🎾 Unforced Errors And Error Reduction In Tennis¶
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Tóm tắt nội dung (trích từ tài liệu gốc): Unforced errors and error reduction in tennis about:reader?url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2577482/ ncbi.nlm.nih.gov Unforced errors and error reduction in tennis H Brody 21-26 ph�t 2006 May; 40(5): 397�400. This article has been cited by other articles in PMC. Abstract Only at the highest level of tennis is the number of winners comparable to the number of unforced errors. As the average player loses many more points due to unforced errors than due to winners by an opponent, if the rate of unforced errors can be reduced, it should lead to an increase in points won. This artic
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Unforced errors and error reduction in tennis about:reader?url=https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2577482/
ncbi.nlm.nih.gov
Unforced errors and error reduction in
tennis
H Brody
21-26 ph�t
2006 May; 40(5): 397�400.
This article has been cited by other articles in PMC.
Abstract
Only at the highest level of tennis is the number of winners
comparable to the number of unforced errors. As the average
player loses many more points due to unforced errors than due to
winners by an opponent, if the rate of unforced errors can be
reduced, it should lead to an increase in points won. This article
shows how players can improve their game by understanding and
applying the laws of physics to reduce the number of unforced
errors.
Keywords: tennis, unforced errors
There are a number of ways in which a player's error rate can be
reduced. Errors come about because the ball has hit the net, gone
long (an error of depth), or gone wide (a lateral error). The first and
second parts of this article discuss lateral and depth errors, and
explain how spin and the speed of the hit can increase or
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decrease the likelihood of an error. The third part describes the
theory behind the fastest serve and how players can increase their
chances of hitting the serve into the service box. The final part
focuses on the "sweet spots"--that is, where exactly on the racket
head a player should hit the ball, with specific reference to the
maximum power point. It explains how this sweet spot varies from
shot to shot, and how players can use this to their advantage
depending on the situation--for example, court surface, pace of
shot, and use of the wrist.
Reducing lateral errors
Shots aimed straight down the middle of the court give quite a
sizeable margin for error--almost 10� to the right or left before the
ball lands in the alley. However, most players do not want to play
safe and hit every shot down the middle. They want to be
aggressive and go for the corners or down the sideline. They may
want to (or have to) pass an opponent at the net. They may want
to go for an occasional winner or at least make an opponent run
for the ball once in a while. But this invites lateral errors.
Laws of physics
However, the number of errors from shots that go wide can be
reduced even when players go for corners or sidelines if they
remember a piece of critical advice: they should not change the
ball angle! If a shot is coming cross court, they should return it
cross court. If a shot is hit down the line, they should return it down
the line. Changing the ball angle by attempting to return a cross
court shot down the line, or return a down the line shot cross court
is asking for problems with lateral errors. The reason lies in the
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physics of ball/racket interaction.
If a return does not change the ball angle, the ball's impact
direction is perpendicular to the face of the racket at contact. The
ball will then leave the racket in a direction perpendicular to the
face of the racket. It will go out in the direction of the racket
motion, whether the players swings hard, softly, or somewhere in
between. However, this is not the case when a player tries to
change the ball angle. The direction that the outgoing ball takes
relative to the racket face then depends on how hard the racket is
swung. The higher the relative ball/racket speed, the closer the
ball will be to perpendicular to the racket face as it leaves the
racket. This is illustrated in fig 1. If the swing is slow, the ball
leaves the racket at a larger angle.
The same advice holds for the volley. With a hard return, the ball
will go close to where it is aimed. However, if a player just tries to
block the ball on a volley and is changing angles, the ball will slide
off at a large angle, possibly going wide.
Changing angles
However, an opponent will quickly catch on if every shot is
returned to where it came from. A player who knows the facts
about ball/racket interaction can reduce the errors that may occur
even when changing the ball angle. If the ball is not going to be hit
hard, it should be aimed a little closer to the centre of the court.
With a hard swing, the shot can be aimed closer to the sideline or
the corner with confidence.
The famous statement that the angle of reflection equals the angle
of incidence holds for light reflecting from a plane mirror, but not
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for tennis balls rebounding from a racket.
Often, in a match, players ease up when well ahead and do not hit
shots quite so hard. This can reduce the errors of depth, but can
also lead to a problem. If the ball is still aimed the same way, but
the swing is no longer as hard, balls that previously went down the
line may now end in the alley.
A similar problem can result from changing the game plan in the
middle of a match. A player may become concerned about the
final outcome, so instead of hitting out and playing his or her
regular game, may decide to play it safer and ease up on the
strokes. Again, balls that previously went down the line may now
end in the alley. The player ends up making more, not fewer
errors. People will claim that the player "choked", but what actually
happened is that they did not understand the laws of physics (fig 1
).
