically the horizontal component of velocity
dominates the total velocity
of a tennis ball.
What do we observe?
The more topspin on the ball
the less the ball speed is reduced after the bounce.
For underspin, aside from the grass court, the more underspin
on the ball before the bounce, the greater the reduction in speed.
Why the difference? Remember after the bounce
just about all balls have topspin on them.
A ball hit with underspin is going to change spin direction into topspin
after the bounce.
Changing direction slows the ball down.
Flat
Velocity Out - Distance
Court: | Ball: |
Velocity Before Bounce (MPH): |
Velocity After Bounce (MPH): |
Velocity Reduction |
Green Clay | Wilson US Open | 33
| 20 | 39% |
Green Clay | Wilson Clay | 34
| 21 | 38% |
Red Clay | Wilson US Open | 29
| 18 | 38% |
Red Clay | Roland Garros | 31
| 19 | 39% |
Hard | US Open | 32
| 20 | 38% |
Grass | US Open | 35
| 18 | 49% |
Grass | Wimbledon | 35
| 18 | 49% |
Low Topspin
Velocity Out - Distance
Court: | Ball: |
Velocity Before Bounce (MPH): |
Velocity After Bounce (MPH): |
Velocity Reduction |
Green Clay | Wilson US Open | 34
| 23 | 32% |
Green Clay | Wilson Clay | 33
| 23 | 30% |
Red Clay | Wilson US Open | 31
| 21 | 32% |
Red Clay | Roland Garros | 32
| 21 | 34% |
Hard | US Open | 35
| 24 | 31% |
Grass | US Open | 38
| 21 | 45% |
Grass | Wimbledon | 37
| 22 | 41% |
Medium Topspin
Velocity Out - Distance
Court: | Ball: |
Velocity Before Bounce (MPH): |
Velocity After Bounce (MPH): |
Velocity Reduction |
Green Clay | Wilson US Open | -NA-
| -NA- | -NA- |
Green Clay | Wilson Clay | 36
| 27 | 25% |
Red Clay | Wilson US Open | 35
| 26 | 26% |
Red Clay | Roland Garros | -NA-
| -NA- | -NA- |
Hard | US Open | 37
| 28 | 24% |
Grass | US Open | 39
| 24 | 38% |
Grass | Wimbledon | 39
| 26 | 33% |
Heavy Topspin
Velocity Out - Distance
Court: | Ball: |
Velocity Before Bounce (MPH): |
Velocity After Bounce (MPH): |
Velocity Reduction |
Green Clay | Wilson US Open | 37
| 31 | 16% |
Green Clay | Wilson Clay | 37
| 32 | 14% |
Red Clay | Wilson US Open | 36
| 30 | | 17% |
Red Clay | Roland Garros | 35
| 29 | 17% |
Hard | US Open | 35
| 31 | 11% |
Grass | US Open | 39
| 28 | 28% |
Grass | Wimbledon | 41
| 30 | 27% |
Medium Underspin
Velocity Out - Distance
Court: | Ball: |
Velocity Before Bounce (MPH): |
Velocity After Bounce (MPH): |
Velocity Reduction |
Green Clay | Wilson US Open | 32
| 17 | | 47% |
Green Clay | Wilson Clay | 31
| 16 | 48% |
Red Clay | Wilson US Open | 31
| 17 | 45% |
Red Clay | Roland Garros | 28
| 15 | 46% |
Hard | US Open | 29
| 15 | | 48% |
Grass | US Open | 36
| 18 | 50% |
Grass | Wimbledon | 35
| 17 | 51% |
Heavy Underspin
Velocity Out - Distance
Court: | Ball: |
Velocity Before Bounce (MPH): |
Velocity After Bounce (MPH): |
Velocity Reduction |
Green Clay | Wilson US Open | 23
| 13 | 43% |
Green Clay | Wilson Clay | 33
| 19 | 42% |
Red Clay | Wilson US Open | 31
| 18 | 42% |
Red Clay | Roland Garros | 30
| 17 | 43% |
Hard | US Open | 28
| 16 | 43% |
Grass | US Open | 33
| 16 | 52% |
Grass | Wimbledon | 33
| 16 | | 52% |
The velocity charts were very interesting!
Below we've summarized the differences in velocity reduction
after the bounce for the
"slow" (red clay, green clay and hard courts), versus the "fast" (grass court).
The "slow" average is the average of those 3 courts.
Keep in mind that a low velocity reduction means that the velocity
after the bounce remained closer to the value of the
velocity before the bounce. Compare the flat average reduction
to the topspin reductions. As we add more topspin, the balls' velocity
after the bounce
is not reduced as much. You can see the velocity
reduction numbers drop from low topspin to
heavy topspin.
Compare the medium underspin and heavy underspin
to the flat and topspin balls. Medium underspin in our study
reduced the ball's velocity the most.
Look at the reductions for the grass court in
the first chart! The results show the following: grass courts
reduce the velocity of the ball more than the other courts. How can this be?
Grass is supposed to be the "fast" court! Note also that
in all cases the grass court velocity in was higher or equal to the
other court/ball's velocity in. So what does "fast" mean!
Spin Type |
Average Velocity Reduction for "Slow" Courts
Red, Green, Hard: |
Average Velocity Reduction for "Fast" Court Grass:
|
Flat | 38.4 | 49.0
|
Low Topspin | 31.8 | 43.0
|
Medium Topspin | 25.0 | 35.5
|
Heavy Topspin | 15.0 | 27.5
|
Medium Underspin | 46.8 | 50.5
|
Heavy Underspin | 42.6 | 52.0
|
Ball/Court Interaction
What Does "Fast" Mean?
I'll be the first to admit grass courts are a challenge to conduct
studies on - just ask any of the folks doing ball/green
interaction in golf. After all the grass is "living", it has moisture on it and
in it which changes throughout the day. Blades of
grass change direction with the sun and with shade. Having
seen the pristine manicured
courts at Wimbledon, I can tell you the courts we used - well, didn't look
like those at Wimbledon. With this in mind, I can say that these are the
results our team obtained; under different
environmental conditions and on a differently maintained court
different results might be seen. On the other hand, other
researchers studying typical grass courts (versus Wimbledon) might find
this information useful as a comparison.
In
Part I we discussed
the effects we expected to see. According to Professor
Howard Brody's book,
Tennis Science for Tennis Players, interaction between
the ball and the court:
- causes the angle out to change from the angle in;
- the smaller the friction the smaller the rebound angle;
- the smaller the friction the faster the court;
- the larger the friction the greater the rebound angle;
- the greater the friction the slower the court.
We know that the coefficient of restitution (parameter
which deals with ball rebound and bounce) affects the vertical
velocity and the coefficient of friction (parameter which
deals with the friction effects of the ball
rubbing against the court) affects the horizontal velocity.
We call the horizontal velocity Vx and
vertical velocity Vy. The velocity we have been reporting
in our charts has been the total velocity V.
We captured Vx and Vy from the
video footage and calculated V using the
following equation:
V=Vx2 + Vy2)1/2.
We also used Vx and Vy to get our rebound angle.
The rebound angle is a ratio of Vy to Vx.
Prof. Brody's book tells us that more
friction means a smaller rebound angle and
a faster court. Clearly, we saw much smaller rebound
angles on the grass court. What makes
a small rebound angle? Look at the diagram below.
You can see that the smaller the rebound angle the
smaller the vertical velocity or the larger the horizontal velocity.
A small vertical velocity means a small coefficient of restitution - the ball
isn't going to bounce high; a larger horizontal velocity component signifies
low friction, a small rebound angle. The large horizontal
component of velocity means one more thing - the ball will reach you faster.
The diagram below demonstrates this.
In the diagram the different colored balls represent the same point in time.
(The red balls are all at the same point in time but not in space; the
blue balls are all at the same point in time but not in space , etc.)
Let's assume that the balls both have the same velocity when they
first bounce off of the court.
Court 1 acts like the grass court - its trajectory is a straighter line.
Court 2 acts like one of the slower courts - its trajectory is more of
a curve. You can see that the red ball has traveled farther on Court 1 in the same amount of time. If you are standing 7 feet away from the ball you
will have less time to react to get to the ball.
Another short analysis was conducted to prove this.
Four of the original (not average) test cases were selected;
one for each court type using the US Open ball.
In each of these test cases the velocity after the bounce
was roughly 19 miles/hour.
We examined which ball would reach a player
standing at the same position on the different courts, first.
We arbitrarily selected
7 feet from the bounce.
Green Clay - Grass
Hard - Red Clay
The results are clear, the grass court ball
not only reached the player first, but it had a faster
velocity when it reached the player.
This was because its horizontal velocity Vx was faster than
the balls from the other courts.
There are some very interesting things to note in these charts - and they are
fun to play around with. When you open the charts up you will
see columns for time, Vx, Vy, V and the distance
from the bounce in inches.
Seven feet is 84 inches. Go down the distance
column for the grass court until
you reach 84 inches. (Actually, there is one entry at 83.1 inches
and the next entry at 85.3 inches.)
Look at the time and velocities: the time is roughly .3 seconds, the horizontal
velocity is 15.66 miles/hour, the total velocity is about 15.70 miles/hour.
Look at the data for the green court. The ball doesn't reach 84 inches until
the time is .337, the horizontal velocity is 13.6 and the total velocity is
14.08. That's almost 2 miles/hour less.
The grass ball reaches a player sooner. You have less time to react
and that could qualify this grass court as "faster".
If you look farther down the grass court court
at 98.4 inches from the bounce, you will notice
something else, the vertical velocity becomes negative. This means the
ball is now dropping. If you look at the
green clay court the ball is still climbing. The grass ball starts dropping
to the ground sooner than the balls off of the other court - a player has
less time to react for this reason as well.
Summary of Results
Finally, just to put it all together and into perspective, here is a summary of
all of the results from all three parts of this article: velocity
and angle before and after the bounce, rebound height, horizontal (down
the court) distance, for all four ball types and court surfaces under the
defined spin rates.