Figure 1Ball angle as it leaves the racket versus racket head
speed for an incident ball at 20� and 60 ft/s.
Reducing errors of depth
For a groundstroke to be good, it must clear the net and yet not
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land beyond the baseline. For a given set of initial conditions (ball
speed, hitting height, spin, etc), there is a minimum angle for the
ball trajectory off of the strings that will just clear the net. For the
same initial conditions, there is also a maximum ball angle off of
the strings that will allow the ball to land within the court. To be a
"good" shot, a ball must be launched between these two angles,
and the difference (maximum angle minus minimum angle) is
defined as the vertical angular acceptance or the angular window
of acceptance. The larger this acceptance window, the more likely
it is for a shot to be good and the less likely it will end up being an
error. The size of this acceptance window depends on how hard
the ball is hit, how much spin is put on it, the location of the player
on the court, and how high above the ground the ball/racket impact
takes place. If this window is large compared with the player's
variation in vertical angle from shot to shot, the player will be
"steady". If this window is small or comparable to the shot to shot
angular variation, the player will make lots of errors.
A computer program has been written that calculates the window
size as the initial conditions that are under the control of the player
are varied, such as ball speed and spin. Figure 2 shows how the
angular window for a flat (no spin) groundstroke varies with initial
ball speed if all the other variables are held constant. From these
data, it is clear that the harder the ball is hit, the smaller is the
window through which the ball must go in order to be a good shot.
This is independent of the fact that the shot to shot variation in
angle may increase as the racket head speed is increased (some
players tend to lose some racket head control when they attempt
to hit the ball harder).
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6 trong 16 Figure 2Angular window versus ball speed.
Ball speed
Figure 2 shows that, as the incident ball speed is increased from
50 to 60 mph (which is from 80 to 96km/h), the acceptance
window shrinks by 43%. If the ball is hit even harder increasing the
speed to 70 mph (112km/h), the window decreases until it is only
one third of its original size. This is because the only force that
makes a flat (no spin) shot land in the court is gravity. When the
ball is hit hard, gravity has less time to pull it down into the court
and also the ball has greater resistance to being pulled down. No
wonder it is difficult to get those hard shots to land in the court.
The player is fighting against both geometry and Sir Isaac Newton,
as well as the opponent! What should the player do?
Some players want to hit the ball hard and it is more important to
them to do so than to lose points through making errors. There is
no advice for them, because they will not heed it. Other players
just want to win. This second type of player should reduce their
ball speed and by doing so reduce their errors of depth. By how
much should they reduce their racket head speed and their ball
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speed? As fig 2 shows, the window keeps increasing as the ball
speed decreases. However, when the window is considerably
larger than the "spray" (the variation in vertical angle from shot to
shot) and the player is making very few errors of depth, they no
longer need to slow their shots down. Hitting harder does have the
advantage that it may cause the opponent to make more errors.
Spin
What else can players do to open up their acceptance window,
besides not hitting the ball as hard? Hitting the ball when it is
higher in its trajectory will increase the window size, but the most
effective way is to add topspin, if the shot can be controlled. Figure
3 shows how the acceptance window depends on the spin of the
ball. Topspin acts like an additional downward force, helping
gravity to pull the ball into the court. The more topspin the ball has,
the greater the downward force (called the Magnus force) and the
bigger the window.
Figure 3Vertical acceptance window versus spin for 65 and 80
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mph groundstrokes.
If topspin is such a great thing, why does everyone not hit with lots
of topspin and why are beginners not taught to hit that way? When
you work out the physics of applying topspin to groundstrokes, you
discover that a player must swing the racket much harder to
achieve topspin than for a flat shot and twice as hard as for a
sliced shot. This is because the ball is being hit after it has
bounced, and, because of the bounce, the ball acquires a great
deal of topspin before it reaches the player. For players to hit with
their own topspin, they must not only turn the ball's direction
around, but also completely reverse its spin direction. This is why
a much higher racket head speed is needed to hit with topspin. For
many players, this higher racket head speed is not possible or they
lose control of the racket head when they try to do it. So they end
up hitting flat strokes or even chopping at the ball, which requires
the least racket head speed and the least racket preparation.
The 149 mph (240km/h) serve
The present world record for serve speed (149 mph or 240km/h)
is held by Rusedski and recently Roddick. Is there an upper limit
set by physics and geometry on how fast a serve can be? No! For
any player six foot (1.83m) tall or taller, there is no limit on serve
speed set by physics and the geometry of the tennis court.