Ball/Spin/Court | Velocity In |
Velocity Out | Angle In |
Angle Out | Rebound Height |
Horizontal Distance |
Grass - US Open | Velocity In | Velocity Out
| Angle In | Angle Out | Rebound Height |
Horizontal Distance |
Flat | 35 | 18
| 25 | 29 | 26 | 87 |
Low Top | 38 | 21
| 25 | 29 | 33 | 114 |
Medium Top | 39 | 24
| 23 | 23 | 30 | 128 |
High Top | 39 | 28
| 25 | 19 | 26 | 144 |
Medium Under | 36 | 18
| 22 | 24 | 20 | 83 |
Heavy Under | 33 | 16
| 23 | 29 | 23 | 77 |
Grass - Wimbleton | Velocity In | Velocity Out
| Angle In | Angle Out | Rebound Height |
Horizontal Distance |
Flat | 35 | 18
| 24 | 29 | 28 | 94 |
Low Top | 37 | 22
| 24 | 26 | 32 | 123 |
Medium Top | 39 | 26
| 23 | 22 | 31 | 140 |
High Top | 41 | 30
| 23 | 17 | 25 | 148 |
Medium Under | 35 | 17
| 23 | 26 | 21 | 79 |
Heavy Under | 33 | 16
| 23 | 26 | 19 | 72 |
Green - US Open | Velocity In | Velocity Out
| Angle In | Angle Out | Rebound Height |
Horizontal Distance |
Flat | 33 | 20
| 27 | 38 | 51 | 122 |
Low Top | 34 | 23
| 28 | 36 | 58 | 148 |
Medium Top | -- | --
| -- | -- | -- | -- |
High Top | 37 | 31
| 28 | 28 | 61 | 209 |
Medium Under | 32 | 17
| 25 | 40 | 44 | 98 |
Heavy Under | 23 | 13
| 21 | 31 | 24 | 72 |
Green - Wilson Clay | Velocity In | Velocity Out
| Angle In | Angle Out | Rebound Height |
Horizontal Distance |
Flat | 34 | 21
| 28 | 41 | 60 | 126 |
Low Top | 33 | 23
| 29 | 36 | 58 | 143 |
Medium Top | 36 | 27
| 25 | 30 | 58 | 186 |
High Top | 37 | 32
| 29 | 29 | 66 | 213 |
Medium Under | 31 | 16
| 26 | 42 | 44 | 92 |
Heavy Under | 33 | 19
| 21 | 31 | 34 | 104 |
Red - US Open | Velocity In | Velocity Out
| Angle In | Angle Out | Rebound Height |
Horizontal Distance |
Flat | 29 | 18
| 27 | 38 | 45 | 104 |
Low Top | 31 | 21
| 26 | 35 | 51 | 130 |
Medium Top | 35 | 26
| 23 | 29 | 49 | 146 |
High Top | 36 | 30
| 25 | 25 | 49 | 186 |
Medium Under | 31 | 17
| 24 | 39 | 41 | 95 |
Heavy Under | 31 | 18
| 21 | 31 | 31 | 99 |
Red - Roland Garros | Velocity In | Velocity Out
| Angle In | Angle Out | Rebound Height |
Horizontal Distance |
Flat | 31 | 19
| 25 | 36 | 45 | 109 |
Low Top | 32 | 21
| 26 | 33 | 49 | 136 |
Medium Top | -- | --
| -- | -- | -- | -- |
High Top | 35 | 29
| 26 | 27 | 51 | 176 |
Medium Under | 28 | 15
| 25 | 39 | 37 | 78 |
Heavy Under | 30 | 17
| 23 | 34 | 33 | 95 |
Hard Court - US Open | Velocity In | Velocity Out
| Angle In | Angle Out | Rebound Height |
Horizontal Distance |
Flat | 32 | 20
| 24 | 35 | 45 | 116 |
Low Top | 35 | 24
| 27 | 33 | 57 | 163 |
Medium Top | 37 | 28
| 22 | 28 | 53 | 184 |
High Top | 35 | 31
| 26 | 25 | 53 | 204 |
Medium Under | 29 | 15
| 25 | 42 | 39 | 81 |
Heavy Under | 28 | 16
| 21 | 31 | 26 | 81 |
The Latest Technology
Although the objective of
this work was to summarize these parameters
for educational purposes and to give
players and coaches a feel for variations, these types of
tests are also conducted to determine court pace (court speed).
Our tests were conducted using high speed video cameras to capture the ball's
behavior with computer software used to calculate the
different parameter results at a later time. (I can tell you this was tough
on all of our eyes during the analysis phase.)
Today, a compact measuring device is used which
is able to calculate ball size (radius), the angle and ball velocity
before and after the bounce, contact time with the surface, and
how far the ball slides when in contact with the surface.
The
Wassing
sestée has been used by the International Tennis Federation,
Lawn Tennis Association (the
governing body for the game of tennis in
Great Britain) and the French Tennis Federation.
Future Article On Shoes
I'm beginning to prepare an article on tennis shoes. If you have shoe
technology or shoe/court interaction questions please feel
free to send them to me using
this form and
I will try and incorporate your questions into the article.
Until Next Month ... Jani