Bruce Elliott has shown that tennis players hit their serve at a
height that is one and a half times their actual height. On this
basis, a six foot tall player will strike the ball at a height of nine
feet. Rusedski, who is six foot four inches tall, hits the ball at a
height of nine feet six inches above the ground. If you take a
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straight line from the service line and just skim the top of the net, it
will cross the plane of the baseline at a height of eight feet nine
inches. This means that any player hitting the ball at that height (or
higher) does not need gravity to pull the ball down into the service
box. Does that mean that it does not matter how tall you are as
long as you are over six feet tall? No! Does that mean it is as easy
to get in a 149 mph serve as a 100 mph serve? No! Let us
examine the effect of gravity and geometry on the ability of a
player to make the serve go in.
Firstly, let us look at the groundstroke. A typical groundstroke is hit
from the baseline at a height of three feet and must clear a three
foot high net. If there were no gravity, the ball would sail over the
opposite baseline at a height of three feet (it would travel in a
straight line). Air resistance will not make the ball's path deviate
from a straight line. Turn on gravity and it will pull the ball into the
court. The more time gravity has to work on the ball, the shorter
the bounce will be. If the ball is hit hard, gravity has less time to
affect the ball, and it will bounce deeper in the court or go long.
The same argument holds for the serve. Even though a serve, for
a tall player, can land in the service box without gravity, turning
gravity on will make it easier to get the ball to bounce within the
box. Hitting the ball hard reduces the time gravity has to act and
makes it more difficult to get the serve to go in. The higher the ball
is when hit, the more of the service box is available for the ball to
land in, just from geometry. So hitting the serve from a higher
impact point and not hitting it as hard will increase the chances of
the serve being good.
You can think of this in terms of a window at the net (it is called the
acceptance window). A player must make the ball go through a
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certain window if the serve is to be good. The higher the ball
impact location, the bigger the window. The higher the ball speed,
the smaller the window. Players cannot do much about the height
of the ball impact, except be fully extended when they strike the
ball. However, no amount of practice will change their own
physical dimensions. Players also want to hit their serves hard to
make them difficult to return, yet they want to make most of them
good. What can they do to get more serves in? Add some topspin.
Topspin opens the window by providing an additional downward
force (the Magnus force) on the ball. It is as if gravity were
increased.
To put topspin on a serve, the racket usually must be moving
upward as well as forward at the instant of impact. However, if the
racket is moving upward at impact, the server is not hitting the ball
at full extension. The topspin will enlarge the window, whereas
hitting below full extension will close the window a little, usually
leaving a net increase in the acceptance window, which means
more serves will go in. Putting topspin on the serve is not as easy
to achieve on the court as it is to talk about here, but there is a
way around this problem.
Many players hit their serve when the ball they have tossed up
reaches its peak. If instead, the player tosses the ball up about 8
inches (20cm) above the eventual impact point and hits the ball as
it is falling, topspin is automatically added to the ball, with no
additional effort by the server. It would not be a lot of topspin
(about 10 rev/s), but enough to open up the window and allow
more serves to go in. If the player is already hitting the ball at a
height of 9 feet or more and not hitting it very hard (about 120 mph
or 193km/h), this extra spin will open the window by about 29% as
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the window is already large (fig 4). If the player tries to hit the
serve very hard (150 mph) and succeeds, the acceptance window
will be small, but the 10 rev/s of topspin will help to get an extra
41% of the serves in.
Figure 4Height of acceptance window at the net versus serve
speed as it leaves the racket for a shot hit from a height of 9 feet
with no spin and with 10 rev/s topspin.
Getting back to the 149 mph serve. How much better is it than a
120 mph serve, assuming that it can be made to go in? It takes a
120 mph serve 0.59second to go from the racket, through the
bounce, and to the opposite baseline. It takes a 149 mph serve
0.47second for the same trip. This is a difference of 0.12second,
or about one eighth of a second. Whereas a player may have
some chance of returning a 120 mph serve (if it is hit near
him/her), take away one eighth of a second from the 120 mph time
and it is unlikely that it will be returned, unless a correct guess is
taken as to where it will be going.
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Where on the head should a player hit the ball?
There are three sweet spots on a racket--that is, locations where
it feels good to hit the ball. They are the node (minimum vibration
point), the centre of percussion (minimum shock or jar point), and
the maximum power point (highest ball rebound speed). The
location of the node and centre of percussion points of the racket
are fixed by the physical parameters of the frame (length, balance,
moment of inertia, flexibility, etc). They are located near the centre
of the strung area and are usually very close to each other, so if
you hit one, you generally hit the other. The maximum power point
location is also determined by these same physical parameters
and in addition, the style of the stroke and the incoming ball speed.
Where the location of the node and centre of percussion can easily
be determined in the laboratory (see chapter 6 of The physics and
technology of tennis by Howard Brody, Rod Cross, and Crawford
Lindsey, RacquetTech Publishers, (an imprint of the USRSA) 2002,
Solana Beach, CA. www.racquettech.com), the location of the
maximum power point can, and does, vary from shot to shot and
player to player. This section describes how the location of the
maximum power point is found, why it varies in position from shot
to shot, and where on the racket head certain balls thus should be
hit.
When rackets are tested for power in the laboratory, balls are fired
at a freely suspended racket at rest, and the ratio of ball rebound
speed to incident ball speed is determined for various impact
points on the head. This ratio (Vrebound/Vincident) is called the
apparent coefficient of restitution (ACOR). The term "apparent" is
used because the recoil speed of the racket is neglected. The
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value of the ACOR tends to maximise near the balance point
(centre of mass) of the racket and falls off as the ball impact
location moves away from balance point toward the tip. The
reason for this variation comes from the basic physics of the
interaction. When a ball impacts at the centre of mass, no energy
goes into racket rotation, as the racket just recoils and does not
rotate. The further the ball impact point is from the centre of mass,
the greater is the impulsive torque tending to rotate the racket
about its centre. As more energy goes into racket rotation, less
goes into the ball's rebound, so the ACOR decreases. For a free
racket at rest, this leads to lower values of ACOR as the impact
point moves away from the balance point and toward the tip of the
frame.
If, when a player swings at the ball, the racket is translated
(straight line motion only), the maximum ACOR point would be the
maximum power location because all points in the racket are
moving with the same speed. However, a racket is swung in an
arc, not translated in a straight line, so the tip has a higher velocity
than the throat. This moves the location of the maximum power
point higher up on the head. There is a simple formula for
determining the rebounding ball speed if the racket head speed,
ACOR, and incoming ball speed are known:
V(hit ball) = ACOR � V(incident ball) + (1 + ACOR) � V(racket)
where V(hit ball) is the rebounding ball speed, V(incident ball) is the
incoming ball speed, and V(racket) is the speed of the racket head
at the ball impact point.
The variation with respect to location of the racket head speed
depends on the nature of the swing (is it "wristy", etc?). The ACOR
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also varies with location and depends somewhat on the racket
construction. As the formula shows, the ball rebound speed also
depends on the incoming ball speed and the racket head speed. A
swing that uses a great deal of wrist action will have a much
greater racket speed near the tip than near the throat. This will
move the maximum power location higher up in the head. Note
that the incoming ball speed is multiplied by ACOR, whereas the
factor multiplying the racket head speed is (1 + ACOR). As the
values of ACOR run from about 0.1 to 0.5, the (1 + ACOR) term
does not depend too strongly on the value of ACOR. This effect
moves the location of the maximum power point down toward the
throat (maximum ACOR location) as the incoming ball speed
increases or as the racket head speed decreases. As the incoming
ball speed decreases or the racket head speed increases, the
maximum power point location moves upward toward the tip.
The limit of all of these factors is the serve, with a swing having a
great deal of wrist action, no incoming ball speed, and a large
racket head speed. For a typical serve, the maximum power point
is up toward the tip of the racket, well above the centre of the
head. This extra height above the ground for the ball impact
location not only results in higher serve speeds, but also increases
the window of acceptance for the serve--that is, the chance that it
will go in.
What is already known on this topic
Most of the information available on error reduction in tennis is
anecdotal
The advice given ranges from "Don't hit the ball so hard" to
"concentrate" to "practice more"
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What this study adds
On the basis of computer generated ball trajectories and the
physics of ball/racket interaction, specific advice is given on how to
reduce errors in tennis shots
Conclusion
Players can reduce the number of errors if they keep the laws of
physics in mind.
The first is not to change the ball angle. If a shot is coming cross
court, it should be returned cross court. If a shot is hit down the
line, it should be returned down the line. Changing the ball angle
by attempting to return a cross court shot down the line, or return a
down the line shot cross court is asking for problems with lateral
errors.
The second piece of advice is to reduce ball speed in order to
reduce errors of depth. How much depends on the variation in the
shots. If the acceptance window is larger than the spray and very
few errors of depth are being made, there is no need for players to
slow their shots down any more.
Thirdly, to hit the serve hard to make it difficult to return, but also to
get most of them in, some topspin should be added. A way to do
this is to toss the ball up about 8 inches (20cm) above the
eventual impact point and hit it as it is falling; topspin is
automatically added to the ball, with no additional effort by the
server.
Finally, players should try to hit groundstrokes closer to their hand
on fast courts (grass, etc) and when their opponent hits a hard
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shot. They should try to hit shots further out on the racket when
playing on slow (clay) courts or against an opponent who hits a
soft shot. When they really crank up and try to blast shots, they
should aim to hit the ball a bit higher on the racket head. The more
wrist used in the stroke, the further out on the head the player
should hit the ball.
Footnotes
Competing interests: none declared
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